
    UNITED STATES of America, State of Texas, State of Connecticut, State of Alabama, State of Alaska, State of Arizona, State of Arkansas, State of Colorado, State of Delaware, State of Idaho, State of Illinois, State of Indiana, State of Iowa, State of Kansas, State of Louisiana, State of Maryland, Commonwealth of Massachusetts, State of Michigan, State of Missouri, State of Nebraska, State of New Mexico, State of New York, State of North Dakota, State of Ohio, Commonwealth of Pennsylvania, State of South Dakota, State of Tennessee, State of Utah, State of Vermont, Commonwealth of Virginia, State of West Virginia, State of Wisconsin, Commonwealth of Puerto Rico, and District of Columbia, Plaintiffs-Appellees, v. APPLE, INC., Simon & Schuster, Inc., Verlagsgruppe Georg Von Holtzbrinck GmbH, Holtzbrinck Publishers, LLC, DBA Macmillan, Simon & Schuster Digital Sales, Inc., Defendants-Appellants, Hachette Book Group, Inc., HarperCollins Publishers L.L.C., The Penguin Group, a Division of Pearson PLC, Penguin Group (USA), Inc., Defendants.
    Nos. 13-3741-cv, 13-3748-cv, 13-3783-cv, 13-3857-cv, 13-3864-cv, 13-3867-cv.
    United States Court of Appeals, Second Circuit.
    Argued: Dec. 15, 2014.
    Decided: June 30, 2015.
    
      Malcolm L. Stewart, Deputy Solicitor General, U.S. Department of Justice, Washington, DC, William J. Baer, Assistant Nicholson, David Seidman, Finnuala K. Tessier, Lawrence B. Buterman, Attorneys, U.S. Department of Justice Antitrust Division, Washington, DC, for the United States.
    George Jepsen, Attorney General of Connecticut, W. Joseph Nielsen, Assistant Attorney General, Office of Attorney General of Connecticut, Hartford, CT, Greg Abbott, Attorney General of Texas, Daniel T. Hodge, First Assistant Attorney General of Texas, John Scott, Deputy Attorney General of Texas, Jonathan F. Mitchell, Solicitor General of Texas, Andrew Old-ham, Deputy Solicitor General of Texas, John T. Prud’homme, Kim van Winkle, Eric Lipman, Assistant Attorneys General, Office of Attorney General of Texas, Austin, TX, for Plaintiff-States.
    Eric T. Schneiderman, Attorney General of the State of New York, Won S. Chin, Assistant Solicitor General, Office of Attorney General of New York, New York, N.Y., for the State of New York.
    Theodore J. Boutros, Jr., Daniel G. Swanson, Blaine H. Evanson, Gibson, Dunn & Crutcher LLP, Los Angeles, CA, Cynthia E. Richman, Gibson, Dunn & 
      Crutcher LLP, Washington, DC, Orin S. Snyder, Gibson, Dunn & Crutcher LLP, New York, N.Y., for Apple, Inc.
    Eamon P. Joyce, Joel M. Mitnick, Mark D. Taticchi, Sidley Austin LLP, New York, N.Y., for Verlagsgruppe Georg von Holtz-brinck GmbH, Holtzbrinck Publishers, LLC, d/b/a Macmillan.
    Gregory Silbert, Yehuda L. Buchweitz, James W. Quinn, Weil, Gotshal & Manges LLP, New York, N.Y., for Simon & Schus-ter, Inc. and Simon & Schuster Digital Sales, Inc.
    Before: JACOBS, LIVINGSTON, and LOHIER, Circuit Judges.
   RAYMOND J. LOHIER (Circuit Judge) files a separate concurring opinion, joining in the judgment and in the majority opinion except for Part II.B.2.

DENNIS JACOBS (Circuit Judge) files a separate dissenting opinion.

DEBRA ANN LIVINGSTON, Circuit Judge:

Since the invention of the printing press, the distribution of books has involved a fundamentally consistent process: compose a manuscript, print and bind it into physical volumes, and then ship and sell the volumes to the public. In late 2007, Amazon.com, Inc. (“Amazon”) introduced the Kindle, a portable device that carries digital copies of books, known as “ebooks.” This innovation had the potential to change the centuries-old process for producing books by eliminating the need to print, bind, ship, and store them. Amazon began to popularize the new way to read, and encouraged consumers to buy the Kindle by offering desirable books — new releases and New York Times bestsellers — for $9.99. Publishing companies, which have traditionally stood at the center of the multi-billion dollar book-producing industry, saw Amazon’s ebooks, and particularly its $9.99 pricing, as a threat to their way of doing business.

By November 2009, Apple, Inc. (“Apple”) had plans to release a new tablet computer, the iPad. Executives at the company saw an opportunity to sell ebooks on the iPad by creating a virtual marketplace on the device, which came to be known as the “¡Bookstore.” Working within a tight timeframe, Apple went directly into negotiations .with six of the major publishing companies in the United States. In two months, it announced that five of those companies — Hachette, HarperCollins, Macmillan, Penguin, and Simon & Schus-ter (collectively, the “Publisher Defendants”) — had agreed to sell ebooks on the iPad under arrangements whereby the publishers had the authority to set prices, and could set the prices of new releases and New York Times bestsellers as high as $19.99 and $14.99, respectively. Each of these agreements, by virtue of its terms, resulted in each Publisher Defendant receiving less per ebook sold via Apple as opposed to Amazon, even given the higher consumer prices. Just a few months after the ¡Bookstore opened, however, every one of the Publisher Defendants had taken control over pricing from Amazon and had raised the prices on many of their ebooks, most notably new releases and bestsellers.

The United States Department of Justice (“DOJ” or “Justice Department”) and 33 states and territories (collectively, “Plaintiffs”) filed suit in the United States District Court for the Southern District of New York, alleging that Apple, in launching the ¡Bookstore, had conspired with the Publisher Defendants to raise prices across the nascent ebook market. This agreement, they argued, violated § 1 of the Sherman Antitrust Act, 15 U.S.C. § 1 et seq. (“Sherman Act”), and state antitrust laws. All five Publisher Defendants settled and signed consent decrees, which prohibited them, for a period, from restricting ebook retailers’ ability to set prices. Then, after a three-week bench trial, the district court (Cote, J.) concluded that, in order to induce the Publisher Defendants to participate in the iBookstore and to avoid the necessity of itself competing with Amazon over the retail price of ebooks, Apple orchestrated a conspiracy among the Publisher Defendants to raise the price of ebooks — particularly new releases and New York Times bestsellers. United States v. Apple Inc., 952 F.Supp.2d 638, 647 (S.D.N.Y.2013). The district court found that the agreement constituted a per se violation of the Sherman Act and, in the alternative, unreasonably restrained trade under the rule of reason. See id. at 694. On September 5, 2013, the district court entered final judgment on the liability finding and issued an injunctive order that, inter alia, prevents Apple from entering into agreements with the Publisher Defendants that restrict its ability to set, alter, or reduce the price of ebooks, and requires Apple to apply the same terms and conditions to ebook applications sold on its devices as it does to other applications.

On appeal, Apple contends that the district court’s liability finding was erroneous and that the provisions of the injunction related to its pricing authority and ebook applications are not necessary to protect the public. Two of the Publisher Defendants — Macmillan and Simon & Schus-ter — join the appeal, arguing that the portion of the injunction related to Apple’s pricing authority either unlawfully modifies their consent decrees or should be judicially estopped. We conclude that the district court’s decision that Apple orchestrated a horizontal conspiracy among the Publisher Defendants to raise ebook prices is amply supported and well-reasoned, and that the agreement unreasonably restrained trade in violation of § 1 of the Sherman Act. We also conclude that the district court’s injunction js lawful and consistent with preventing future anticompeti-tive harms.

Significantly, the dissent agrees that Apple intentionally organized a conspiracy among the Publisher Defendants to raise ebook prices. Nonetheless, it contends that Apple was entitled to do so because the conspiracy helped it become an ebook retailer. In arriving at this startling conclusion — based in large measure on an argument that Apple itself did not assert— the dissent makes two fundamental errors. The first is to insist that the vertical organizer of a horizontal price-fixing conspiracy may escape application df the per se rule. This conclusion is based on a misreading of Supreme Court precedent, which establishes precisely the opposite. The dissent fails to apprehend that the Sherman Act outlaws agreements that unreasonably restrain trade and therefore requires evaluating the nature of the restraint, rather than the identity of each party who joins in to impose it, in determining whether the per se rule is properly invoked. Finally (and most fundamentally) the dissent’s conclusion rests on an erroneous premise: that one who organizes a horizontal price-fixing conspiracy — the “supreme evil of antitrust,” Verizon Commc’ns Inc. v. Law Offices of Curtis V. Trinko, LLP, 540 U.S. 398, 408, 124 S.Ct. 872, 157 L.Ed.2d 823 (2004) — among those competing at a different level of the market has somehow done less damage to competition than its co-conspirators.

The dissent’s second error is to assume, in effect, that Apple was entitled to enter the ebook retail market on its own terms, even if these terms could be achieved only via its orchestration of and entry into a price-fixing agreement with the Publisher Défendants. The dissent tells a story of Apple organizing this price-fixing conspiracy to rescue ebook retailers from, a monopolist with insurmountable retail power. But this tale is not spun from any factual findings of the district court. And the dissent’s armchair analysis wrongly treats the number of ebook retailers at any moment in the emergence of a new and trans-formative technology for book distribution as the sine qua non of competition in the market for trade ebooks.

More fundamentally, the dissent’s theory — that the presence of a strong competitor justifies a horizontal price-fixing conspiracy- — endorses a concept of marketplace vigilantism that is wholly foreign to the antitrust laws. By organizing a price-fixing conspiracy, Apple found an easy path to opening its iBookstore, but it did so by ensuring that market-wide ebook prices would rise to a level that it, and the Publisher Defendants, had jointly agreed upon. Plainly, competition is not served by permitting a market entrant to eliminate price competition as a condition of entry, and it is cold comfort to consumers .that they gained a new ebook retailer at the expense of passing control over all ebook prices to a cartel of book publishers — publishers who, with Apple's help, collectively agreed on a new pricing model precisely to raise the price of ebooks and thus protect their profit margins and their very existence in the marketplace in the face of the admittedly strong headwinds created by the new technology.

Because we conclude that the district court did not err in deciding that Apple violated § 1 of the Sherman Act, and because we also conclude that the district court’s injunction was lawful and consistent with preventing future anticompetitive harms, we affirm.

BACKGROUND

I. Factual Background

We begin not with Kindles and iPads, but with printed “trade books,” which are “general interest fiction and non-fiction” books intended for a broad readership. Apple, 952 F.Supp.2d at 648 n. 4. In the United States, the six largest publishers of trade books, known in the publishing world as the “Big Six,” are Hachette, HarperCollins, Macmillan, Penguin, Random House, and Simon & Schuster. Together, the Big Six publish many of the biggest names in fiction and non-fiction; during 2010, their titles accounted for over 90% of the New York Times bestsellers in the United States. Id. at 648 n. 5.

For decades, trade book publishers operated under a fairly consistent business model. When a new book was ready for release to the public, the publisher would sell hardcover copies to retailers at a “wholesale” price and recommend resale to consumers at a markup, known as the “list” price. After the hardcover spent enough time on the shelves — often a year — publishers would release a paperback copy at lower “list” and “wholesale” prices. In theory, devoted readers would pay the higher hardcover price to read the book when it first came out, while more casual fans would wait for the paperback.

A. Amazon’s Kindle

On November 19, 2007, Amazon released the Kindle: a portable electronic device that allows consumers to purchase, download, and read ebooks. At the time, there was only one other ereader available in the emerging ebook market, and Amazon’s Kindle quickly gained traction. In 2007, ebook revenue in North America was only $70 million, a tiny amount relative to the approximately $30 billion market for physical trade books. The market was growing, however; in 2008 ebook revenue was roughly $140 million and, by the time Barnes & Noble, Inc. (Barnes & Noble) launched its Nook ereader in November 2009, Amazon was responsible for 90% of all ebook sales. Apple, 952 F.Supp.2d at 648-49.

Amazon followed a “wholesale” business model similar to the one used with print books: publishers recommended a digital list price and received a wholesale price for each ebook that Amazon sold. In exchange, Amazon could sell the publishers’ ebooks on the Kindle and determine the retail price. At least early on, publishers tended to recommend a digital list price that was about 20% lower than the print list price to reflect the fact that, with an ebook, there is no cost for printing, storing, packaging, shipping, or returning the books.

Where Amazon departed from the publishers’ traditional business model was in the sale of new releases and New York Times bestsellers. Rather than selling more expensive versions of these books upon initial release (as publishers encouraged by producing hardcover books before paperback copies), Amazon set the Kindle price at one, stable figure — $9.99. At this price, Amazon was selling “certain” new releases and bestsellers at a price that “roughly matched,” or was slightly lower than, the wholesale price it paid to the publishers. Apple, 952 F.Supp.2d at 649. David Naggar, a Vice President in charge of Amazon’s Kindle content, described this as a “classic loss-leading strategy” designed to encourage consumers to adopt the Kindle by discounting new releases and New York Times bestsellers and selling other ebooks without the discount. J.A. 1485. The district court .also referred to this as a “loss leader[ ]” strategy, Apple, 952 F.Supp.2d at 650, 657, 708, and explained that Amazon “believed [the $9.99] pricing would have long-term benefits for its consumers,” id. at 649. Contrary to the dissent’s portrayal uf the opinion, the district court did not find that Amazon used the $9.99 price point to “assure[ ] its domination” in the ebook market, or that its pricing strategy acted as a “barrier to entry” for other retailers. Dissenting Op. at 6-7. Indeed, in November 2009 — -just a few months before Apple’s launch of the iBookstore- — Barnes & Noble entered the ebook retail market by launching the Nook, Apple, 952 F.Supp.2d at 649 n. 6, and as early as 2007 Google Inc. (“Google”) had been planning to enter the market using a wholesale model, id. at 686.

B. The Publishers’ Reactions

Despite the small number of ebook sales compared to the overall market for trade books, top executives in the Big Six saw Amazon’s $9.99 pricing strategy as a threat to their established way of doing business. Those executives included: Ha-chette and Hachette Livre Chief Executive Officers (“CEOs”) David Young and Ar-naud Nourry; HarperCollins CEO Brian Murray; Macmillan CEO John Sargent; Penguin USA CEO David Shanks; Random House Chief Operating Officer Madeline McIntosh; and Simon & Schuster President and CEO Carolyn Reidy. In the short term, these members of the Big Six thought that Amazon’s lower-priced ebooks would make it more difficult for them to sell hardcover copies of new releases, “which were often priced,” as the district court noted, “at thirty dollars or more,” Apple, 952 F.Supp.2d at 649, as well as New York Times bestsellers. Further down the road, the publishers feared that consumers would become accustomed to the uniform $9.99 price point for these ebooks, permanently driving down the price they could charge for print versions of the books. Moreover, if Amazon became powerful enough, it could demand lower wholesale prices from the Big Six or allow authors to publish directly with Amazon, cutting out the publishers entirely. As Hachette’s Young put it, the idea of the “wretched $9.99 price point becoming a de facto standard” for-ebooks “sickened” him. J.A. 289.

The executives of the Big Six also recognized that their problem was a collective one. Thus, an August 2009 Penguin strategy report (concluded only a few months before Apple commenced its efforts to launch the iBookstore) noted that “Mom-petition for the attention of readers will be most intense from digital companies whose objective may be to [cut out] traditional publishers altogether.... It will not be possible for any individual publisher to mount an effective response, because of both the resources necessary and the risk of retribution, so the industry needs to develop a common strategy.” J.A. 287. Similarly, Reidy from Simon & Schuster opined in September 2009 that the publishers had “no chance of success in getting Amazon to change its pricing practices” unless they acted with a “critical mass,” and expressed the “need to gather more troops and ammunition” before implementing a move against Amazon. J.A. 290 (internal quotation marks omitted).

Conveniently, the Big Six operated in a close-knit industry and had no qualms communicating about the need to act together. As the district court found (based on the Publisher Defendants’ own testimony), “[o]n a fairly regular basis, roughly once a quarter, the CEOs of the [Big Six] held dinners in the private dining rooms of New York restaurants, without counsel or assistants present, in order to discuss the common challenges they faced.” Apple, 952 F.Supp.2d at 651. Because they “did not compete with each other on price,” but over authors and agents, the publishers “felt no hesitation in freely discussing Amazon’s prices with each other and their joint strategies for raising those prices.” Id. Those strategies included eliminating the discounted wholesale price for ebooks and possibly creating an alternative ebook platform.

The most significant attack that the publishers considered and then undertook, however, was to withhold new and bestselling books from Amazon until the hardcover version had spent several months in stores, a practice known as “windowing.” Members of the Big Six both kept one another abreast of their plans to window, and actively pushed others toward the strategy. By December 2009, the Wall Street Journal and New York Times were reporting that four of the Big Six had announced plans to delay ebook releases until after the print release, and the two holdouts — Penguin and Random House— faced pressure from their peers.

Ultimately, however, the publishers viewed even this strategy to save their business model as self-destructive. Employees inside the publishing companies noted that windowing encouraged piracy, punished ebook consumers, and harmed long-term sales. One author wrote to Sargent in December 2009 that the “old model has to change” and that it would be better to “embrace e-books,” publish them at the same time as the hardcovers, “and pray to God they both sell like crazy.” J.A. 325. Sargent agreed, but expressed the hope that ebooks could eventually be sold for between $12.95 and $14.95. “The question is,” he mused, “how to get there?” J.A. 325.

C. Apple’s Entry into the Ebook Market

Apple is one of the world’s most innovative and successful technology companies. Its hardware sells worldwide and supports major software marketplaces like iTunes and the App Store. But in 2009, Apple lacked a dedicated marketplace for ebooks or a hardware device that could offer an outstanding reading experience. The pending release of the iPad, which Apple intended to announce on January 27, 2010, promised to solve that hardware deficiency.

Eddy Cue, Apple’s Senior Vice President of Internet Software and Services and the director of Apple’s digital content stores, saw the opportunity for an ebook marketplace on the iPad. By February 2009, Cue and two colleagues — Kevin Saul and Keith Moerer — had researched the ebook market and concluded that it was poised for rapid expansion in 2010 and beyond. While Amazon had an estimated 90% market share in trade ebooks, Cue believed that Apple could become a powerful player in the market in large part because consumers would be able to do many tasks on the iPad, and would not want to carry a separate Kindle for reading alone. In an email to Apple’s then-CEO, Steve Jobs, he discussed the possibility of Amazon selling ebooks through an application on the iPad, but felt that “it would be very easy for [Apple] to compete with and ... trounce Amazon by opening up our own ebook store” because “[t]he book publishers would do almost anything for [Apple] to get into the ebook business.” J.A. 282.

Jobs approved Cue’s plan for an ebook marketplace — which came to be known as the iBookstore — in November 2009. Although the iPad would go to market with or without the iBookstore, Apple hoped to announce the ebook marketplace at the January 27, 2010 iPad launch to “ensure maximum consumer exposure” and add another “dramatic component” to the event. Apple, 952 F.Supp.2d at 655. This left Cue and his team only two months amidst the holiday season both to create a business model for the iBookstore and to assemble a group of publishers to participate. Cue also had personal reasons to work quickly. He knew that Jobs was seriously ill, and that, by making the iBookstore a success, he could help Jobs achieve a longstanding goal of creating a device that provides a superior reading experience.

Operating under a tight timeframe, Cue, Saul, and Moerer streamlined their efforts by focusing on the Big Six publishers. They began by arming themselves with some important information about the state of affairs within'the publishing industry. In particular, they learned that the publishers feared that Amazon’s pricing model could change their industry, that several publishers had engaged in simultaneous windowing efforts to thwart Amazon, and that the industry as a whole was in a state of turmoil. “Apple understood,” as the district court put it, “that the Publishers wanted to pressure Amazon to raise the $9.99 price point for e-books, that the Publishers were searching for ways to do that, and that they were willing to coordinate their efforts to achieve that goal.” Id. at 656. For its part, as the district court found, Apple was willing to sell ebooks at higher prices, but “had decided that it would not open the iBookstore if it could not make money on the store and compete effectively with Amazon.” Id.

D. Apple’s Negotiations with the Publishers

1. Initial Meetings

Apple held its first meetings with each of the Big Six between December 15 and 16. The meetings quickly confirmed Cue’s suspicions about the industry. As he wrote to Jobs after speaking with three of the publishers, “[c]learly, the biggest issue is new release pricing” and “Amazon is definitely not liked much because of selling below cost for NYT Best Sellers.” J.A. 326-27. Many publishers also emphasized that they were searching for a strategy to regain control over pricing. Apple informed each of the Big Six that it was negotiating with the other major publishers, that it hoped to begin selling ebooks within the next 90 days, and that it was seeking a critical mass of participants in the iBookstore and would launch only if successful in reaching this goal. Apple informed the publishers that it did not believe the iBookstore would succeed unless publishers agreed both not to window books and to sell ebooks at a discount relative to their physical counterparts. Apple noted that ebook prices in the iBookstore needed to be comparable to those on the Kindle, expressing the view, as Reidy recorded, that it could not “tolerate a market where the product is sold significantly more cheaply elsewhere.” Apple, 952 F.Supp.2d at 657 (internal quotation marks omitted). Most importantly for the publishers, however, Cue’s team also expressed Apple’s belief that Amazon’s $9.99 price point was not ingrained in consumers’ minds, and that Apple-could sell new releases and New' York Times bestsellers for somewhere between $12.99 and $14.99. In return, Apple requested that the publishers decrease their wholesale prices so that the company could make a small profit on each sale.

These meetings spurred a flurry of communications reporting on the “[t]errifie news[,]” as Reidy put it in an email to Leslie Moonves, her superior at parent company CBS Corporation (“CBS”), that Apple “was not interested in a low price point for digital books” and didn’t want “Amazon’s $9.95 [sic] to continue.” Apple, 952 F.Supp.2d at 658 (first alteration in original) (internal quotation marks omitted). Significantly, these communications included numerous exchanges between executives at different Big Six publishers who, the district court found, “hashed over their meetings with Apple with one another.” Id. The district court found that the frequent telephone calls among the Publisher Defendants during the period of their negotiations with Apple “represented a departure from the ordinary pattern of calls among them.” Id. at 655 n. 14.

2. The Agency Model

Meanwhile, Cue, Moerer, and Saul returned to Apple’s headquarters to develop a business model for the iBookstore. Although the team was optimistic about the initial meetings, they remained concerned about whether the publishers would reduce wholesale prices on new releases and bestsellers by a large enough margin to allow Apple to offer competitive prices and still make a profit. One strategy that the team considered was to ask publishers for a 25% wholesale discount on all of these titles, so if a physical book sold at $12 wholesale (the going rate for the majority of New York Times bestsellers) Apple could purchase the ebook version for $9 and offer it on the iBookstore at a small markup. But Cue was aware that some publishers had increased Amazon’s digital wholesale prices in 2009 in an unsuccessful effort to convince Amazon to change its pricing. Id. at 650; J.A. 1771. Cue felt it would be difficult to negotiate wholesale prices down far enough “for [Apple] to generally compete profitably with Amazon’s below-cost pricing on the most popular e-books.” J.A. 1772. As Cue saw it, Apple’s most valuable bargaining chip came from the fact that the publishers were desperate “for an alternative to Amazon’s pricing policies and excited about ... the prospect that [Apple’s] entry [into the ebook market] would give them leverage in their negotiations with Amazon.” Apple, 952 F.Supp.2d at 659.

It was at this point that Cue’s team, recognizing its opportunity, abandoned the wholesale business model for a new, agency model. Unlike a wholesale model, in an agency relationship the publisher sets the price that consumers will pay for each ebook. Then, rather than the retailer paying the publisher for each ebook that it sells, the publisher pays the retailer a fixed percentage of each sale. In essence, the retailer receives a commission for distributing the publisher’s ebooks. Under the system Apple devised, publishers would have the freedom to set ebook prices in the iBookstore, and would keep 70% of each sale. The remaining 30% would go to Apple as a commission.

This switch to an agency model obviated Apple’s concerns about negotiating wholesale prices with the Big Six while ensuring that Apple profited on every sale. It did not, however, solve all of the company’s problems. Because the agency model handed the publishers control over pricing, it created the risk that the Big Six would sell ebooks in the iBookstore at far higher prices than Kindle’s $9.99 offering. If the prices were too high, Apple could be left with a brand new marketplace brimming with titles, but devoid of customers.

To solve this pricing problem, Cue’s team initially devised two strategies. First, they realized that they could maintain “realistic prices” by establishing price caps for different types of books. J.A. 359. Of course, these caps would need to be higher than Amazon’s $9.99 price point, or Apple would face the same difficult price negotiations that it sought to avoid by switching away from the wholesale model. But at this point Apple was not content to open its iBookstore offering prices higher than the competition. For as the district court found, if the Publisher Defendants “wanted to end Amazon’s $9.99 pricing,” Apple similarly desired “that there be no price competition at the retail level.” Apple, 952 F.Supp.2d at 647.

Apple next concluded, then, as the district court found, that “[t]o ensure that the iBookstore would be competitive at higher prices, Apple ... needed to eliminate all retail price competition.” Id. at 659. Thus, rather than simply agreeing to price caps above Amazon’s $9.99 price point, Apple created a second requirement: publishers must switch all of their other ebook retailers — including Amazon — to an agency pricing model. The result would be that Apple would not need to compete with Amazon on'price, and publishers would be able to eliminate Amazon’s $9.99 pricing. Or, as Cue would later describe the plan to executives at Simon & Schuster, Macmillan, and Random House, the plan “solve[d] [the] Amazon issue” by allowing the publishers to wrest control over pricing from Amazon. Id. at 661 (internal quotation marks omitted).

On January 4 and 5, Apple sent essentially identical emails to each member of the Big Six to explain its agency model proposal. Each email described the commission split between Apple and the publishers and recommended three price caps: $14.99 for hardcover books with list prices above $35; $12.99 for hardcover books with list prices below $35; and $9.99 for all other trade books. The emails also explained that, “to sell ebooks at realistic prices ... all [other] resellers of new titles need to be in [the] agency model” as well. J.A. 360. Or, as Cue told Reidy, “all publishers” would need to move “all retailers” to an agency model. J.A. 2060.

3. The “Most-Favored-Nation” Clause

Cue’s thoughts on the agency model con- • tinued to evolve after the emails on January 4 and 5. Most significantly, Saul— Cue’s in-house counsel — devised an alternative to explicitly requiring publishers to switch other retailers to agency. This alternative involved the use of a “most-favored nation” clause (“MFN Clause” or “MFN”). In general, an MFN Clause is a contractual provision that requires one party to give the other the best terms that it makes available to any competitor. In the context of Apple’s negotiations, the MFN Clause mandated that, “[i]f, for any particular New Release in hardcover format, the ... Customer Price [in the iBook-store] at any time is or becomes higher than a customer price offered by any other reseller ..., then [the] Publisher shall designate a new, lower Customer Price [in the iBookstore] to meet such lower [customer price].” J.A. 559. Put differently, the MFN would require the publisher to offer any ebook in Apple’s iBookstore for no more than what the same ebook was offered elsewhere, such as from Amazon.

On January 11, Apple sent each of the Big Six a proposed eBook Agency Distribution Agreement (the “Contracts”). As described in the January 4 and 5 emails, these Contracts would split the proceeds from each ebook sale between the publisher and Apple, with the publisher receiving 70%, and would set price caps on ebooks at $14.99, $12.99, and $9.99 depending on the book’s hardcover price. But unlike the initial emails, the Contracts contained MFN Clauses in place of the requirement that publishers move all other retailers to an agency model. Apple then assured each member of the Big Six that it was being offered the same terms as the others.

The Big Six understood the economic incentives that the MFN Clause created. Suppose a new hardcover release sells at a list price of $25, and a wholesale price of $12.50. With Amazon, the publishers had been receiving the wholesale price (or a slightly lower digital wholesale price) for every ebook copy of the volume sold on Kindle, even if Amazon ultimately sold the ebook for less than that wholesale price. Under Apple’s initial agency model — with price caps but no MFN Clause — the publishers already stood to make less money per ebook with Apple. Because Apple capped the ebook price of a $25 hardcover at $12.99 and took 30% of that price, publishers could only expect to make $8.75 per sale. But what the publishers sacrificed in short-term revenue, they hoped to gain in long-term stability by acquiring more control over pricing and, accordingly, the ability to protect their hardcover sales.

The MFN Clause changed the situation by making it imperative, not merely desirable, that the publishers wrest control over pricing from ebook retailers generally. Under the MFN, if Amazon stayed at a wholesale model and continued to sell ebooks at $9.99, the publishers would be forced to sell in the iBookstore, too, at that same $9.99 price point. The result would be the worst of both worlds: lower short-term revenue and no control over pricing. The publishers recognized that, as a practical matter, this meant that the MFN Clause would force them to move Amazon to an agency relationship. As Beidy put it, her company would need to move all its other ebook retailers to agency “unless we wanted to make even less money” in this growing market. Apple, 952 F.Supp.2d at 666 (internal quotation marks omitted). This situation also gave each of the publishers a stake in Apple’s quest to have a critical mass of publishers join the iBook-store because, “[wjhile no one Publisher could effect an industry-wide shift in prices or change the public’s perception of a book’s value, if they moved together they could.” Id. at 665; see also J.A. 1981.

Apple understood this dynamic as well. As the district court found, “Apple did not change its thinking” when it replaced the explicit requirement that the publishers move other retailers to an agency model with the MFN. Indeed, in the following weeks, Apple assiduously worked to make sure that the shift to agency occurred. Apple, 952 F.Supp.2d at 663. But Apple also understood that, as Cue bluntly put it, “any decent MFN forces the model” away from wholesale and to agency. Id. (internal quotation marks omitted). Or as the district court found, “the MFN protected Apple from retail price competition as it punished a Publisher if it failed to impose agency terms on other e-tailers.” Id. at 665.

Thus, the terms of the negotiation between Apple and the publishers became clear: Apple wanted quick and successful entry into the ebook market and to eliminate retail price competition with Amazon. In exchange, it offered the publishers an opportunity “to confront Amazon as one of an organized group ... united in an effort to eradicate the $9.99 price point.” Id. at 664. Both sides needed a critical mass of publishers to achieve their goals. The MFN played a pivotal role in this quid pro quo by “stiffening] the spines of the [publishers] to ensure that they would demand new terms from Amazon,” and protecting Apple from retail price competition. Id. at 665.

4. Final Negotiations

The proposed Contracts sparked intense negotiations as Cue’s team raced to assemble enough publishers to announce the iBookstore by January 27. The publishers’ first volley was to push back on Apple’s price caps, which they recognized would become the “standard across the industry” for pricing. J.A. 571. In a set of meetings between January 13 and 14, the majority of the Big Six expressed a general willingness to adopt an agency model, but refused to do so with the price limits Apple demanded. Cue responded by asking Jobs for permission to create a more lenient price cap system. Under this new regime, New York Times bestsellers could sell for $14.99 if the hardcover was listed above $30, and for $12.99 if listed below that price. As for new releases, a $12.99 cap would apply to hardcovers priced between $25 and $27.50; a $14.99 cap would apply to hardcovers selling for up to $30; and, if the hardcover sold for over $30, publishers could sell the ebook for between $16.99 and $19.99. Jobs responded that he could “live with” the pricing “as long as [the publishers] move Amazon to the agen[ey] model too.” J.A. 499.

Cue proposed this new pricing regime to the Big Six on January 16 and, with only 11 days remaining before the iPad launch, turned up the pressure. In each email conveying the new prices, Cue reminded the publishers that, if they did not agree to the iBookstore by the 27th, other companies, including Amazon and Barnes & Noble, would certainly build their own book store apps for the iPad. Correspondence from within the publishing companies also shows that Cue promoted the proposal as the “best chance for publishers to challenge the 9.99 price point,” and emphasized that Apple would “not move forward with the store [unless] 5 of the 6 [major publishers] signed the agreement.” J.A. 522-23. As Cue said at trial, he attempted to “assure [the publishers] that they weren’t going to be alone, so that [he] would take the fear awa[y] of the Amazon retribution that they were all afraid of.” J.A. 2068 (internal quotation marks omitted). “The Apple team reminded the Publishers,” as the district court found, “that this was a rare opportunity for them to achieve control over pricing.” Apple, 952 F.Supp.2d at 664.

By January 22, two publishers — Simon & Schuster and Hachette — had verbally committed to join the iBookstore, while a third, Penguin, had agreed to Apple’s terms in principle. As for the others, Cue was frustrated that they kept “chickening out” because of the “dramatic business change” that Apple was proposing. J.A. 547. To make matters worse, “[p]ress reports on January 18 and 19 alerted the publishing world and Amazon to the Publishers’ negotiations with Apple,” Apple, 952 F.Supp.2d at 670-71, and Amazon learned from Random House that it was facing “pressure from other publishers ... to move to [the] agency model because Apple had made it clear that unless all of the Big Six participated, they wouldn’t bother with building a bookstore,” J.A. 1520. Representatives from Amazon descended on New York for a set of long-scheduled meetings with the publishers. As the district court found, “[i]n separate conversations on January 20 and over the next few days, the Publisher Defendants all told Amazon that they wanted to change to an agency distribution model with Amazon.” Apple, 952 F.Supp.2d at 672.

Macmillan, however, presented an issue for Apple. The district court found that at a January 20 lunch between John Sargent and Amazon, Sargent “announced that Macmillan was planning to offer Amazon the option to choose either an agency [or wholesale] model.” Id. But at dinner with Cue that night, according to the district court, Cue made sure that Sargent understood the consequences of the MFN, explaining “that Macmillan had no choice but to move Amazon to an agency model if it wanted to sign an agency agreement with Apple.” Id. The next day, Sargent emailed Cue to express his continued reservations about switching Macmillan’s other retailers to an agency relationship.

With the iPad launch fast approaching, Cue enlisted the help of others. Cue had received an email from Simon & Schuster’s Carolyn Reidy, who had already verbally committed to Apple’s terms and whom Cue would later call the “real leader of the book industry,” moments after hearing from Sargent. J.A. 621. Cue then spoke with Reidy for twenty minutes before reaching out to Brian Murray, who, as the district court found, “was fully supportive of the requirement that all e-tailers be moved to an agency model.” Apple, 952 F.Supp.2d at 673 n. 39. After the discussions, Cue asked Sargent to speak with both Reidy and Murray. Sargent complied, and “spoke to both Murray and Reidy by telephone for eight and fifteen minutes, respectively.” Id. at 673. Minutes later, Sargent called the Amazon representative to inform him that Macmillan planned to sign an agreement that “required” the company to conduct business with Amazon through an agency model. Id. By January 23, Macmillan had verbally agreed to join the iBookstore.

Cue followed a similar strategy with Penguin. While Penguin’s CEO David Shanks agreed to Apple’s terms on January 22, he informed Cue that he would join the iBookstore only if four other publishers agreed to participate. By January 25, Apple had signatures from three publishers but Penguin was still noncommittal. Cue called Shanks, and the two spoke for twenty minutes. “Less than an hour [later], Shanks called Reidy to discuss Penguin’s status in its negotiations with Apple.” Id. at 675. Penguin signed the Contract that afternoon.

HarperCollins was the fifth, and final, publisher to agree in principle to Apple’s proposal. Murray, its CEO, “remained unhappy over the size of Apple’s commission and the existence of price caps.” Id. at 673 n. 39. Unable to negotiate successfully with Murray, Cue asked Jobs to contact James Murdoch, the CEO of the publisher’s parent company, and “tell him we have 3 signed so there is no leap of faith here.” Id. at 675 (internal quotation marks omitted). After a series of emails, Jobs summarized Apple’s position to Murdoch:

[W]e simply don’t think the ebook market can be successful with pricing higher than $12.99 or $14.99. Heck, Amazon is selling these books at $9.99, and who knows, maybe they are right and we will fail even at $12.99. But we’re willing to try at the prices we’ve proposed.... As I see it, [HarperCollins] has the following choices: (1) Throw in with [A]pple and see if We can all make a go of this to create a real mainstream ebooks market at $12.99 and $14.99. (2) Keep going with Amazon at $9.99. You will make a bit more money in the short term, but in the medium term Amazon will tell you they will be paying you 70% of $9.99. They have shareholders too. (3) Hold back your books from Amazon. Without a way for customers to buy your ebooks, they will steal them.

Id. at 677. Cue also emailed Murray to inform him that four other publishers had signed their agreements. Murray then called executives at both Hachette and Macmillan before agreeing to Apple’s terms.

As the district court found, during the period in January during which Apple concluded its agreements with the Publisher Defendants, “Apple kept the Publisher Defendants apprised about who was in and how many were on board.” Id. at 673. The Publisher Defendants also kept in close communication. As the district court noted, “[i]n the critical negotiation period, over the three days between January 19 and 21, Murray, Reidy, Shanks, Young, and Sargent called one another 34 times, with 27 calls exchanged on January 21 alone.” Id. at 674.

By the January 27 iPad launch, five of the Big Six — Hachette, HarperCollins, Macmillan, Penguin, and Simon & Schus-ter — had agreed to participate in the iBookstore.’ The lone holdout, Random House, did not join because its executives believed it would fare better under a wholesale pricing model and were unwilling to make a complete switch to agency pricing. Steve Jobs announced the iBook-store as part of his presentation introducing the iPad. When asked after the presentation why someone should purchase an ebook from Apple for $14.99 as opposed to $9.99 with Amazon or Barnes & Noble, Jobs confidently replied, ,“[t]hat won’t be the case ... the price will be the same.... [Publishers will actually withhold their [e]books from Amazon ... because they are not happy with the price.” A day later, Jobs told his’biographer the publishers’ position with Amazon: “[y]ou’re going to sign an agency contract or we’re not going to give you the books.” J.A. 891 (internal quotation marks omitted).

E. Negotiations with Amazon

Jobs’s boast proved to be prophetic. While the Publisher Defendants were signing Apple’s Contracts, they were also informing Amazon that they planned on changing the terms of their agreements with it to an agency model. However, their move against Amazon began in earnest on January 28, the day after the iPad launch. That afternoon, John Sargent flew to Seattle to deliver an ultimatum on behalf of Macmillan: that Amazon would switch its ebook sales agreement with Macmillan to an agency model or suffer a seven-month delay in its receipt of Macmil-Ian’s new releases. Amazon responded by removing the option to purchase Macmillan’s print and ebook titles from its website.

Sargent, as. the district court found, had informed Cue of his intention to confront Amazon before ever leaving for Seattle. Apple, 952 F.Supp.2d at 678. On his return, he emailed Cue to inform him about Amazon’s decision to remove Macmillan ebooks from Kindle, adding a note to say that he wanted to “make sure you are in the loop.” J.A. 640. Sargent also wrote a public letter to Macmillan’s authors and agents, describing the Amazon negotiations. Hachette’s Arnaud Nourry emailed the CEO of Macmillan’s parent company to express his “personal support” for Macmillan’s actions and to “ensure [him] that [he was] not going to find [his] company alone in the battle.” J.A. 643. A Penguin executive wrote to express similar support for Macmillan’s position.

The district court found that while Amazon was “opposed to adoption of the agency model and did not want to cede pricing authority to the Publishers,” it knew that it could not prevail in this position against five of the Big Six. Apple, 952 F.Supp.2d at 671, 680. When Amazon told Macmillan that it would be willing to negotiate agency terms, Sargent sent Cue an email titled “URGENT!!” that read: “Hi Eddy, I am gonna need to figure out our final agency terms of sale tonight. Can you call me please?” J.A. 642. Cue and Sargent spoke that night and, while Cue denied at trial that the conversation concerned Macmillan’s negotiations with Amazon, the district court found that “his denial was not credible.” Apple, 952 F.Supp.2d at 681 n. 52. By February 5, Amazon had agreed to agency terms with Macmillan.

The other publishers who had joined the iBookstore quickly followed Macmillan’s lead. On February 11, Reidy wrote to the head of CBS that Simon & Schuster was beginning agency negotiations with Amazon. She informed him that she was trying to “delay” negotiations because it was “imperative ... that the other publishers with whom Apple has announced deals push for resolution on their term changes” at the same time, “thus not leaving us out there alone.” J.A. 701. Each of the Publisher Defendants then informed Amazon that they were under tight deadlines to negotiate new agency agreements, and kept one another informed about the details of their negotiations. As David Nag-gar, one of Amazon’s negotiators, testified, whenever Amazon “would make a concession on an important deal point,” it would “come back to us from another publisher asking for the same thing or proposing similar language.” J.A. 1491.

Once again, Apple closely monitored the negotiations with Amazon. The Publisher Defendants would inform Cue when they had completed agency agreements, and his team monitored price changes on the Kindle. When Penguin languished behind the others, Cue informed Jobs that Apple was “changing a bunch of Penguin titles to 9.99” in the iBookstore “because they didn’t get their Amazon deal done.” Apple, 952 F.Supp.2d at 682 (internal quotation marks omitted). By March 2010, Macmillan, HarperCollins, Hachette, and Simon & Schuster had completed agency agreements with Amazon. When Penguin completed its deal in June, the company’s executive proudly announced to Cue that “[t]he playing field is now level.” Id. (internal quotation marks omitted).

F. Effect on Ebook Prices

As Apple and the Publisher Defendants expected, the iBookstore price caps quickly became the benchmark for ebook versions of new releases and New York Times bestsellers. In the five months following the launch of the iBookstore, the publishers who joined the marketplace and switched Amazon to an agency model priced 85.7% of new releases on Kindle and 92.1% of new releases on the iBookstore at, or just below, the price caps. Apple, 952 F.Supp.2d at 682. Prices for New York Times bestsellers took a similar leap as publishers began to sell 96.8% of their bestsellers on Kindle and 99.4% of their bestsellers on the iBookstore at, or just below, the Apple price caps. Id. During that same time period, Random House, which had not switched to an agency model, saw virtually no change in the prices for its new releases or New York Times bestsellers.

The Apple price caps also had a ripple effect on the rest of the Publisher Defendants’ catalogues. Recognizing that Apple’s price caps were tied to the price of hardcover books, many of these publishers increased the prices of their newly released hardcover books to shift the ebook version into a higher price category. Id. at 683. Furthermore, because the Publisher Defendants who switched to the agency model expected to make less money per sale than under the wholesale model, they also increased the prices on their ebooks that were not new releases or bestsellers to make up for the expected loss of revenue. Based on data from February 2010 — just before the Publisher Defendants switched Amazon to agency pricing — to February 2011, an expert retained by the Justice Department observed that the weighted average price of the Publisher Defendants’ new releases increased by 24.2%, while bestsellers' increased by 40.4%, and other ebooks increased by 27.5%, for a total weighted average ebook price increase of 23.9%. Indeed, even Apple’s expert agreed, noting that, over a two-year period, the Publisher Defendants increased their average prices for hardcovers, new releases, and other ebooks.

Increasing prices reduced demand for the Publisher Defendants’ ebooks. According to one of Plaintiffs’ experts, the publishers who switched to agency sold 77,307 fewer ebooks over a two-week period after the switch to agency than in a comparable two-week period before the switch, which amounted to selling 12.9% fewer units. Id. at 684. Another expert relied on data from Random House to estimate how many ebooks the Publisher Defendants who switched Amazon to agency would have sold had they stayed with the wholesale model, and concluded that the agency switch and price increases led to 14.5% fewer sales. Id.

Significantly, these changes took place against the backdrop of a rapidly changing ebook market. Amazon introduced the Kindle in November 2007, just over two years before Apple launched the iPad in January 2010. During that short period, Apple estimated that the market grew from $70 million in ebook sales in 2007 to $280 million in 2009, and the company projected those figures to grow significantly in following years. Apple’s expert witnesses argued that overall ebook sales continued to grow in the two years after the creation of the iBoókstore and that the average ebook price fell during those years. But as Plaintiffs’ experts pointed out, the ebook market had been expanding rapidly even before Apple’s entry and average prices had been falling as lower-end publishers entered the market and larger numbers of old books became available in digital form. “Apple’s experts did not present any analysis that attempted to control for the many changes that the e-book market was experiencing during these early years of its growth,” Apple, 952 F.Supp.2d at 685, nor did they estimate how the market would have grown but for Apple’s agreement with the Publisher Defendants to switch to an agency model and raise prices. To the contrary, the undisputed fact that the Publisher Defendants raised prices on their ebooks, which accounted for roughly 50% of the trade ebook market in the first quarter of 2010, necessitated “a finding that the actions taken by Apple and the Publisher Defendants led to an increase in the price of e-books.” Id.

Finally, in response to the dissent’s claim that Apple’s conduct “deconcentrat[ed] ... the e-book retail market” and thus was “pro-competitive,” Dissenting Op. at 351, it is worth noting that the district court’s economic analysis and the parties’ submissions at trial focused entirely on the price and sales figures for trade ebooks. This is because both parties agreed that the relevant market in this case is “the trade e-books market, not the e-reader market or the ‘e-books system’ market.” United States v. Apple, Inc., 889 F.Supp.2d 623, 642 (S.D.N.Y.2012); Apple, 952 F.Supp.2d at 694 n. 60. The district court did not analyze the state of competition between ebook retailers or determine that Amazon’s pricing policy acted, as the dissent accuses, as a “barrier[] to entry” for other potential retailers. Dissenting Op. at 348-49, 351.

II. Procedural History

On April 11, 2012, Plaintiffs filed a pair of civil antitrust actions in the United States District Court for the Southern District of New York. The complaints alleged that Apple and the Publisher Defendants — Hachette, HarperCollins, Macmillan, Penguin, and Simon & Schuster — conspired to raise, fix, and stabilize the retail price for newly released and bestselling trade ebooks in violation of § 1 of the Sherman Act and various state laws. The litigation then proceeded along two.separate trajectories, one for the Publisher Defendants and the other for Apple.

A. Publisher Defendants

Hachette, HarperCollins, and Simon & Schuster agreed to settle with DOJ by signing consent decrees on the same day that the Justice Department filed its complaint. Pursuant to the Tunney Act, 15 U.S.C. § 16 et seq., “at least 60 days prior to the effective date” of a consent judgment, the United States must file a “competitive impact statement,” which includes, inter alia, “the nature and purpose of the proceeding,” “a description of the practices or events giving rise to the alleged violation of the antitrust laws,” and an explanation of the relief obtained by the consent judgment “and the anticipated. effects on competition of such relief.” Id. § 16(b). In compliance with these requirements, DOJ issued a competitive impact statement that outlined the remedies it planned to impose on Hachette, HarperCollins, and Simon & Schuster. Two of those proposed remedies required that, for two years, the three publishers “not restrict, limit, or impede an E-book Retailer’s ability to set, alter, or reduce the Retail Price of any E-book or to offer price discounts or any other form of promotions,” and that they not “enter into any agreement” with retailers that limit such practices. J.A. 17 1126-27.

Alter the 60-day comment period, the Justice Department moved in the district court for a decision that “the entry of the judgment is in the public interest,” 15 U.S.C. § 16(e), and for approval of the consent decree. In defense of the two-year limitations provisions, DOJ explained that the Publisher Defendants had used retail price restrictions to “effectuat[e] the conspiracy” and that two years was sufficient to “allow movement in the marketplace away from collusive conditions” without “altering] the ultimate development of the competitive landscape in the still-evolving e-books industry.” J.A. 1054-55. On September 5, 2012, the district court approved the consent decree and found the two-year ban on retail-price restrictions “wholly appropriate given the Settling Defendants’ alleged abuse of such provisions ..., the Government’s recognition that such terms are not intrinsically unlawful, and the nascent state of competition in the e-books industry.” J.A. 1088.

The remaining Publisher Defendants, Penguin and Macmillan, settled in quick succession. On December 18, 2012, Penguin agreed to a consent decree with essentially the same terms that Hachette, HarperCollins, and Simon & Schuster received. A few months later, in February 2013, Macmillan also agreed to settle. The terms of Macmillan’s consent decree contained slight modifications. Rather than delaying the prohibition on retail discounts until the court approved the decree, DOJ required Macmillan to begin compliance within three days of signing the decree. In exchange, the Justice Department agreed to back-date the beginning of the limitations period to December 18, 2012 and to reduce its length from two years to 23 months, explaining that “[cjonsumers are better served by bringing more immediate retail price competition to the market” and that a “23-month cooling-off period is sufficient” to restore competition. J.A. 1162-63. The district court approved Penguin’s consent decree on May 17, 2013, and Macmillan’s on August 12, 2013.

B. Apple

Unlike the Publisher Defendants, Apple opted to take the case to trial. Fact and expert discovery concluded on March 22, 2013 and, after filing pretrial motions, the parties agreed to a bench trial on Apple’s liability and injunctive relief, to be followed by a separate trial on damages on the state claims if the states prevailed.

On July 10, 2013, after conducting a three-week bench trial, the district court concluded that Apple had violated § 1 of the Sherman Act and various state antitrust laws. In brief, the court found that Apple “orchestrat[ed]” a conspiracy among the Publisher Defendants to “eliminate retail price competition [in the e-book market] in order to raise the retail prices of e-books.” Apple, 952 F.Supp.2d at 697. Because this conspiracy consisted of a group of competitors — the Publisher Defendants — assembled by Apple to increase prices, it constituted a “horizontal price-fixing conspiracy” and was a per se violation of the Sherman Act. Id. at 694. It concluded, moreover, that even if the agreement to raise prices and eliminate retail price competition were analyzed under the rule of reason, it would still constitute an unreasonable restraint of trade in violation of § 1. Id. In the district court’s view, Plaintiffs’ experts persuasively demonstrated that the agreement facilitated an “aeross-the board price increase in e-books sold by the- Publisher Defendants” and a corresponding drop in sales. Id. Apple, on the other hand, failed to show that “the execution of the Agreements,” as opposed to the launch of the iPad and “evolution of digital publishing more generally” (which were independent of the Agreements), “had any pro-competitive effects.” Id.

After the district court issued its liability decision, the parties submitted briefing on injunctive relief. The court conducted a hearing on the issue and, on September 5, 2013, issued a final injunctive order against Apple and entered' final (1) “Prohibited Conduct,” which prevents Apple from enforcing MFNs with ebook publishers, retaliating against publishers for signing agreements with other retailers, or agreeing with any of the Publisher' Defendants to restrict, limit, or impede Apple’s ability to set ebook retail prices; (2) “Required Conduct,” which, among other things, forces Apple to modify its agency agreements with the Publisher Defendants and to treat ebook apps sold in the iTunes store like any other app sold there; (3) “Antitrust Compliance,” which requires Apple to improve its internal system for preventing antitrust violations.; and (4) “External Compliance Monitoring],” which allows the court to appoint an external monitor to ensure Apple’s compliance with the injunctive order.

After the entry of the district court’s injunctive order, Apple, Macmillan, and Simon & Schuster filed this appeal. The parties have not yet conducted a trial to assess the damages stemming from the state antitrust claims.

DISCUSSION

To hold a defendant liable for violating § 1 of the Sherman Act, a district court must find “a combination or some form of concerted action between at least two legally distinct economic entities” that “constituted an unreasonable restraint of trade.” Capital Imaging Assocs. v. Mohawk Valley Med. Assocs., 996 F.2d 537, 542 (2d Cir.1993); see 15 U.S.C. § 1. On appeal, Apple challenges numerous aspects of the district court’s § 1 analysis and also contends that the injunctive order that the district court imposed on the company is unlawful. Macmillan and Simon & Schuster have joined Apple’s challenge to the injunction, arguing that it impermissibly interferes with, their consent decrees and is barred by the doctrine of judicial estop-pel. We conclude that the district court’s liability determination was sound and its injunctive order lawful. We therefore affirm the judgment of the district court.

I. Standard of Review

Following a bench trial, this Court reviews the “district court’s findings of fact for clear error” and its “conclusions of law and mixed questions de novo.” Connors v. Conn. Gen. Life Ins. Co., 272 F.3d 127, 135 (2d Cir.2001); see Fed.R.Civ.P. 52(a). The district court’s evidentiary rulings and its fashioning of equitable relief are reviewed for abuse of discretion. See Zerega Ave. Realty Corp. v. Hornbeck Offshore Transp., LLC, 571 F.3d 206, 212-13 (2d Cir.2009) (evidentiary rulings); Abrahamson v. Bd. of Educ. Of the Wappingers Falls Cent. Sch. Dist., 374 F.3d 66, 76 (2d Cir.2004) (equitable relief).

II. Apple’s Liability Under § 1

This appeal requires us to address the important distinction between “horizontal” agreements to set prices, which involve coordination “between competitors at the same level of [a] market structure,” and “vertical” agreements on pricing, which are created between parties “at different levels of [a] market structure.” Anderson News, L.L.C. v. Am. Media, Inc., 680 F.3d 162, 182 (2d Cir.2012) (internal quotation marks omitted). Under § 1. of the Sherman Act, the former are, with limited exceptions, per se unlawful, while the latter are unlawful only if an assessment of market effects, known as a rule-of-reason analysis, reveals that they unreasonably restrain trade. See Leegin Creative Leather Prods., Inc. v. PSKS, Inc., 551 U.S. 877, 893, 127 S.Ct. 2705, 168 L.Ed.2d 623 (2007).

Although this distinction is sharp in theory, determining the orientation of an agreement can be difficult as a matter of fact and turns on more than simply identifying whether the participants are at the same level of the market structure. For instance, courts have long recognized the existence of “hub-and-spoke” conspiracies in which an entity at one level of the market structure, the “hub,” coordinates an agreement among competitors at a different level, the “spokes.” Howard Hess Dental Labs. Inc. v. Dentsply Int’l, Inc., 602 F.3d 237, 255 (3d Cir.2010); see also Toys “R” Us, Inc. v. FTC, 221 F.3d 928, 932-34 (7th Cir.2000). These arrangements consist of both vertical agreements between the hub and each spoke and a horizontal agreement among the spokes “to adhere to the [hub’s] terms,” often because the spokes “would not have gone along with [the vertical agreements] except on the understanding that the other [spokes] were agreeing to the same thing.” VI Phillip E. Areeda & Herbert Hovenkamp, Antitrust Law ¶ 1402c (3d ed.2010) (citing PepsiCo, Inc. v. Coca-Cola Co., 315 F.3d 101 (2d Cir.2002)); see also Am. Bar Ass’n, Antitrust Law Developments 24-26 (6th ed.2007); XII Areeda & Hovenkamp, supra, ¶ 2004c.

Apple characterizes its Contracts with the Publisher Defendants as a series of parallel but independent vertical agreements, a characterization that forms the basis for its two primary arguments against the district court’s decision. First, Apple argues that the distrifit court imper-missibly inferred its involvement in a horizontal price-fixing conspiracy from the Contracts themselves. Because (in. Apple’s view) the Contracts were vertical, lawful, and in Apple’s independent economic interest, the mere fact that Apple agreed to the same terms with multiple publishers cannot establish that Apple consciously organized a conspiracy among the Publisher Defendants to raise consumer-facing ebo'ok prices — even if the effect of its Contracts was to raise those prices. Second, Apple argues that, even if it did orchestrate a horizontal price-fixing conspiracy, its conduct should not be subject to per se condemnation. According to Apple, proper application of the rule of reason reveals that its conduct was not unlawful.

For the reasons set forth below, we reject these arguments. On this record, the district court did not err in determining that Apple orchestrated an agreement with and among the Publisher Defendants, in characterizing this agreement as a horizontal price fixing-conspiracy, or in holding that the conspiracy unreasonably restrained trade in violation of § 1 of the Sherman Act.

A. The Conspiracy with the Publisher Defendants

Section 1 of the Sherman Act bans restraints on trade “effected by a contract, combination, or conspiracy.” Bell Atl. Corp. v. Twombly, 550 U.S. 544, 553, 127 S.Ct. 1955, 167 L.Ed.2d 929 (2007) (internal quotation marks omitted). The |irst “crucial question in a Section 1 case is therefore whether the challenged conduct ‘stem[s] from independent decision or from an agreement, tacit or express.’ ” Starr v. Sony BMG Music Entm’t, 592 F.3d 314, 321 (2d Cir.2010) (alteration in original) (quoting Theatre Enters., Inc. v. Paramount Film Distrib. Corp., 346 U.S. 537, 540, 74 S.Ct. 257, 98 L.Ed. 273 (1954)).

Identifying the existence and nature of a conspiracy requires determining whether the evidence “reasonably tends to prove that the [defendant] and others had a conscious commitment to a common scheme designed to achieve an unlawful objective.” Monsanto Co. v. Spray-Rite Serv. Corp., 465 U.S. 752, 764, 104 S.Ct. 1464, 79 L.Ed.2d 775 (1984) (internal quotation marks omitted). Parallel action is not, by itself, sufficient to pr'ove the existence of a conspiracy; such behavior could be the result of “coincidence, independent responses to common stimuli, or mere .interdependence unaided by an advance understanding among the parties.” Twombly, 550 U.S. at 556 n. 4, 127 S.Ct. 1955 (internal quotation marks omitted). Indeed, parallel behavior that does not result from an agreement is not unlawful even if it is anticompetitive. See In re Text Messaging Antitrust Litig., 782 F.3d 867, 873-79 (7th Cir.2015); In re Flat Glass Antitrust Litig., 385 F.3d 350, 360-61 (3d Cir.2004). Accordingly, to prove an antitrust conspiracy, “a plaintiff must show the existence of additional circumstances, often referred to as ‘plus’ factors, which, when viewed in conjunction with the parallel acts, can serve to allow a fact-finder to infer a conspiracy.” Apex Oil Co. v. DiMauro, 822 F.2d 246, 253 (2d Cir.1987).

These additional circumstances can, of course, consist of “direct evidence that the defendants entered into an agreement” like “a recorded phone call in which two competitors agreed to fix prices.” Mayor & City Council of Baltimore, Md. v. Citigroup, Inc., 709 F.3d 129, 136 (2d Cir.2013). But plaintiffs may also “present circumstantial facts supporting the inference that a conspiracy existed.” Id. Circumstances that may raise an inference of conspiracy include “a common motive to conspire, evidence that shows that the parallel acts were against the apparent individual economic self-interest of the alleged conspirators, and evidence of a high level of interfirm communications.” Id. (internal quotation marks omitted). Parallel conduct alone may support an inference of conspiracy, moreover, if it consists of “complex and historically unprecedented changes in pricing structure made at the very same time by multiple competitors, and made for no other discernible reason.” Id. at 137 (internal quotation marks omitted).

Because of the risk of condemning parallel conduct that results from independent action and not from an actual unlawful agreement, the Supreme Court has cautioned against drawing an inference of conspiracy from evidence that is equally consistent with independent conduct as with illegal conspiracy — or, as the Court has called it, “ambiguous” evidence. Matsushita Elec. Indus. Co. v. Zenith Radio Corp., 475 U.S. 574, 597 n. 21, 106 S.Ct. 1348, 89 L.Ed.2d 538 (1986). Thus, a finding of conspiracy requires “evidence that tends to exclude the possibility” that the defendant was “acting independently.” Monsanto, 465 U.S. at 764, 104 S.Ct. 1464. This requirement, however, “[does] not mean that the plaintiff must disprove all noneonspiratorial explanations for the defendants’ conduct”; rather, the evidence need only be sufficient “to allow a reasonable fact finder to infer that the conspiratorial explanation is more likely than not.” In re Publ’n Paper Antitrust Litig., 690 F.3d 51, 63 (2d Cir.2012) (quoting Phillip E. Areeda & Herbert Hovenkamp, Fundamentals of Antitrust Law § 14.03(b), at 14-25 (4th ed.2011)); accord Matsushita, 475 U.S. at 588, 106 S.Ct. 1348 (requiring that “the inference of conspiracy is reasonable in light of the competing inferences of independent action”); In re High Fructose Com Syrup Antitrust Litig., 295 F.3d 651, 655-56 (7th Cir.2002).

Apple portrays its Contracts with the Publisher Defendants as, at worst, “unwittingly facilitating]” their joint conduct. Apple Br. at 23. All Apple did, it claims, was attempt to enter the market on profitable terms by offering contractual provisions — an agency model, the MFN Clause, and tiered price caps — which ensured the company a small profit on each ebook sale and insulated it from retail price competition. This had the effect of raising prices because it created an incentive for the Publisher Defendants to demand that Amazon adopt an agency model and to seize control over consumer-facing ebook prices industry-wide. But although Apple knew that its contractual terms would entice the Publisher Defendants (who wanted to do away with Amazon’s $9.99 pricing) to seek control over prices from Amazon and other ebook retailers, Apple’s success in capitalizing on the Publisher Defendants’ preexisting incentives, it contends, does not suggest that it joined a conspiracy among the Publisher Defendants to raise prices. In sum, Apple’s basic argument is that because its Contracts with the Publisher Defendants were fully consistent with its independent business interests, those agreements provide only “ambiguous” evidence of a § 1 conspiracy, and the district court therefore erred under Matsushita and Monsanto in inferring such a conspiracy.

We disagree. At the start, Apple’s benign portrayal of its Contracts with the Publisher Defendants is not persuasive— not because those Contracts themselves were independently unlawful, but because, in context, they provide strong evidence that Apple consciously orchestrated.a conspiracy among the Publisher Defendants. As explained below, and as the district court concluded, Apple understood that its proposed Contracts were attractive to the Publisher Defendants only if they collectively shifted their relationships with Amazon to an agency model — which Apple knew would result in higher consumer-facing ebook prices. In addition to these Contracts, moreover, ample additional evidence identified by the district-court established both that the Publisher Defendants’ shifting to an agency model with Amazon was the result of express collusion among them and that Apple consciously played a key role in organizing that collusion. The district court did not err in concluding that Apple was more than an innocent bystander.

Apple offered each Big Six publisher a proposed Contract that would be attractive only if the publishers acted collectively. Under Apple’s proposed agency model, the publishers stood to make less money per sale than under their wholesale agreements with Amazon, but the Publisher Defendants were willing to stomach this loss because the model allowed them to sell new releases and bestsellers for more than $9.99. Because of the MFN Clause, however, each new release and bestseller sold in the iBookstore would cost only $9.99 as long as Amazon continued to sell ebooks at that price. So in order to receive the perceived benefit of Apple’s proposed Contracts, the Publisher Defendants had to switch Amazon to an agency model as well — something no individual publisher had sufficient leverage to do on its own. Thus, each Publisher Defendant would be able to accomplish the shift to agency— and therefore have an incentive to sign Apple’s proposed Contracts — only if it acted in tandem with its competitors. See Starr, 592 F.3d at 324; Flat Glass, 385 F.3d at 360-61; see also J.A. 1974 (noting that the agreements would “not fix the publishers’ problems” if they could riot move Amazon to an agency model). By the very act of signing a Contract with Apple containing an MFN Clause, then, each of the Publisher Defendants signaled a clear commitment to move against Amazon, thereby facilitating their collective action. As the district court explained, the MFNs “stiffened the spines” of the Publisher Defendants. Apple, 952 F.Supp.2d at 665.

As a sophisticated negotiator, Apple was fully aware that its proposed Contracts would entice a critical mass of publishers only if these publishers perceived an opportunity collectively to shift Amazon to agency. In fact, this was the very purpose of the MFN, which Apple’s Saul devised as an elegant alternative to a provision that would have explicitly required the publishers to adopt an agency model with other retailers. As Cue put it, the MFN “force[d] the model” from wholesale to agency. J.A. 865. Indeed, the MFN’s capacity for forcing collective action by the publishers was precisely what enabled Jobs to predict with confidence that “the price will be the same” on the iBookstore and the Kindle when he announced the launch of the iPad — the same, Jobs said, because the publishers would make Amazon “sign ... agency contracts]” by threatening to withhold their ebooks. J.A. 891. Apple was also fully aware that once the Publisher Defendants seized control over consumer-facing ebook prices, those prices would rise. It knew from the outset that the publishers hated Amazon’s $9.99 price point, and it put price caps in its agreements because it specifically anticipated that once the publishers gained control over prices, they would push them higher than $9.99, higher than Apple itself deemed “realistic.” Apple, 952 F.Supp.2d at 692 (internal quotation marks omitted).

On appeal, Apple nonetheless defends the Contracts that it proposed to the publishers as an “aikido move” that shrewdly leveraged market conditions to its own advantage. Apple Br. at 17. “[Ajikido move” or not, the attractiveness of Apple’s offer to the Publisher Defendants hinged on whether it could successfully help organize them to force Amazon to an agency model and then to use their newfound collective control to raise ebook prices. The Supreme Court has defined an agreement for Sherman Act § 1 purposes as “a conscious commitment to a common scheme designed to achieve an unlawful objective.” Monsanto, 465 U.S. at 764, 104 S.Ct. 1464 (internal quotation marks omitted). Plainly, this use of the promise of higher prices as a bargaining chip to induce the Publisher Defendants to participate in the iBookstore constituted a conscious commitment to the goal of raising ebook prices. “Antitrust law has never required identical motives among conspirators” when their independent reasons for joining together lead to collusive action. Spectators’ Commc’n Network Inc. v. Colonial Country Club, 253 F.3d 215, 220 (5th Cir.2001) (emphasis added). Put differently, “independent reasons” can also be “interdependent,” and the fact that Apple’s conduct was in its own economic interest in no way undermines the inference that it entered an agreement to raise ebook prices. VI Areeda & Hovenkamp, supra, ¶ 1413a (internal quotation marks omitted).

Nor was the Publisher Defendants’ joint action against Amazon a result of parallel decisionmaking. As we have explained, conduct resulting solely from competitors’ independent - business decisions — and not from any “agreement” — is not unlawful under § 1 of the Sherman Act, even if it is anticompetitive. See Text Messaging, 782 F.3d at 873-79. But to generate a permissible inference of agreement, a plaintiff need only present sufficient evidence that such agreement conclude that it was not equally likely that the near-simultaneous signing of Apple’s Contracts by multiple publishers — which led to all of the Publisher Defendants moving against Amazon — resulted from the parties’ independent decisions, as opposed to a “meeting of [the] minds.” Monsanto, 465 U.S. at 765, 104 S.Ct. 1464; see Toys “R” Us, 221 F.3d at 935-36 (holding that exclusive-dealing agreements between a retailer and manufacturers that were contrary to the manufacturers’ individual self-interest but consistent with their collective interest supported the inference of a horizontal conspiracy in which the retailer participated); VI Areeda & Hovenkamp, supra, ¶ 1425a, d (“[A] conspiracy may be inferred if a defendant’s action would have been contrary to its self-interest in the absence of advance agreement.” Id. ¶ 1425a). That the Publisher Defendants were in constant communication regarding their negotiations with both Apple and Amazon can hardly be disputed. Indeed, Apple never seriously argues that the Publisher Defendants were not acting in concert.

Even so, Apple claims, it cannot have organized the conspiracy among the Publisher Defendants if it merely “unwittingly facilitated [their] joint conduct.” Apple Br. at 23. But this argument founders — and dramatically so — on the factual findings of the district court. As the district court explained, Apple’s Contracts with the publishers “must be considered in the context of the entire record.” Apple, 952 F.Supp.2d at 699. Even if Apple was unaware of the extent of the Publisher Defendants’ coordination when it first approached them, its subsequent communications with them as negotiations progressed show that Apple consciously played a key role in organizing their express collusion. From the outset, Cue told the publishers that Apple would launch its iBookstore only if a sufficient number of them agreed to participate and that each publisher would receive identical terms, assuring them that a critical mass of major publishers would be prepared to move against Amazon. Later on, Cue and his team kept the publishers updated about how many of their peers signed Apple’s Contracts, and reminded them that it was offering “the best chance for publishers to challenge the 9.99 price point” before it became “cement[ed]” in “consumer expectations.” J.A. 522. When time ran short, Apple coordinated phone calls between the publishers who had agreed and those who remained on the fence. As Cue said at trial, Apple endeavored to “assure [the publishers] that they weren’t going to be alone, so that [Apple] would take the fear awa[y] of the Amazon retribution that they were all afraid of.” J.A. 2068.

Apple’s involvement in the conspiracy continued even past the signing of its agency agreements. Before Sargent flew to Seattle to meet with Amazon, he told Cue. Apple stayed abreast of the Publisher Defendants’ progress as they set coordinated deadlines with Amazon and shared information with one another during negotiations. Apple’s communications with the Publisher Defendants thus went well beyond legitimately “exchanging] information” within “the normal course of business,” Monsanto, 465 U.S. at 762-63, 104 S.Ct. 1464 (internal quotation marks omitted), or “friendly banter among business partners,” Apple Br. at 38; see Monsanto, 465 U.S. at 765-66, 104 S.Ct. 1464 (concluding that message about getting “the market place in order” could lead to inference of conspiracy (internal quotation marks omitted)); see also Starr, 592 F.3d at 324; Apex Oil, 822 F.2d at 255-57.

Apple responds to this evidence— which the experienced judge who oversaw the trial characterized repeatedly as “overwhelming” — by explaining how each piece of evidence standing alone is “ambiguous” and therefore insufficient to support an inference of conspiracy. We are not persuaded. In antitrust cases, “[t]he character and effect of a conspiracy are not to be judged by dismembering it and viewing its separate parts, but only by looking at it as a whole.” Cont’l Ore Co. v. Union Carbide & Carbon Corp., 370 U.S. 690, 699, 82 S.Ct. 1404, 8 L.Ed.2d 777 (1962). Combined with the unmistakable purpose of the Contracts that Apple proposed to the publishers, and with the collective move against Amazon that inevitably followed the signing of those Contracts, the emails and phone records demonstrate that Apple agreed with the Publisher Defendants, within the meaning of the Sherman Act, to raise consumer-facing ebook prices by eliminating retail price competition. The district court did not err in rejecting Apple’s argument that the evidence of its orchestration of the Publisher Defendants’ conspiracy was “ambiguous.”

Given the record and the district court’s factual findings, we do not share Apple and its amici’s concern that we will stifle productive enterprise by inferring an agreement among Apple and the Publisher Defendants on the basis of otherwise lawful contract terms, such as an agency model and MFNs. To begin with, it is well established that vertical agreements, lawful in the abstract, can in context “be useful evidence for a plaintiff attempting to prove the existence of a horizontal cartel,” Leegin, 551 U.S. at 893, 127 S.Ct. 2705, particularly where multiple competitors sign vertical agreements that would be against their own interests were they acting independently, see, e.g., Interstate Circuit v. United States, 306 U.S. 208, 222, 59 S.Ct. 467, 83 L.Ed. 610 (1939); Toys “R” Us, 221 F.3d at 935-36. The MFNs in Apple’s Contracts created a set of economic incentives pursuant to which the. Contracts were only attractive to the Publisher Defendants to the .extent they acted collectively. That these contract terms had such an effect under the particular circumstances of this case — and therefore furnish part of the evidence of Apple’s agreement with the Publisher Defendants — says nothing about their broader legality. It should be self-evident that our analysis is informed by the particular context in which Apple’s contract terms were deployed. In any event, we are breaking no new ground in concluding that MFNs, though surely proper in many contexts, can be “Misused to anticompetitive ends in some cases.” - Blue Cross & Blue Shield United of Wis. v. Marshfield Clinic, 65 F.3d 1406, 1415 (7th Cir.1995); see Starr, 592 F.3d at 324 (finding MFN evidence of conspiracy). Under the right circumstances, an MFN can “facilitate anticompetitive horizontal coordination” by “reducing] [a company’s] incentive to deviate from a coordinated horizontal arrangement.” Jonathan B. Baker, Vertical Restraints with Horizontal Consequences: Competitive Effects of “Most-Favored-Customer” Clauses, 64 Antitrust L.J. 517, 520-21 (1996); see also Jonathan B. Baker & Judith A. Chevalier, The Competitive Consequences of Mostr-Favored-Nation Provisions, Antitrust, Spring 2013, at 20-26, available at http:// digitalcommons.wcl.american.edu/cgi/ viewcontent.cgi?article=1280 & context=facsch_Iawrev.

In short, we have no difficulty on this récord rejecting Apple’s argument that the district court erred in concluding that Apple “conspir[ed] with the Publisher Defendants to eliminate retail price competition and to raise e-book prices.” Apple, 952 F.Supp.2d at 691. Having concluded that the district court correctly identified an agreement between Apple and the Publisher Defendants to raise consumer-facing ebook prices, we turn to Apple’s and the dissent’s arguments that this agreement did not violate § 1 of the Sherman Act.

B. Unreasonable Restraint of Trade

“Although the Sherman Act, by its terms, prohibits every agreement ‘in restraint of trade,’ [the Supreme] Court has long recognized that Congress intended to outlaw only unreasonable restraints.” State Oil Co. v. Khan, 522 U.S. 3, 10, 118 S.Ct. 275, 139 L.Ed.2d 199 (1997). Thus, to succeed on an antitrust claim, a plaintiff must prove that the common scheme designed by the conspirators “constituted an unreasonable restraint of trade either per se or under the rule of reason.” Capital Imaging, 996 F.2d at 542.

In antitrust cases, “[p ]er se and rule-of-reason analysis are ... two methods of determining whether a restraint is ‘unreasonable,’ i.e., whether its anticompetitive effects outweigh its pro-competitive effects.” Atl. Richfield Co. v. USA Petroleum Co., 49.5 U.S. 328, 342, 110 S.Ct. 1884, 109 L.Ed.2d 333 (1990). Because this balancing typically requires case-by-case analysis, “most antitrust claims are analyzed under [the] ‘rule of reason,’ according to which the finder of fact must decide whether the questioned practice imposes an unreasonable restraint on competition.” Khan, 522 U.S. at 10, 118 S.Ct. 275; see also Gatt Commc’ns, Inc. v. PMC Assocs., L.L.C., 711 F.3d 68, 75 n. 8 (2d Cir.2013). However, some restraints “have such predictable and pernicious anticompetitive effect, and such limited potential for procompetitive benefit, that they are deemed unlawful per se.” Khan, 522 U.S. at 10, 118 S.Ct. 275. This rule “reflect[s] a longstanding judgment” that case-by-case analysis is unnecessary for certain practices that, “by their nature[,] have a substantial potential” to unreasonably restrain competition. FTC v. Sup.Ct. Trial Lawyers Ass’n, 493 U.S. 411, 433, 110 S.Ct. 768, 107 L.Ed.2d 851 (1990) (internal quotation marks omitted).

Horizontal price-fixing conspiracies traditionally have been, and remain, the “archetypal example” of a per se unlawful restraint on trade. Catalano, Inc. v. Target Sales, Inc., 446 U.S. 643, 647, 100 S.Ct. 1925, 64 L.Ed.2d 580 (1980). By contrast, the Supreme Court in recent years has clarified that vertical restraints — including those that restrict prices — should generally be subject to the rule of reason. See Leegin, 551 U.S. at 882, 127 S.Ct. 2705 (holding that the rule of reason applies to vertical minimum price-fixing); Khan, 522 U.S. at 7, 118 S.Ct. 275 (holding that the rule of reason applies to vertical maximum price-fixing).

In this case, the district court held that the agreement between Apple and the Publisher Defendants was unlawful under the per se rule; in the alternative, even assuming that a rule-of-reason analysis was required, the district court concluded that the agreement was still unlawful. See Apple, 952 F.Supp.2d at 694. On appeal, we consider three primary arguments against application of the per se rule. First, Apple and our dissenting colleague argue that the per se rule is inappropriate in this case because Apple’s Contracts with the Publisher Defendants were vertical, not horizontal. Even if the challenged agreement here was horizontal, Apple argues next, it promoted “enterprise and productivity.” Finally, Apple contends that even if the agreement was horizontal, it was not, in fact, a “price-fixing” conspiracy of the kind that deserves per se condemnation. We address, and reject, these arguments in turn. Because the ebook industry, however, is new and at least arguably involves some new ways of doing business, I also consider, writing only for myself, Apple’s rule-of-reason argument.

1. Whether the Per Se Rule Applies

a. Horizontal Agreement

In light of our conclusion that the district court did not err in determining that Apple organized a price-fixing conspiracy among the Publisher Defendants, Apple and the dissent’s initial argument against the per se rule — that Apple’s conduct must be subject to rule-of-reason analysis because it involved merely multiple independent, vertical agreements with the Publisher Defendants — cannot succeed.

“The true test of legality” under § 1 of the Sherman Act “is whether the restraint imposed is such as merely regulates and perhaps thereby promotes competition or whether it is such as may suppress or even destroy competition.” Bd. of Trade of City of Chi. v. United States, 246 U.S. 231, 238, 38 S.Ct. 242, 62 L.Ed. 683 (1918) (emphasis added). By agreeing to orchestrate a horizontal price-fixing conspiracy, Apple committed itself to “achievfing] [that] unlawful objective,” Monsanto, 465 U.S. at 764, 104 S.Ct. 1464 (internal quotation marks omitted): namely, collusion with and among the Publisher Defendants to set ebook prices. This type of agreement, moreover, is a restraint “that would always or almost always tend to restrict competition and decrease output.” Leegin, 551 U.S. at 886, 127 S.Ct. 2705 (internal quotation marks omitted).

The response, raised by Apple and our dissenting colleague, that Apple engaged in “vertical conduct” that is unfit for per se condemnation therefore misconstrues the Sherman Act analysis. It is the type of restraint Apple agreed to impose that determines whether the per se rule or the rule of reason is appropriate. These rules are means of evaluating “whether [a] restraint is unreasonable,” not the reasonableness of a particular defendant’s role in the scheme. Atl. Richfield, 495 U.S. at 342, 110 S.Ct. 1884 (emphasis added) (internal quotation marks omitted); see also Nat’l Collegiate Athletic Ass’n v. Bd. of Regents of the Univ. of Okla., 468 U.S. 85, 103, 104 S.Ct. 2948, 82 L.Ed.2d 70 (1984) (“Both per se rules and the Rule of Reason are employed to form a judgment about the competitive significance of the restraint.” (internal quotation marks omitted)).

Consistent with this principle, the Supreme Court and our Sister Circuits have held all participants in “hub-and-spoke” conspiracies liable when the objective of the conspiracy was a per se unreasonable restraint of trade. See Richard A. Posner, The Next Step in the Antitrust Treatment of Restricted Distribution: Per Se Legality, 48 U. Chi. L.Rev. 6, 22 (1981) (“[C]ases in which dealers or distributors collude ... among themselves and bring in the manufacturer to enforce their cartel, ... can be dealt with under the conventional rules applicable to horizontal price-fixing conspiracies.”). In Klor’s, Inc. v. Broadway-Hale Stores, Inc., for example, the Supreme Court considered whether a prominent retailer of electronic appliances could be held liable under § 1 of the Sherman Act for fostering an agreement with and among its distributors to have those companies boycott a competing retailer. 359 U.S. 207, 79 S.Ct. 705, 3 L.Ed.2d 741 (1959). The Court characterized this arrangement as a “[g]roup boycott[]” supported by a “wide combination consisting of manufacturers, distributors and a retailer.” Id. at 212-13, 79 S.Ct. 705. It then decided that, if the combination were proved at trial, holding the retailer liable would be appropriate because “[g]roup boycotts, or concerted refusals by traders to deal with other traders,” are per se unreasonable restraints of trade. Id. at 212, 79 S.Ct. 705.

The Supreme Court followed a similar approach in United States v. General Motors Corp., 384 U.S. 127, 86 S.Ct. 1321, 16 L.Ed.2d 415 (1966), when it considered whether § 1 prohibited a car manufacturer, General Motors, from coordinating a group of dealerships to prevent other dealers from selling cars at discount prices. The majority called this arrangement a “classic conspiracy in restraint of trade” and refused to entertain General Motors’ request to consider the company’s reasons for creating the conspiracy. Id. at 140, 86 S.Ct. 1321. The Court explained that “[tjhere can be no doubt that the effect of the combination ... here was to restrain trade and commerce within the meaning of the Sherman Act” because “[ejlimination, by joint collaborative action, of discounters from access to the market is a per se violation of the Act.” Id. at 145, 86 S.Ct. 1321; see, e.g., Toys “R” Us, 221 F.3d at 936; Denny’s Marina, Inc. v. Renfro Prods., Inc., 8 F.3d 1217, 1220-21 (7th Cir.1993); United States v. MMR Corp. (LA), 907 F.2d 489, 498 (5th Cir.1990); see also Albert Foer & Randy Stutz, Private Enforcement of Antitrust Law in the United States 29 (2012).

Because the reasonableness of a restraint turns on its anticompetitive effects, and not the identity of each actor who participates in imposing it, Apple and the dissent’s observation that the Supreme Court has refused to apply the per se rule to certain vertical agreements is inappo-site. The rule of reason is unquestionably appropriate to analyze an agreement between a manufacturer and its distributors to, for instance, limit the price at which the distributors sell the manufacturer’s .goods or the locations at which they sell them. See Leegin, 551 U.S. at 881, 127 S.Ct. 2705; Cont’l T.V., Inc. v. GTE Sylvania Inc., 433 U.S. 36, 57, 97 S.Ct. 2549, 53 L.Ed.2d 568 (1977). These vertical restrictions “are widely used in our free market economy,” can enhance int'erbrand competition, and do not inevitably have a “pernicious effect on competition.” Cont’l T.V., 433 U.S. at 57-58, 97 S.Ct. 2549 (internal quotation marks omitted). But the relevant “agreement in restraint of trade” in this case is not Apple’s vertical Contracts with the Publisher Defendants (which might well, if challenged, have to be evaluated under the rule of reason); it is the horizontal agreement that Apple organized among the Publisher Defendants to raise ebook prices. As explained below, horizontal agreements with the purpose and effect of raising prices are per sé unreasonable because they pose a “threat to the central nervous system of the economy,” United States v. Socony-Vacuum Oil Co., 310 U.S. 150, 224 n. 59, 60 S.Ct. 811, 84 L.Ed. 1129 (1940); that threat is just as significant when a vertical market participant organizes the conspiracy. Indeed, as the dissent notes, the Publisher Defendants’ coordination to fix prices is uncontested on appeal. See Dissenting Op. at 348. The competitive effects of that same restraint are no different merely because a different conspirator is the defendant.

Accordingly, when the Supreme Court has applied the rule of reason to vertical agreements, it. has explicitly distinguished situations in which a vertical player organizes a horizontal cartel. For instance, in Business Electronics Corp. v. Sharp Electronics Corp., the Court concluded that an agreement “between a manufacturer and a dealer to terminate” another dealer is a “vertical nonprice restraint” that should be evaluated under the rule of reason. 485 U.S. 717, 726, 108 S.Ct. 1515, 99 L.Ed.2d 808 (1988). The Court distinguished General Motors and Klor’s on the grounds that “both cases involved horizontal combinations,” id. at 734, 108 S.Ct. 1515, and noted that “a facially vertical restraint imposed by a manufacturer only because it has been coerced by a ‘horizontal carte[l]’ ... is in reality a horizontal restraint,” id. at 730 n. 4, 108 S.Ct. 1515 (alteration in original). More recently, in NYNEX Corp. v. Discon, Inc., the Court ruled that “a buyer’s decision to buy from one seller rather than another” is subject to analysis under the rule of reason. 525 U.S. 128, 130, 119 S.Ct. 493, 142 L.Ed.2d 510 (1998). In arriving at this conclusion, the Court took care to distinguish, rather than overturn, Klor’s, noting that per se liability was appropriate for the organizer of the conspiracy in that case because the agreement at issue was not “simply a ‘vertical’ agreement between supplier and customer, but [also] a ‘horizontal’ agreement among competitors.” Id. at 136, 119 S.Ct. 493 (citing Bus. Elecs. Corp., 485 U.S. at 734, 108 S.Ct. 1515).

The Court’s decision in Leegin Creative Leather Products, Inc. v. PSKS, Inc., is no different. 551 U.S. 877, 127 S.Ct. 2705, 168 L.Ed.2d 623 (2007). In Leegin, a leather manufacturer entered into separate agreements with each of its retailers, which required them to sell its goods at certain prices. The plaintiff — a retailer who refused to comply with the requirement — argued that these resale price maintenance agreements constituted per se violations of the Sherman Act. The Supreme Court disagreed, concluding that “vertical price restraints are to be judged by the rule of reason.” Id. at 882, 127 S.Ct. 2705. Its analysis was careful to distinguish between vertical restraints and horizontal ones. Vertical price restraints are unfit for the per se rule because they can be used to encourage retailers to invest in promoting a product by ensuring that other retailers will not undercut their prices for that good. See id. at 890-92, 127 S.Ct. 2705. However, vertical price restraints can also be used to organize horizontal cartels to increase prices, which are, “and ought to be, per se unlawful.” Id. at 893, 127 S.Ct. 2705. When used for such a purpose, the vertical agreement may be “useful evidence ... to prove the existence of a horizontal cartel.” Id.; see also VI Areeda & Hovenkamp, supra, ¶ 1402c. The Court made clear that it was addressing only the lawfulness of the manufacturer’s vertical agreements and not the plaintiffs claim that the manufacturer also “participated in an unlawful horizontal cartel with competing retailers.” Id. at 907-08, 127 S.Ct. 2705; see also PSKS, Inc. v. Leegin Creative Leather Prods., Inc., 615 F.3d 412 (5th Cir.2010) (considering plaintiffs “hub-and-spoke” theory on remand).

Our dissenting colleague suggests that Leegin also “rejected per se liability for hub-and-spokes agreements.” Dissenting Op. at 346. This position relies on a single sentence from the opinion’s analysis of how vertical resale price restraints can harm competition, which states that, if a “vertical agreement setting minimum resale prices is entered upon to facilitate” a horizontal cartel, it “would need to be held unlawful under the rule of reason.” Leegin, 551 U.S. at 893, 127 S.Ct. 2705. If the Supreme Court meant to overturn General Motors and Klor’s — precedents that it has consistently reaffirmed — this cryptic sentence was certainly an odd way to accomplish that result. The Supreme Court “does not normally overturn, or so dramatically limit, earlier authority sub silentio.” Shalala v. Ill. Council on Long Term Care, Inc., 529 U.S. 1, 18, 120 S.Ct. 1084, 146 L.Ed.2d 1 (2000); see also, e.g., Nestor v. Pratt & Whitney, 466 F.3d 65, 72 n. 8 (2d Cir.2006) (“It is not within our purview to anticipate whether the Supreme Court may one day overrule its existing precedent.” (quoting United States v. Santiago, 268 F.3d 151, 155 n. 6 (2d Cir.2001) (internal quotation marks omitted))).

We need not worry about the possibility that Leegin covertly changed the law governing hub-and-spoke conspiracies, however, because the passage relied upon by the dissent is entirely consistent with holding the “hub” in such a conspiracy liable for the horizontal agreement that it joins. A horizontal conspiracy can use vertical agreements to facilitate coordination without the other parties to those agreements knowing about, or agreeing to, the horizontal conspiracy’s goals. For example, a cartel of manufacturers could ensure compliance with a scheme to fix prices by having every member “require its dealers to adhere to specified resale prices.” VIII Areeda & Hovenkamp, supra, ¶ 1606b. Because it may be difficult to distinguish such facilitating practices from procompetitive vertical resale price agreements, the quoted passage from Leegin notes that those “vertical agreements] ... would need to' be held unlawful under the rule of reason.” 551 U.S. at 893, 127 S.Ct. 2705. But there is no such possibility for confusion in the hub-and-spoke context, where the vertical organizer has not only committed to vertical agreements, but has also agreed to participate in the horizontal conspiracy. In that situation, the court need not consider whether the vertical agreements restrained trade because all participants agreed to the horizontal restraint, which is “and ought to be, per se unlawful.” Id.

In short, the relevant “agreement in restraint of trade” in this case is the .price-firing conspiracy identified by the district court, not Apple’s vertical contracts with the Publisher Defendants. How the law might treat Apple’s vertical agreements in the absence of a finding that Apple agreed to create the horizontal restraint is irrelevant. Instead, the question is whether the vertical organizer of a horizontal conspiracy designed to raise prices has agreed to a restraint that is any less anticompetitive than its co-conspirators, and can therefore escape per se liability. We think not. Even in light of this conclusion, however, we must address two additional arguments that Apple raises against application of the per se rule.

b. “Enterprise and Productivity”

Apple seeks refuge from the per se rule by invoking a line of cases in which courts have permitted defendants to introduce procompetitive justifications for horizontal price-fixing arrangements that would ordinarily be condemned per se if those agreements “when adopted could reasonably have been believed to promote ‘enterprise and productivity.’ ” Apple Br. at 50 (quoting In re Sulfuric Acid Antitrust Litig., 703 F.3d 1004, 1011 (7th Cir.2012)) (internal quotation mark omitted). The decisions falling in this line are narrow, and they do not support Apple’s position. In Broadcast Music, Inc. v. Columbia Broadcasting System, Inc. (“BMI ”), the defendants were corporations formed by copyright owners to negotiate “blanket licenses” allowing licensees to perform any of the licensed works for a flat fee. 441 U.S. 1, 4-6, 99 S.Ct. 1551, 60 L.Ed.2d 1 (1979). Although this scheme literally amounted to “price fixing” by the defendants’ members, the Court upheld it under the rule of reason because blanket licenses were the only way to eliminate the “prohibitive” cost of each copyright owner’s individually negotiating licenses, monitoring licensees’ use of their work, and enforcing the licenses’ terms. Id. at 20-21, 99 S.Ct. 1551. In National Collegiate Athletic Ass’n v. Board of Regents of the University of Oklahoma (“NCAA"), the Court relied on BMI in applying the rule of reason to (but ultimately striking down) restrictions placed by the National Collegiate Athletic Association (“NCAA”) on the number of football games that its members could agree with television networks to broadcast. 468 U.S. 85, 103, 104 S.Ct. 2948, 82 L.Ed.2d 70 (1984). Many of the NCAA’s restrictions on its members were “essential if the product [amateur athletics] is to be available at all,” so a' “fair evaluation” of the broadcast restrictions’ “competitive ’ character required] consideration of the NCAA’s justifications for the restraints.” Id. at 101, 103, 104 S.Ct. 2948.

The Supreme Court has characterized these decisions as limited to situations where the “restraints on competition are essential if the product is to be available at all.” Am. Needle, Inc. v. Nat’l Football League, 560 U.S. 183, 203, 130 S.Ct. 2201, 176 L.Ed.2d 947 (2010) (quoting NCAA, 468 U.S. at 101, 104 S.Ct. 2948) (internal quotation marks omitted). But even if read broadly, these cases, and others in this category, apply the rule of reason only when the restraint at issue was imposed in connection with some kind of potentially efficient joint venture. XI Areeda & Hovenkamp, supra, ¶ 1908b; see, e.g., Sulfuric Acid, 703 F.3d at 1013 (describing joint venture formed by defendants). Put differently, a participant in a price-fixing agreement may invoke only certain, limited kinds of “enterprise and productivity” to receive the rule of reason’s advantages. As the Supreme Court has explained — including in BMI itself, see 441 U.S. at 8 & n. 11, 99 S.Ct. 1551 — the per se rule would lose all the benefits of being “per se ” if conspirators could seek to justify their conduct on the basis of its purported competitive benefits in every case. Here, there was no joint venture or other similar productive relationship between any of the participants in the conspiracy that Apple joined. Apple also does not claim, nor could it, that creating an ebook retail market is possible only if the participating publishers coordinate with one another on price.

c. Price-Fixing Conspiracy

As noted, the Supreme Court has for nearly 100 years held that horizontal collusion to raise prices is the “archetypal example” of a per se unlawful restraint of trade. Catalano, 446 U.S. at 647, 100 S.Ct. 1925. If successful, these conspiracies concentrate the power to set prices among the conspirators, including the “power to control the market and to fix arbitrary and unreasonable prices.” United States v. Trenton Potteries Co., 273 U.S. 392, 397, 47 S.Ct. 377, 71 L.Ed. 700 (1927). And even if unsuccessful or “not ... aimed at complete elimination of price competition,” the conspiracies pose a “threat to the central nervous system of the economy” by creating a dangerously attractive opportunity for competitors to enhance their power at the expense of others. Socony-Vacuum Oil, 310 U.S. at 224 n. 59, 60 S.Ct. 811 (1940). Thus:

[P]rice-fixing cartels are condemned per se because the conduct is tempting to businessmen but very dangerous to society. The conceivable social benefits are few in principle, small in magnitude, speculative in occurrence, and always premised on the existence of price-fixing power which is likely to be exercised adversely to the public.... And even if power is usually established while any defenses are not, litigation will be complicated, condemnation delayed, would be price-fixers encouraged to hope for escape, and criminal punishment less justified. Deterrence of a generally pernicious practice would be weakened.

Trial Lawyers Ass’n, 493 U.S. at 434 n. 16, 110 S.Ct. 768 (quoting 7 Philip Areeda, Antitrust Law ¶ 1509, at 412-13 (1986)).

Apple and its amici argue that the horizontal agreement among the publishers was not actually a “price-fixing” conspiracy that deserves per se treatment in the first place. But it is well established that per se condemnation is not limited to agreements that literally set or restrict prices. Instead, any conspiracy “formed for the purpose and with the effect of raising, depressing, fixing, pegging, or stabilizing the price of a commodity ... is illegal per se,” and the precise “machinery employed ... is immaterial.” Socony-Vacuum Oil, 310 U.S. at 223, 60 S.Ct. 811; see also Catalano, 446 U.S. at 647-48, 100 S.Ct. 1925 (collecting cases); XII Areeda & Hovenkamp, supra, ¶ 2022a, d. The conspiracy among Apple and the Publisher Defendants comfortably qualifies as a horizontal price-fixing conspiracy.

As we have already explained, the Publisher Defendants’ primary objective in expressly colluding to shift the entire ebook industry to an agency model (with Apple’s help) was to eliminate Amazon’s $9.99 pricing for new releases and bestsellers, which the publishers believed threatened their short-term ability to sell hardcovers at higher prices and the long-term consumer perception of the price of a new book. They had grown accustomed to a business in which they rarely competed with one another on price and could, at least partially, control the price of new releases and bestsellers by releasing hardcover copies before paperbacks. Amazon, and the ebook, upset that model, and reduced prices to consumers by eliminating the need to print, store, and ship physical volumes. Its $9.99 price point for new releases and bestsellers represented a small loss on a small percentage of its sales designed to encourage consumers to adopt the new technology.

Faced with downward pressure on prices but unconvinced that withholding books from Amazon was a viable strategy, the Publisher Defendants — their coordination orchestrated by Apple — combined forces to grab control over price. Collectively, the Publisher Defendants accounted for 48.8% of ebook sales in 2010. J.A. 1571. Once organized, they had sufficient clout to demand control over pricing, in the form of agency agreements, from Amazon and other ebook distributors. This control over pricing facilitated their ultimate goal of raising ebook prices to the price caps. See VIII Areeda & Hoven-kamp, supra, ¶ 1606b (“Even when specific prices are not agreed upon, an express horizontal agreement that each manufacturer will use resale price maintenance or other distribution restraints should be illegal. Its only business function is to facilitate price coordination among manufacturers.”). In other words, the Publisher Defendants took by collusion what they could not win by competition. And Apple used the publishers’ frustration with Amazon’s $9.99 pricing as a bargaining chip in its negotiations and structured its Contracts to coordinate their push to raise prices throughout the industry. A coordinated effort to raise prices across the relevant market was present in every chapter of this story.

This conspiracy to raise prices also had its intended effect. Immediately after the Publisher Defendants switched Amazon to an agency model, they increased the Kindle prices of 85.7% of their new releases and 96.8% of their New York Times bestsellers to within 1% of the Apple price caps. They also increased the prices of their other ebook offerings. Within two weeks of the move to agency, the weighted average price of the Publisher Defendants’ ebooks — which accounted for just under half of all ebook sales in 2010 — had increased by 18.6%, while the prices for Random House and other publishers remained relatively stable.

This sudden increase in prices reduced ebook sales by the Publisher Defendants and proved to be durable. One analysis compared two-week periods before and after the Publisher Defendants took control over pricing and found that they sold 12.9% fewer ebooks after the switch. Another expert for Plaintiffs conducted a regression analysis, which showed that, over a six-month period following the switch, the Publisher Defendants sold 14.5% fewer ebooks than they would have had the price increases not occurred. Nonetheless, ebook prices for the Publisher Defendants over those six months, controlling for other factors, remained 16.8% higher than before the switch. And even Apple’s expert produced a chart showing that the Publisher Defendants’ prices for new releases, bestsellers, and other offerings remained elevated a full two years after they took control over pricing.

Apple points out that, in the two years following the conspiracy, prices across the ebook market as a whole fell slightly and total output increased. However, when the agreement at issue involves price fixing, the Supreme Court has consistently held that courts need not even conduct an extensive analysis of “market power” or a “detailed market analysis” to demonstrate its anticompetitive character. FTC v. Ind. Fed’n of Dentists, 476 U.S. 447, 460, 106 S.Ct. 2009, 90 L.Ed.2d 445 (1986); see also Nat’l Soc’y of Prof'l Eng’rs v. United States, 435 U.S. 679, 692-93, 98 S.Ct. 1355, 55 L.Ed.2d 637 (1978). The district court’s assessment of Apple’s and the Publisher Defendants’ motives, coupled with the unambiguous increase in the prices of their ebooks, was sufficient to confirm that price fixing was the goal, and the result, of the conspiracy. See Cal. Dental Ass’n v. FTC, 526 U.S. 756, 779-80, 119 S.Ct. 1604, 143 L.Ed.2d 935 (1999).

Moreover, Apple’s evidence regarding long-term growth and prices in the ebook industry is not inconsistent with the conclusion that the price-fixing conspiracy succeeded in actually raising prices. The popularization of ebooks fundamentally altered the publishing industry by eliminating many of the marginal costs associated with selling books. When Apple launched the iBookstore just two years after Amazon introduced the Kindle, the ebook market was already experiencing rapid growth and falling prices, and those trends were expected to continue. J.A. 1630, 1647. The district court found that the Publisher Defendants’ collective move to retake control of prices — and to eliminate Amazon’s $9.99 price point for new releases and New York Times bestsellers — tapped the brakes on those trends, causing prices to rise across- their offerings and slowing their sales growth relative to other publishers. No court can presume to know the proper price of an ebook, but the long judicial experience applying the Sherman Act has shown that “[a]ny combination which tampers with price structures ... would be directly interfering with the free play of market forces.” Socony-Vacuum Oil, 310 U.S. at 221, 60 S.Ct. 811; see also Arizona v. Maricopa Cnty. Med. Soc’y, 457 U.S. 332, 346, 102 S.Ct. 2466, 73 L.Ed.2d 48 (1982). By setting new, durable prices through collusion rather than competition, Apple and the Publisher Defendants imposed their view of proper pricing, supplanting the market’s free play. This evidence, viewed in conjunction with the district court’s findings as to and analysis of the conspiracy’s history and purpose, is sufficient to support the conclusion that the agreement to raise ebook prices was a per se unlawful price-fixing conspiracy.

2. Rule of Reason

As explained above, neither Apple nor the dissent has presented any particularly strong reason to think that the conspiracy we have identified should be spared per se condemnation. My concurring colleague would therefore affirm the district court’s decision on that basis alone. I, too, believe that per se condemnation is appropriate in this case and view Apple’s sloganeering references to “innovátion” as a distraction from the straightforward nature of the conspiracy proven at trial. Nonetheless, I am mindful of Apple’s argument that the nascent ebook industry has some new and unusual features and that the per se rule is not fit for “business relationships where the economic impact of certain practices is not immediately obvious.” Leegin, 551 U.S. at 887, 127 S.Ct. 2705 (internal quotation marks omitted); accord Major League Baseball Props., Inc. v. Salvino, Inc., 542 F.3d 290, 316 (2d Cir.2008) (“Per se treatment is not appropriate ... where the economic and competitive effects of the challenged practice are unclear.”); Sulfuric Acid, 703 F.3d at 1011 (“It is a bad idea to subject a novel way of doing business ... to per se treatment under antitrust law.”). I therefore assume, for the sake of argument, that it is appropriate to apply the rule of reason and to analyze the competitive effects of Apple’s horizontal agreement with the Publisher Defendants.

Notably, however, the ample evidence here concerning the purpose and effects of Apple’s agreement with the Publisher Defendants affects the scope of the rule-of-reason analysis called for in this case. Under a prototypically robust rule-of-reason analysis, the plaintiff must demonstrate an “actual adverse effect” on competition in the relevant market before the “burden shifts to the defendants to offer evidence of the pro-competitive effects of their agreement.” Geneva Pharms. Tech. Corp. v. Barr Labs. Inc., 386 F.3d 485, 506-07 (2d Cir.2004) (internal quotation marks omitted). The factfinder then weighs the competing evidence “to determine if the effects of the challenged restraint tend to promote or destroy competition.” Id. at 507. But not every case that requires rule of reason analysis “is a candidate for plenary market examination.” Cal. Dental Ass’n, 526 U.S. at 779, 119 S.Ct. 1604. “What is required, rather, is an enquiry meet for the case, looking to the circumstances, details, and logic of a restraint.” Id. at 781, 119 S.Ct. 1604.

To that end, the Supreme Court has applied an abbreviated version of the rule of reason — otherwise known as “quick look” review — to agreements whose anti-competitive effects are easily ascertained. See id. at 779, 119 S.Ct. 1604. This “quick look” effectively relieves the plaintiff of its burden of providing a robust market analysis, see id., by shifting the inquiry directly to a consideration of the defendant’s pro-competitive justifications. See XI Areeda & Hovenkamp, supra, ¶ 1914d (“[W]hen the restraint appears ‘on its face’ to be one that tends to ... increase price,” an abbreviated rule-of-reason analysis “operates to shift the burden of proof rather than to cut off the inquiry, as is usually true in a per se case.”). Thus, in NCAA, the Supreme Court refrained from applying the per se rule to the challenged television broadcast restrictions, but it did not require an “elaborate industry analysis ... to demonstrate [their] anticompetitive character.” 468 U.S. at 109, 104 S.Ct. 2948 (internal quotation marks omitted). And in Indiana Federation of Dentists, the Court did not apply the per se rule to a group boycott when, in the relevant market, the economic impact was “not immediately obvious,” but it nonetheless dispensed with a full analysis of the agreement’s anticom-petitive character. 476 U.S. at 459, 106 S.Ct. 2009; see also Major League Baseball, 542 F.3d at 317; United States v. Brown Univ., 5 F.3d 658, 669 (3d Cir.1993).

Here, the same evidence supporting our determination that per se condemnation is the correct way to dispose of this appeal also supports at most a “quick look” inquiry under the rule of reason. Contrary to the dissent’s suggestion, this approach does not somehow “taint” the rule-of-reason analysis. The dissent concedes that the conscious object of Apple’s signing its Contracts with the Publisher Defendants was to organize a horizontal conspiracy among them to raise consumer-facing ebook prices. See Dissenting Op. at 346 (noting that “price increases” were “the expected result” of the defendants’ agreement). It is unsurprising in these circumstances that we are easily able to discern the anticompetitive effects of that horizontal conspiracy. A quick-look approach operates only to shift the rule-of-reason analysis directly to Apple’s procompetitive justifications for organizing the conspiracy; I do not give those defenses any shorter shrift than I otherwise would under a more robust analysis. My rejection of Apple’s defenses thus has nothing to do with my application of the quick-look approach and everything to do with how unpersuasive those defenses are.

a. Market Entry

Apple’s initial argument that its agreement with the Publisher Defendants was procompetitive (an argument presented principally in an amicus brief adopted wholeheartedly by the dissent) is that by eliminating Amazon’s $9.99 price point, the agreement enabled Apple and other ebook retailers to enter the market and challenge Amazon’s dominance. But this defense— that higher prices enable more competitors to enter a market — is no justification for a horizontal price-fixing conspiracy. As the Supreme Court has cogently explained:

[I]n any case in which competitors are able to increase the price level or to curtail production by agreement, it could be argued that the agreement has the effect of making the market more attractive to potential new entrants. If that potential justifies horizontal agreements among competitors imposing one kind of voluntary restraint or another on their competitive freedom, it would seem to follow that the more successful an agreement is in raising the price level, the safer it is from antitrust attack. Nothing could be more inconsistent with our cases.

Catalano, 446 U.S. at 649, 100 S.Ct. 1925.

Nor does this argument become stronger when it is asserted, as here, that a horizontal cartel at one level of the market promoted market entry at another, enhancing competition. My dissenting colleague’s view that “deconcentrating,” Dissenting Op. at 349-50, Amazon’s share of retail ebook sales justifies concentrating power over pricing in the hands of the Publisher Defendants reflects a basic misunderstanding of the nature of the competition that antitrust law protects. New entrants to a market are desirable to the extent that consumers would choose to buy them products at the price offered. When a market is concentrated and an incumbent firm is charging supracompetitive prices, a new entrant can benefit consumers by undercutting the incumbent’s prices, thus offering better value for the same goods. Dominant firms who want to deter competition — so that they can keep charging supracompetitive prices — may erect barriers to entry to keep these new competitors out, and the dissent is quite right that these barriers are generally undesirable.

Market dominance may, however, arise “as a consequence of a superior product, business acumen, or historic accident,” and is “not only not unlawful; it is an important element of the free market system.” Trinko, 540 U.S. at 407, 124 S.Ct. 872 (internal quotation marks omitted). The ability to provide goods at particularly low prices is one way that a firm can gain such an edge in the marketplace. Competitors are, of course, entitled to challenge dominant firms by offering, among other things, superior products and lower prices. But success is not guaranteed. A dominant firm charging low prices may have proven itself more efficient than its competitors, such that a potential new entrant’s inability to earn a profit would result not from any artificial “barriers to entry,” but rather from the fact that, in light of the value proposition offered by the dominant firm, consumers would not choose to buy the new entrant’s products at the price it is willing and able to offer. See Einer Elhauge, United States Antitrust Law and Economics 2 (2d ed. 2011) (“If a firm makes a better mousetrap, and the world beats a path to its door, it may drive out all rivals and establish a monopoly; but that is a good result, not a bad one.”).

From this perspective, the dissent’s contention that Apple could not have entered the ebook retail market without the price-fixing conspiracy, because it could not have profited either by charging more than Amazon or by following Amazon’s pricing, is a complete non sequitur. The posited dilemma is the whole point of competition: if Apple could not turn a profit by selling new releases and bestsellers at $9.99, or if it could not make the iBookstore and iPad so attractive that consumers would pay more than $9.99 to buy and read those ebooks on its platform, then there was no place for its platform in the ebook retail market. Neither the district court nor Plaintiffs had an obligation to identify a “viable alternative” for Apple’s profitable entry because Apple had no entitlement to enter the market on its preferred terms. Dissenting Op. at 352-53.

Although low prices that deter new entry may simply reflect the dominant firm’s efficiency, it is true that below-cost pricing can, under certain circumstances, be anti-competitive. The dissent suggests that Amazon’s pricing gave it an unfair advantage, so that even if Apple had priced ebooks at an efficient level (whatever that might have been), it still would not have been able to enter the market on a profitable basis. But Amazon was taking a risk by engaging in loss-leader pricing, losing money on some sales in order to encourage readers to adopt the Kindle. “That below-cost pricing may impose painful losses on its target is of no moment to the antitrust laws if competition is not injured: It is axiomatic that the antitrust laws were passed for ‘the protection of competition, not competitors.’ ” Brooke Grp. Ltd. v. Brown & Williamson Tobacco Corp., 509 U.S. 209, 224, 113 S.Ct. 2578, 125 L.Ed.2d 168 (1998) (quoting Brown Shoe Co. v. United States, 370 U.S. 294, 320, 82 S.Ct. 1502, 8 L.Ed.2d 510 (1962)). Because lower prices improve consumer welfare (all else being equal), below-cost pricing is unlawfully anticompetitive only if there is a “dangerous probability” that the firm engaging in it will later recoup its losses by raising prices to monopoly levels after driving its rivals out of the market. Id. If Apple and the Publisher Defendants thought that Amazon’s conduct was truly anticompetitive under this standard, they could have sued under § 2 of the Sherman Act. (Whether DOJ would have pursued its own enforcement action is of unclear relevance given the availability of a private remedy.) Failing that, Amazon’s pricing was part of the competitive landscape that competing ebook retailers had to accept.

Instead, the dissent invites conduct that is strictly prohibited by the Sherman Act — horizontal collusion to fix prices — to cure a perceived abuse of market power. Whatever its merit in the abstract, that preference for collusion over dominance is wholly foreign to antitrust law. See Trinko, 540 U.S. at 408, 124 S.Ct. 872 (referring to collusion as the “supreme evil of antitrust”). Because of the long-term threat to competition, the Sherman Act does not authorize horizontal price conspiracies as a form of marketplace vigilantism to eliminate perceived “ruinous competition” or other “competitive evils.” Maricopa Cnty. Med. Soc’y, 457 U.S. at 346, 102 S.Ct. 2466 (quoting Socony-Vacuum Oil, 310 U.S. at 221, 60 S.Ct. 811). Indeed, the attempt to justify a conspiracy to raise prices “on the basis of the potential threat that competition poses ... is nothing less than a frontal assault on the basic policy of the Sherman Act.” Nat'l Soc’y of Prof'l Eng’rs, 435 U.S. at 695, 98 S.Ct. 1355. And it is particularly ironic that the “terms” that Apple was able to insist upon by organizing a cartel of Publisher Defendants to move against Amazon — namely, the elimination of retail price competition — accomplished the precise opposite of what new entrants to concentrated markets are ordinarily supposed to provide. In short, Apple and the dissent err first in equating a symptom (a single-retailer market) with a disease (a lack of competition), and then err again by prescribing the disease Itself as the cure.

The dissent’s “frontal assault” on competition law is not only wrong as a legal matter for all the reasons just given; it is also, despite its professed fidelity to the district court’s view of the facts, premised on various mischaracterizations of the record. Put simply, it is far from clear that either Apple itself or other ebook retailers could not have entered the ebook retail market without Apple’s efforts with the Publisher Defendants to eliminate price competition. As the district court noted, “[Apple] did not attempt to argue or show at trial that the price of admission to new markets must be or is participation in illegal price-fixing schemes” and did not “suggest[] that the only way it could have entered the e-book market was to agree with the Publisher Defendants to raise e-book prices.” Apple, 952 F.Supp.2d at 708.

The district court’s statement that Apple feared “losing money if it tried or was forced to match Amazon’s pricing,” Id. at 658 — the peg on which the dissent largely hangs its argument — is hardly a conclusive finding that Apple would have lost money had it entered a market that featured retail price competition. Barnes & Noble, for its part, had chosen to enter and stay in the market in the face of Amazon’s pricing. Google, too, had plans to enter the ebook market before Apple launched the iBookstore. Moreover, the district court never found that Apple could not have entered the market on a wholesale model while charging more than Amazon for new releases and bestsellers. To fill this hole in its theory, the dissent suggests that Apple would have “impairfed] its brand” by charging more than Amazon. Dissenting Op. at 352 (internal quotation marks omitted). But putting aside the fact that Apple’s perception of its brand value is irrelevant — does the dissent really think it is desirable to require more efficient competitors to charge the same as their less efficient rivals solely so the latter will be spared the indignity of not charging the best price? — the district court actually found that Apple believed it would have been “unrealistic[ ]” to charge more than its price caps after switching to an agency model, Apple, 952 F.Supp.2d at 692, a finding that says nothing about what Apple would have been willing to charge under a wholesale model.

The record makes clear the flaws in the dissent’s argument. When Cue was still contemplating a wholesale model, his objective was not for Apple’s pricing to match Amazon’s precisely, but rather for that pricing to be “generally competitive.” J.A. 1758. And had Apple opted to compete on both price and platform but concluded that it could not match Amazon’s $9.99 pricing, some consumers might well have paid somewhat more to read new releases and bestsellers on the iPad, a revolutionary ereader boasting many more features than the Kindle. The iPad was coming to market with or without a price-fixing conspiracy, and some iPad owners who wanted to read ebooks surely would not have wanted to buy a separate Kindle solely to benefit from Amazon’s $9.99 pricing for new releases and bestsellers. (Whether Apple would have viewed its profits under that scenario as large enough to justify entry is not an antitrust concern.)

In actuality, the district court’s fact-finding illustrates that Apple organized the Publisher Defendants’ price-fixing conspiracy not because it was a necessary precondition to market entry, but because it was a convenient bargaining chip. Apple was operating under a looming deadline and recognized that, by aligning its interests with those of the Publisher Defendants and offering them a way to raise prices across the ebook market, it could gain quick entry into the market on extremely favorable terms, including the elimination of retail price competition from Amazon. But the offer to orchestrate a horizontal conspiracy to raise prices is not a legitimate way to sweeten a deal.

The facts also do not support the conclusion that Amazon’s market position would have discouraged other ebook retailers from entering the market absent the price-fixing conspiracy orchestrated by Apple. Amazon popularized ebooks with the launch of the Kindle in late 2007, and enjoyed a strong market position because of its innovation. Cf. Trinko, 540 U.S. at 407, 124 S.Ct. 872 (noting that the opportunity to gain market power “induces risk taking that produces innovation and economic growth”). Barnes & Noble was Amazon’s first major competitor, and when it entered the market — on a wholesale model — with the introduction of the Nook in 2009, it began to erode Amazon’s market share. The iPad itself also promised to introduce more competition with or without Apple’s iBookstore by providing a platform for companies to build ebook marketplaces without investing in tablet development. These new entrants gave publishers more leverage to negotiate for alternative sales models or different pricing. Indeed, publishers were already in separate discussions about an agency model with Barnes & Noble before Apple offered a way to swap the rigors of competition for the comfort of collusion.

To summarize, the district court made no finding that a horizontal conspiracy to eliminate price competition in the ebook retail market was necessary to bring more retailers into the market to challenge Amazon, nor does the record evidence support this conclusion. More importantly, even if there were such evidence, the fact that a competitor’s entry into the market is contingent on a horizontal conspiracy to raise prices only means (absent monopolistic conduct by the market’s dominant firm, which cannot lawfully be challenged by collusion) that the competitor is inefficient, i.e., that its entry will not enhance consumer welfare. For these reasons, I would reject the argument that Apple’s entry into the market represented an important procompetitive benefit of the horizontal price-fixing conspiracy it orchestrated.

b. Other Justifications

Apart from its and other retailers’ entry into the market, Apple points to other purported procompetitive benefits of its agreement with the Publisher Defendants, namely, eventual price decreases in the ebook industry and the various technological innovations embedded in the iPad. The district court correctly concluded that Apple failed to establish a connection between these benefits and the conspiracy among Apple and the Publisher Defendants. Apple, 952 F.Supp.2d at 694; see NCAA, 468 U.S. at 113-15, 104 S.Ct. 2948 (concluding that the need to coordinate to produce intercollegiate athlétics was not related to coordination on television rights); XI Areeda & Hovenkamp, supra, ¶ 1908b.

While it may be true that ebook prices eventually declined industry-wide, new publishers were adopting the digital format and prices were falling even before Apple’s entry into the market. Apple did not introduce any admissible evidence linking the continued influx of new titles into the ebook market to its agreement with the Publisher Defendants. Nor did it provide an explanation for how this price-fixing agreement altered the business and pricing decisions of other publishers in a procompetitive direction. The district court’s refusal to give Apple credit for these trends was therefore proper.

The technological innovations embedded in the iPad are similarly unrelated to Apple’s agreement with the Publisher Defendants. The iPad’s backlit touchscreen, audio and video capabilities, and ability to offer consumers a number of services on a single device revolutionized tablet computing. But, as Apple’s witnesses testified, the company had every intention of bringing the iPad to market with or without the iBookstore. Moreover, Apple was not the only entity that could use the iPad’s new features to enhance the ebook experience — other retailers, or the publishers themselves, could have designed and launched ebook applications on the platform. The district court was correct not to score these hardware innovations as procompetitive benefits of the agreement between Apple and the Publisher Defendants to raise prices.

Accordingly, I agree with the district court’s decision that, under the rule of reason, the horizontal agreement to raise consumer-facing ebook prices that Apple orchestrated unreasonably restrained trade. But given the clear applicability of the per se rule in this context, the analysis here is largely offered in response to the dissent. I also confidently join with my concurring colleague in affirming the district court’s conclusion that Apple committed a per se violation of § 1 of the Sherman Act.

III. The Injunctive Order

Next, Apple and two of the Publisher Defendants — Macmillan and Simon & Schuster — challenge specific portions of the district court’s September 5, 2013 in-junctive order. In particular, Macmillan and Simon & Schuster ask us to vacate the provision which prohibits Apple, for a period of time, from entering agreements with the Publisher Defendants that restrict its ability to set ebook prices. S.P.A. 205. Apple separately seeks vacatur of a provision requiring it to apply the same terms and conditions to ebook applications in its App Store as it does to other applications, and of the district court’s decision to appoint a compliance monitor. We address each of the parties’ arguments in turn.

A. Macmillan and Simon & Schuster

In the September 5, 2013 injunctive order, the district court mandated that “Apple shall not enter into or maintain any agreement with a Publisher Defendant that restricts, limits, or impedes Apple’s ability to set, alter, or reduce the Retail Price of any E-book or to offer price discounts or any other form of promotions.” S.P.A. 205. This prohibition began upon entry of the order and expires at different times for each of the Publisher Defendants. The earliest expiration date lifts the ban for agreements between Apple and Hachette beginning 24 months after entry of the injunctive order. Expiration dates for agreements with each of the other Publisher Defendants are then set in six-month intervals, with Simon & Schuster’s ban expiring 36 months after entry of the final judgment and Macmillan’s ban ending after 48 months.

Macmillan and Simon & Schuster seek vacatur of this prohibition. Both publishers are subject to separate consent decrees, which prohibit them from signing agreements with any ebook retailers which restrict the retailer’s ability to “set, alter, or reduce” ebook prices, “or to offer price discounts.” J.A. 1126; J.A. 1148. The prohibition lasts two years for Simon & Schuster and 23 months for Macmillan. According to both Publisher Defendants, the district court’s injunctive order against Apple, in light of these consent decrees, is unlawful for two reasons. First, they contend that the injunctive order impermissi-bly modifies their consent decrees by extending the time during which they cannot negotiate to restrict the price at which Apple sells ebooks. Second, they argue that DOJ should have been judicially es-topped from seeking a prohibition on agreements limiting Apple’s discounting authority that lasts longer than two years because, in the filings in support of the consent decrees, it argued that two years was a sufficient amount of time to restore competition in the ebook market. Neither objection is persuasive.

We begin with the argument that the injunctive order impermissibly amended the Publisher Defendants’ consent decrees. Federal Rule of Civil Procedure 60(b) establishes the grounds for seeking “relief from a final judgment, order, or proceeding,” Fed.R.Civ.P. 60(b), including modifications of consent decrees. Rufo v. Inmates of Suffolk Cnty. Jail, 502 U.S. 367, 378-79, 112 S.Ct. 748, 116 L.Ed.2d 867 (1992); United States v. Eastman Kodak Co., 63 F.3d 95, 101 (2d Cir.1995). The rule adopts a flexible approach, enumerating specific reasons for modification while also allowing alterations for “any other reason that justifies relief.” Fed.R.Civ.P. 60(b). “[A] party seeking an alteration” under this catch-all provision bears the “burden of establishing that a significant change in circumstances warrants the modification.” United States v. Sec’y of Hous. & Urban Dev., 239 F.3d 211, 217 (2d Cir.2001).

The Publisher Defendants’ argument rests on the premise that the district court’s injunctive order modified their consent decrees and therefore should have complied with Rule 60(b)’s requirements. The premise is incorrect. Macmillan’s and Simon & Schuster’s consent decrees prohibit them from restricting any retailer’s authority to set prices. The injunctive order does not alter the terms of those decrees. Instead, it provides relief against a different party by limiting Apple’s authority to negotiate away its ability to set prices in agreements with any of the Publisher Defendants. The fact that the order also has the effect of preventing the Publisher Defendants from restricting Apple’s pricing authority does not render it “[r]e-lief from a final judgment, order, or proceeding” requiring a motion under Rule 60(b). Fed.R.Civ.P. 60(b). A consent decree is “enforced as [an] order[],” but “construed largely as [a] contract ].” SEC v. Citigroup Global Mkts., Inc., 752 F.3d 285, 297 (2d Cir.2014) (internal quotation marks omitted). Its scope must be discerned within its “four corners, and not by reference to what might satisfy the purposes of one of the parties to it.” United States v. Armour & Co., 402 U.S. 678, 682, 91 S.Ct. 1752, 29 L.Ed.2d 256 (1971); see also Perez v. Danbury Hosp., 347 F.3d 419, 424 (2d Cir.2003). An injunctive order against an entity that is not party to the consent decree and neither changes the terms of nor interprets the decree does not modify the contract and therefore does not require a Rule 60(b) motion. Indeed, as a practical matter, injunctions often alter the options available to other parties. Rule 60(b) does not hold district courts issuing injunctions to a higher standard simply because the injunction may affect rights addressed in a different party’s consent decree.

Macmillan and Simon & Schus-ter’s judicial estoppel argument fares no better. Judicial estoppel is “invoked by a court at its discretion,” and is designed to “protect the integrity of the judicial process by prohibiting parties from deliberately changing positions according to the exigencies of the moment.” New Hampshire v. Maine, 532 U.S. 742, 749-50, 121 S.Ct. 1808, 149 L.Ed.2d 968 (2001) (citation omitted) (internal quotation marks omitted). While the propriety of applying es-toppel depends heavily on the “specific factual context[ ]” before the court, we typically consider whether the party’s argument is “clearly inconsistent with its earlier position,” whether the party “succeeded in persuading a court to accept” that earlier position, and whether the “party seeking to assert an inconsistent position would derive an unfair advantage or impose an unfair detriment on the opposing party if not estopped.” Id. at 750-51, 121 S.Ct. 1808 (internal quotation marks omitted); see also Adelphia Recovery Trust v. Goldman, Sachs & Co., 748 F.3d 110, 116 (2d Cir.2014). “[R]elief is granted only when the ... impact on judicial integrity is certain.” Republic of Ecuador v. Chevron Corp., 638 F.3d 384, 397 (2d Cir.2011) (internal quotation marks omitted).

We conclude that DOJ’s arguments in support of the injunctive order were neither so clearly inconsistent with its earlier arguments nor so unfairly detrimental to the Publisher Defendants as to warrant judicial estoppel. In support of the consent decrees, the Justice Department argued that a two-year ban on restricting retailers’ abilities to set prices was sufficient to “allow movement in the marketplace away from collusive conditions.” J.A. 1055. It then pushed for a longer, five-year restriction on agreements specifically with Apple. While facially inconsistent, we have emphasized the need to “carefully consider the contexts in which apparently contradictory statements are made to determine if there is, in fact, direct and irreconcilable contradiction.” Rodal v. Anesthesia Grp. of Onondaga, P.C., 369 F.3d 113, 119 (2d Cir.2004). And here, context is particularly important. The consent decrees ban certain agreements between the Publisher Defendants and any retailers. The injunctive order, on the other hand, pertained only to the Publisher Defendants’ agreements .with Apple. Given the extensive factfinding at trial about the relationship that Apple developed with the Publisher Defendants and its willingness to, coordinate their conspiracy, DOJ had a basis for distinguishing the length of the restrictions in the consent decrees from those in the injunctive order. This was not a case of a party reversing courses, to the detriment of the legal system, “simply because his interests have changed.” New Hampshire, 532 U.S. at 749, 121 S.Ct. 1808.

Furthermore, the district court did not approve the Justice Department’s request for a five-year ban on all discounting restrictions between Apple and the Publisher Defendants. Instead, the injunctive order adopts an interval-based system, which prevents Apple from agreeing to limit its pricing authority for between 24 and 48 months depending on the Publisher Defendant. The district court imposed this interval system so “there would be no point in time when Apple would be renegotiating with all of the publisher defendants at once[, and] no one point in time when [a] publisher defendant!] could be assured that it was taking the same bargaining position as its peers vis-a-vis Apple.” J.A. 2376. This independent rationale for the injunctive order ensures that DOJ’s argument did not produce “inconsistent results” or compromise the integrity of the judicial process. Simon v. Safelite Glass Corp., 128 F.3d 68, 72 (2d Cir.1997).

B. Apple

Apple, like Macmillan and Simon & Schuster, objects to the portion of the injunctive order preventing it from agreeing to limit its pricing authority. In addition, the company asks us to vacate another provision, which requires it to “apply the same terms and conditions to the sale or distribution of an E-book App through Apple’s App Store as [it] applies to all other apps sold or distributed through [the] App Store.” S.P.A. 207. Apple contends that neither provision is necessary to protect the public. We disagree.

“A Government plaintiff, unlike a private plaintiff, must seek to obtain relief necessary to protect the public from further anticompetitive conduct and to redress anticompetitive harm.”. F. Hoffmann-La Roche Ltd. v. Empagran S.A., 542 U.S. 155, 170, 124 S.Ct. 2359, 159 L.Ed.2d 226 (2004) (emphasis added). Thus, “[wjhen the purpose to restrain trade appears from a clear violation of law, it is not necessary that all untraveled roads to that end be left open and that only the worn one be closed.” Int’l Salt Co. v. United States, 332 U.S. 392, 400, 68 S.Ct. 12, 92 L.Ed. 20 (1947), abrogated on other grounds by Ill. Tool Works Inc. v. Independent Ink, Inc., 547 U.S. 28, 126 S.Ct. 1281, 164 L.Ed.2d 26 (2006). The district court has “large discretion to model [its] judgments to fit the exigencies of the particular case,” id., and “all doubts” about the remedy are to be “resolved in [the Government’s] favor,” United States v. E.I. du Pont de Nemours & Co., 366 U.S. 316, 334, 81 S.Ct. 1243, 6 L.Ed.2d 318 (1961).

The district court was well within its discretion to restrict Apple’s ability to give up its pricing authority and to require that Apple treat ebook applications the same way that it treats other applications. Apple relinquished its authority to set prices as part of its conspiracy with the Publisher Defendants. By delaying Apple’s ability to renegotiate similar restrictions and arranging for the restrictions to expire at different times for each Publisher Defendant, the injunctive order ensured that Apple and the Publisher Defendants would not be able to use that same strategy as part of a new conspiracy. The provision requiring ebook applications in the App Store to receive the same terms and conditions as other applications furthers that goal. The district court expressed concern that Apple and the Publisher Defendants may use ebook applications to circumvent the injunction’s rules about Apple’s pricing authority, or that Apple may impose restrictions on ebook applications to punish publishers who refused to act in concert with their competitors. For instance, the court found evidence that Random House eventually joined the iBook-store on Apple’s desired terms in part because Apple prevented the company from launching an ebook application in the App Store. The district court was therefore correct to decide that these provisions of the injunctive order were “necessary to protect the public from further anticom-petitive conduct.” F. Hoffmanm-La Roche, 542 U.S. at 170, 124 S.Ct. 2359.

CONCLUSION

We have considered the appellants’ remaining arguments and find them to be without merit. Because we conclude that Apple violated § 1 of the Sherman Act by orchestrating a horizontal conspiracy among the Publisher. Defendants to raise ebook prices, and that the injunctive relief ordered by the district court is appropriately designed to guard against future anticompetitive conduct, the judgment of the district court is AFFIRMED.

LOHIER, Circuit Judge,

concurring in part and concurring in the judgment:

I join in the majority opinion except for part II.B.2 relating to the application of the rule of reason. In my view, Apple’s appeal rises or falls based on the application of the per se rule. That rule clearly applies to the central agreement in this case (and the only agreement alleged to be unlawful): the publishers’ horizontal agreement to fix ebook prices. Cf. Leegin Creative Leather Prods., Inc. v. PSKS, Inc., 551 U.S. 877, 893, 127 S.Ct. 2705, 168 L.Ed.2d 628 (2007) (vertical agreements “may ... be useful evidence for a'plaintiff attempting to prove the existence of a horizontal cartel”). I would affirm on that basis alone.

That said, I recognize that the publisher defendants, who used Apple both as powerful leverage against Amazon and to keep each other in collusive check, may appear to be more culpable than Apple. And there is also some surface appeal to Apple’s argument that the ebook market, in light of Amazon’s virtually uncontested dominance, needed more competition. But more corporate bullying is not an appropriate antidote to corporate bullying. It cannot have been lawful for Apple to respond to a competitor’s dominant market power by helping rival corporations (the publishers) fix prices, as the District Court found happened here. However sympathetic Apple’s plight and the publishers’ predicament may have been, I am persuaded that permitting “marketplace vigilantism,” Majority Op. at 298, would do far more harm to competition than good, would be disastrous as a policy matter, and is in any event not sanctioned by the Sherman Act.

DENNIS JACOBS, Circuit Judge,

dissenting:

I respectfully dissent.

This appeal is taken by Apple Inc. from a judgment in the United States District Court for the Southern District of New York (Cote, J.), awarding an antitrust injunction in favor of the United States-, 31 states, the District of Columbia, and the Commonwealth of Puerto Rico. The plaintiffs’ claims are premised on Apple’s conduct as a prospective retailer of e-books. I vote to reverse.

* * *

I have no quarrel with the district court’s conscientious findings of fact; I. affirmatively rely on them, and cite them throughout. The 156 pages of findings track communications and interactions that happened over the 48-day course of events, detail by detail. See United States v. Apple Inc., 952 F.Supp.2d 638, 655-81 (S.D.N.Y.2013) (“Apple I”). All that is needed to decide the case, however, are the schematic facts that show the architecture of the horizontal and vertical arrangements and the dynamics of the competitive forces. They are set out in a nutshell in the following paragraphs, and at somewhat greater length in the Background section of this opinion.

As Apple was preparing the launch of its first iPad tablet in 2009, the company recognized that the device could support e-books, and gave consideration to including an e-book retail platform. However, Amazon had preceded Apple in the market, had established a 90 percent ascendency in sales of e-books, and was effectively excluding new entrants by offering bestsellers at a price ($9.99) that for many books was below the prices Amazon was paying publishers.

Although Apple was positioned to enter the retail market, it was unwilling to do so on terms that would incur a loss on e-book sales (as would happen if it met Amazon’s below-cost price), or that would impair its brand and likely fail (as would happen if it charged more than Amazon). So, as a condition to its entry as a competing buyer for the publishers’ wares, Apple insisted that the publishers agree to a distribution model that would lower that barrier to retail entry.

The new distribution model was implemented by several terms in Apple’s contracts with publishers: agency pricing, tiered price caps, and a most-favored-nation clause. It is conceded that none of those terms is; standing alone, illegal. Apple also encouraged publishers to implement agency pricing in their contracts with other retailers. Although publishers were unhappy about Amazon’s below-cost price for e-books (which eroded the publishers’ hardcover sales) no one publisher alone could counter Amazon. In short order, five of the country’s six largest publishers agreed to Apple’s terms and jointly pressured Amazon to adopt agency pricing. The publishers thereby prevailed in what the district court found to be a horizontal price-fixing conspiracy. The barrier to entry thus removed, Apple entered the retail market as a formidable competitor. In the deconcentrated market, Amazon’s 90 percent market share is now 60 percent.

(I acknowledge that, in adducing facts found by the district court, this opinion unavoidably casts imputations on Amazon. Fairness requires acknowledgment that Amazon has not appeared in this litigation and has not had a full opportunity to dispute the district court’s findings or characterizations. Moreover, the fact of Amazon’s monopoly alone would not support an inference that Amazon’s behavior was in any way unlawful.)

The Department of Justice, 31 states, the District of Columbia, and the Commonwealth of Puerto Rico sued Apple and the five publishers for conspiracy in unreasonable restraint of trade, in violation of § 1 of the Sherman Antitrust Act, 15 U.S.C. § 1. The publishers settled, and Apple proceeded to a bench trial. The district court ruled that Apple’s conduct as a vertical enabler of the publishers’ horizontal price conspiracy constituted a violation per se of § 1, and that (in any event) Apple’s conduct would also violate § 1 under the rule of reason. On this appeal, a majority affirms only on the ground of liability per se. See Op. of Judge Lohier, ante, at 339-40. Since I would reverse, I consider as well the rule of reason. Judge Livingston’s opinion argues (for herself alone) that the judgment could be affirmed on that alternative ground.

The district court committed three decisive errors:

• The district court ruled (and the majority affirms) that a vertical enabler of a horizontal price-fixing conspiracy is in per se violation of the antitrust laws. However, the Supreme Court teaches that a vertical agreement designed to facilitate a horizontal cartel “would need to be held unlawful under the rule of reason. ” Leegin Creative Leather Prods., Inc. v. PSKS, Inc., 551 U.S. 877, 893, 127 S.Ct. 2705, 168 L.Ed.2d 623 (2007) (emphasis added). (POINT I)
• The district court’s alternative ruling under the rule of reason was predetermined by its (erroneous) per se ruling. Thus the district court assessed impacts on competition without recognizing that Apple’s role as a vertical player differentiated it from the publishers. The court should instead have considered Apple as a competitor on the distinct horizontal plane of retailers, where Apple competed with Amazon (and smaller players such as Barnes & Noble). (POINT II)
• Apple’s conduct, assessed under the rule of reason on the horizontal plane of retail competition, was unambiguously and overwhelmingly pro-competitive. Apple was a major potential competitor in a market dominated by a 90 percent monopoly, and was justifiably unwilling to enter a market on terms that would assure a loss on sales or exact a toll on its reputation. In that connection, the district court erroneously deemed the monopolist’s $9.99 price as categorically good for competition because it was lower than cost, and because e-book prices rose after the monopoly was broken. (POINT III)

A further and pervasive error (by the district court and by my colleagues on this appeal) is the implicit assumption that competition should be genteel, lawyer-designed, and fair under sporting rules, and that antitrust law is offended by gloves-off competition.

BACKGROUND

From the 2007 inception of the U.S. retail market for e-books through 2009, Amazon “dominated the e-book retail market, selling nearly 90% of all e-books.” Apple I, 952 F.Supp.2d at 649. It assured its domination by charging its retail customers $9.99 for new releases and bestsellers, below the wholesale price that Amazon was paying to publishers. Id. at 649-50, 708. The popular media reported that Amazon “takes a loss on the sale of the most popular e-books.” Id. at 652. That pricing deterred potential retail competitors from entering the relevant market— “trade e-books in the United States”— because an entrant “would run the risk of losing money if it tried or was forced to match Amazon’s pricing to remain competitive.” Id. at 658.

Amazon’s below-cost pricing was also a threat to publishers, because at a $9.99 price point, e-books cannibalized sales of (more profitable) hardcover editions. Id. at 649. Although the major publishers believed Amazon’s below-cost pricing was “predatory,” id. at 653, each publisher understood that it was powerless to take on Amazon, id. at 650. Publishers feared that Amazon might “compete directly with publishers by negotiating directly with authors and literary agents for rights,” id. at 649, and might “retaliate” against insubordinate publishers “by removing the ‘buy buttons’ on the Amazon site that allow customers to purchase books ... or by eliminating [a publisher’s] products' from its site altogether,” id. at 679. One publisher, Macmillan, suffered such retaliation when Amazon removed the “buy buttons” for print and e-book versions of Macmillan titles. Id.

Amazon’s 90 percent market share constituted a monopoly under antitrust law. See, e.g., Am. Tobacco Co. v. United States, 328 U.S. 781, 797, 66 S.Ct. 1125, 90 L.Ed. 1575 (1946) (characterizing as “a substantial monopoly” a market share of “over 80% of the fíeld”); 3B Areeda & Hovenkamp, Antitrust Law ¶ 801 (3d ed.2008). Amazon’s below-cost pricing was a barrier to entry by Apple in 2009, when it contemplated entry into the e-book retail market via the iPad. Apple I, 952 F.Supp.2d at 654, 658. Apple nevertheless undertook to develop an e-book retail platform in time for the iPad’s launch, scheduled for January 27, 2010. Id. at 654-55. However, “Apple did not have to open an e-bookstore when it launched the iPad”; and it was willing to enter the market only on the condition that its e-book retail business would be profitable, such that Apple could “compete effectively with Amazon” without adopting a loss-leadership and below-cost pricing strategy. Id. at 656-59.

Apple opened extensive negotiations with publishers to determine how if at all it could enter the e-book retail market. Id. at 655-57. Apple met with the leaders of the six largest publishing houses in the United States: Hachette, HarperCollins, Macmillan, Penguin, Random House, and Simon & Schuster. Id. at 647, 655. At the outset, Apple understood that the publishers were unhappy with Amazon’s below-cost pricing of e-books; so Apple knew that the publishers “were willing to coordinate their efforts” to combat the $9.99 price, point. Id. at 656.

After some weeks, Apple and several publishers devised a new model for e-book distribution. Amazon had been paying a wholesale price for each e-book, and reselling (often at a loss) for a retail price of its choosing. Apple’s distribution contracts • would adopt an agency system: publishers would set the retail prices of e-books sold through Apple’s platform and Apple would take a fixed-percent commission on each sale. Id. at 659. However, the agency model would expose Apple (or any retailer) to risk, because publishers might protect hardcover sales by setting retail prices for e-books so high that Apple would appear out of touch with consumers aware of Amazon’s $9.99 price. Id. Apple’s solution was twofold. First, the proposed agency contract included a most favored nation (“MFN”) clause, under which publishers must price their new releases in Apple’s store at or below the lowest price offered by any other e-book retailer. Id. at 662. The district court found that the MFN clause “effectively forced” each publisher that signed Apple’s agency contract to move its other retailers onto the agency model. Id. at 664. That is because, once Apple’s cost was set as a percentage of the retail price, the publishers would suffer if Apple matched Amazon’s $9.99 retail price. Second, the proposed contract included maximum prices for various categories of e-books. Id. at 661-62. The district court found that these tiered price caps had the effect of setting anchor prices across the e-book industry. Id. at 670. Nonetheless, as the district court observed, these terms are not inherently illegal, and “entirely lawful contracts may include an MFN, price caps, or pacing tiers.” Id. at 698.

As Apple negotiated with publishers to sign the agency contract, it told each major publisher that all signing publishers would receive the same terms. Id. at 667. In the end, five of the six largest publishers signed Apple’s agency contract. Id. at 673. (Only Random House, the country’s largest, did not. Id.) As the district court found, the five signatories represented “over 48% of all e-books in the United States” when they signed Apple’s agency contract. Id. at 648. Apple unveiled its e-book retail platform — the “¡Bookstore” — at the first public demonstration of the iPad on January 27, 2010. Id. at 678-79.

After the publishers signed on to Apple’s agency contract, they had to focus on Amazon’s adoption of the agency model because otherwise (as explained above) the MFN clause would allow Apple to match Amazon’s price for bestsellers, and pay the publishers no more than a percentage commission on $9.99. However, “the [publishers feared retaliation from Amazon unless they acted in unison,” id. at 670, and “needed reassurance that they would not be alone,” id. at 674. An Apple executive liaised with each of the five signatory publishers, to encourage a “united front” in their negotiations with Amazon, and to keep the publishers “apprised about who was in and how many were on board.” Id. at 678. The publishers also communicated directly with each other. Id. at 674-77. When Amazon realized that the five publishers were acting in concert, it acceded and signed the agency contracts. Id. at 680-82.

Those are the findings on which Apple was adjudged to have committed an antitrust violation. ' The putative violation amounted to: (a) embedding the agency model (complete with MFN clauses and price caps) in Apple’s own contracts with publishers and (b) encouraging the publishers to coordinate horizontally in their efforts to push the industry-wide adoption of the agency model. Apple and the publishers shared the motive to increase the publishers’ pricing power in order to deprive Amazon of its monopoly. They succeeded: as the district court noted earlier in this litigation, “Amazon’s market share in e-books decreased from 90 to 60 percent in the two years following the introduction of agency pricing.” United States v. Apple, Inc., 889 F.Supp.2d 623, 640 (S.D.N.Y.2012).

The foregoing Background accepts and relies upon the district court’s findings of fact. One cannot say the same of Judge Livingston’s opinion, which supports its legal conclusions and its market analysis with novel findings made now on appeal, i.e., remand by other means. A few examples:

• The notion that Amazon’s below-cost pricing was loss-leadership “designed to encourage consumers to adopt the Kindle,” Op. of Judge Livingston, ante, at 299 (for the Court), is a novelty, supported by neither the fact findings nor the record. At any rate, the effect of e-book pricing outside of the relevant market is irrelevant.
• The majority asserts that Amazon’s below-cost pricing was limited to only “a small loss” on only “a small percentage of its sales.” Id. at 327 (for the Court). These observations are apparently drawn from a submission by Amazon, downplaying the anti-competitive effects of its monopoly-protective pricing. The district court did not rely on these statistics, presumably because they are misleading and self-serving: they ignore that the minority of titles comprising new releases and bestsellers naturally have an outsize impact on the industry. Accordingly, the district court found that the below-cost pricing had consequences on the market, namely that a new entrant “would run the risk of losing money if it tried or was forced to match Amazon’s pricing to remain competitive.” Apple I, 952 F.Supp.2d at 658.
• I can find no record support for the narrative that Amazon’s market share was eroding before Apple’s entry, that the iPad “promised to introduce more competition with or without Apple’s iBookstore,” and that the publishers thereby enjoyed increased negotiating leverage. Op. of Judge Livingston, ante, at 334. Similarly, the assertion that Barnes & Noble disrupted Amazon’s dominance in the e-book market, see id. at 334, is supported neither by the district court’s findings nor by the record.

By contrast, my antitrust analysis relies on the findings made by the district court, and incorporates no others, in order (a) to avoid factual disputes with my colleagues, (b) to defer to the district court’s thorough fact findings in arriving at my legal conclusions, and (c) to respect the limited role of appellate courts.

DISCUSSION

I

The district court’s principal legal error, from which other errors flow, is its conclusion that Apple violated § 1 under the per se rule. Having found that the publishers’ coordinated strategy was a horizontal price-fixing conspiracy, and that Apple had facilitated that conspiracy in its vertical relationship with the publishers, see Apple I, 952 F.Supp.2d at 691, the district court drew the legal conclusion that these facts established a per se violation of the Sherman Act by Apple. This appeal turns on whether purely vertical participation in and facilitation of a horizontal price-fixing conspiracy gives rise to per se liability.

Section 1 of the Sherman Act “outlaw[s] only unreasonable restraints”; so a court weighing an alleged violation “presumptively applies rule of reason analysis, under which antitrust plaintiffs must demonstrate that a particular contract or combination is in fact unreasonable and anticompetitive before it will be found unlawful.” Texaco Inc. v. Dagher, 547 U.S. 1, 5, 126 S.Ct. 1276, 164 L.Ed.2d 1 (2006) (quoting State Oil Co. v. Khan, 522 U.S. 3, 10, 118 S.Ct. 275, 139 L.Ed.2d 199 (1997)). The exception, liability per se, is reserved for those categories of behavior so definitively and universally anti-eom-petitive that a court’s consideration of market forces and reasonableness would be pointless. Id. Traditionally, restraints that are per se unlawful take the form of horizontal agreements “raising, depressing, fixing, pegging, or stabilizing the price of a commodity.” United States v. Socony-Vacuum Oil Co., 310 U.S. 150, 223, 60 S.Ct. 811, 84 L.Ed. 1129 (1940).

Among modern cases, the per se rule takes aim exclusively at horizontal agreements, because “competition among the manufacturers of the same [product] ... is the primary concern of antitrust law.” Continental T.V., Inc. v. GTE Sylvania Inc., 433 U.S. 36, 52 n. 19, 97 S.Ct. 2549, 53 L.Ed.2d 568 (1977). Accordingly, the trend of antitrust law has been a steady constriction of the per se rule in the context of vertical relationships. See, e.g., Leegin Creative Leather Prods., Inc. v. PSKS, Inc., 551 U.S. 877, 901, 127 S.Ct. 2705, 168 L.Ed.2d 623 (2007) (holding that vertical agreements for minimum prices are not per se violations); State Oil Co., 522 U.S. at 7, 118 S.Ct. 275 (holding that vertical agreements for maximum prices are not per se violations); Continental T.V., 433 U.S. at 59, 97 S.Ct. 2549 (holding that vertical non-price restraints are not per se violations); White Motor Co. v. United States, 372 U.S. 253, 261-64, 83 S.Ct. 696, 9 L.Ed.2d 738 (1963) (holding that vertical territorial restraints are not per se violations). The cases have “continued to temper, limit, or overrule once strict prohibitions on vertical restraints.” Leegin, 551 U.S. at 901, 127 S.Ct. 2705.

A vertical relationship that facilitates a horizontal price conspiracy does not amount to a per se violation. In another age, the Supreme Court treated such a hub-and-spokes conspiracy as a per se violation. See Interstate Circuit, Inc. v. Paramount Pictures Distrib. Co., 306 U.S. 208, 226-27, 59 S.Ct. 467, 83 L.Ed. 610 (1939). But the per se rule has been in steady retreat.

The most recent and explicit signal is given in Leegin, which explains that “the Sherman Act’s prohibition on ‘restraints of trade’ evolves to meet the dynamics of present economic conditions,” such that “the boundaries of the doctrine of per se illegality should not be immovable.” 551 U.S. at 899-900, 127 S.Ct. 2705 (alterations omitted). Leegin held that a manufacturer did not commit a per se violation of § 1 when it agreed with several retailers on a minimum price that the retailers could charge — a holding that overruled a century-old principle articulated in Dr. Miles Medical Co. v. John D. Park & Sons Co., 220 U.S. 373, 31 S.Ct. 376, 55 L.Ed. 502 (1911). See Leegin, 551 U.S. at 881, 127 S.Ct. 2705. Leegin reasoned that Dr. Miles had “treated vertical agreements a manufacturer makes with its distributors as analogous to a horizontal combination among competing distributors,” but that, “[i]n later cases, ... the Court rejected the approach of reliance on rules governing horizontal restraints when defining rules applicable to vertical ones.” Leegin, 551 U.S. at 888, 127 S.Ct. 2705. Dr. Miles was held to be inconsistent with “[o]ur recent cases[,] [which] formulate antitrust principles in accordance with the appreciated differences in economic effect between vertical and horizontal agreements, differences the Dr. Miles Court failed to consider.” Id.

Although the express holding of Leegin does not extend beyond the overruling of Dr. Miles, the Court’s analysis reinforces the doctrinal shift that subjects an ever-broader category of vertical agreements to review under the rule of reason. The Court first stated the subsisting scope of per se liability:

A horizontal cartel among competing manufacturers or competing retailers that decreases output or reduces competition in order to increase price is, and ought to be, per se unlawful.

Leegin, 551 U.S. at 893, 127 S.Ct. 2705. The Court then rejected per se liability for hub-and-spokes agreements, in wording that prescribes rule-of-reason review of vertical dealings that facilitate per se unlawful horizontal agreements (the type of agreement that the district court found Apple had undertaken):

To the extent a vertical agreement setting minimum resale prices is entered upon to facilitate either type of cartel [among manufacturers or among retailers], it, too, would need to be held unlawful under the rule of reason.

Id. (emphasis added). After Leegin, we cannot apply the per se rule to a vertical facilitator of a horizontal price-fixing conspiracy; such an actor must be held liable, if at all, “under the rule of reason.” Id.

Leegin is animated by the “appreciated differences in economic effect between vertical and horizontal agreements.” Id. at 888, 127 S.Ct. 2705. Since every challenged restraint is thus classified as either horizontal or vertical, one may draw certain reliable inferences: vertical agreements are not presumptively subject to per se liability; the vertical nature of the agreement is its salient feature; the influence of a vertical arrangement on a horizontal cartel (on another plane of competition) does not render the vertical arrangement per se unlawful.

Our only sister circuit to have considered this wording from Leegin arrived at the conclusion I draw. In Toledo Mack Sales & Service, Inc. v. Mack Trucks, Inc., 530 F.3d 204, 225 (3d Cir.2008), a manufacturer used its contracts with distributors to facilitate and enforce a horizontal conspiracy (among the distributors) that was itself illegal per se. See id. at 210. The Third Circuit held that Leegin’s instruction — that the vertical arrangement “would need to be held unlawful under the rule of reason” — prescribed the rule of reason as the proper analysis for whether the vertical conduct violated § 1. See id. at 225.

Taking the opposite tack, the majority opinion on this appeal insists that a vertical facilitator of a horizontal conspiracy is liable per se, even after Leegin. In support of that argument, the majority cites seven cases that pre-date Leegin, Op. of Judge Livingston, ante, at 322-24 (for the Court). The majority cites only one post-Leegin case that considers this question: namely, the Third Circuit’s analysis of a conspiracy that involved both vertical and horizontal relationships, concluding that the horizontal relationships violated § 1 per se and that pursuant to Leegin the vertical relationships “would have to be analyzed under the traditional rule of reason.” In re Ins. Brokerage Antitrust Litig., 618 F.3d 300, 318 (3d Cir.2010).

The majority’s holding in this case therefore creates a circuit split, and puts us on the wrong side of it.

“[Hjorizontal agreements as a class deserve stricter scrutiny than ... vertical agreements,” because horizontal agreements “pose the most significant dangers of competitive harm.” 11 Areeda & Hovenkamp, supra, ¶ 1902a, at 232. Horizontal price conspiracies are illegal per se because motives of horizontal players are aligned and dominant and create irresistible temptations. See, e.g., Adam Smith, The Wealth of Nations 207 (Collier 1902) (1776) (“People of the same, trade seldom meet together ..., but the conversation ends in a conspiracy against the public, or in some contrivance to raise prices.”).

Collusion among competitors does not describe Apple’s conduct or account for its motive. Apple’s conduct had no element of collusion with a horizontal rival. Its own rival in competition was (and presumably is) Amazon; and that competition takes place on a horizontal plane distinct from the plane of the horizontal conspiracy among the publishers. All Apple’s energy — all it did that has been condemned in this case — was directed to weakening its competitive rival, and pushing it aside to make room for Apple’s entry. On the only horizontal plane that matters to Apple’s e-book business, Apple was in competition and never in collusion. So it does not do to deem Apple’s conduct anti-competitive just because the publishers’ horizontal conspiracy was found to be illegal per se.

“[V]ertieal agreements are a customary and even indispensable part of the market system” and so do not represent the same presumptive threat to competition. 11 Areeda & Hovenkamp, supra, ¶ 1902d, at 240. Even a vertical agreement designed to decrease competition among competitors does not pose the threat to market competition that is posed by a horizontal agreement, for two reasons: (1) market forces (such as countervailing measures by competitors) are categorically more effective in countering anti-competitive vertical agreements, and (2) vertical agreements are so fundamental to the operation of the market that uncertainty about the legality of vertical arrangements would impose vast costs on markets. Id. at 240-41. Such market realities are driving the evolution of antitrust law, which has “rejected the approach of reliance on rules governing horizontal restraints when defining rules applicable to vertical ones.” Leegin, 551 U.S. at 888, 127 S.Ct. 2705.

The present case illustrates why per se treatment is not given to vertical agreements that facilitate horizontal conspiracies. Assuming (as is uncontested on appeal) that the publishers violated § 1 per sé through their coordination, Apple’s promotion of that horizontal conspiracy was limited to vertical dealings. ,

The per se rule is inapplicable here for another independent reason: The per se rule does not apply to arrangements with which the courts are not already well-experienced. Leegin, 551 U.S. at 887, 127 S.Ct. 2705. As the government conceded at oral argument, no court has previously considered a restraint of this kind. Several features make it mi generis: (a) a vertical relationship (b) facilitating a horizontal conspiracy (c) to overcome barriers to entry in a market dominated by a single firm (d) in an industry created by an emergent technology.

As I undertake to show in my analysis under the rule of reason, below, the restrictive market conditions Apple faced and the pro-competitive results of Apple’s conduct make its vertical dealings categorically reasonable. Even if one tests that conclusion under the rule of reason, the analysis is sufficiently complex and yields such substantial pro-competitive results that per se liability is an abdication of the duty to distinguish reasonable restraints from those that are unreasonable."

II

Having concluded first that Apple’s conduct was anti-competitive per se, corollary errors followed when the district court turned to the rule of reason. Once a court finds that a party acted unreasonably per se in a set of transactions, an epiphany is required for the court to conclude that the same party acted reasonably doing the same acts in the samé role at the same time. The influence arising from the district court’s per se accusation of wrongdoing infected all analysis that followed. Once Apple was deemed to have joined a conspiracy that was illegal per se, its goal, motive, and conduct seemingly needed (and got) no additional scrutiny — legal or moral or economic.

Having confirmed Apple’s per se liability by conflating the horizontal plane of competition among publishers with the horizontal plane of competition among retailers, the district court committed the same error in its rule of. reason analysis. Thus the district court (as explained below) overstated the anti-competitive nature of Apple’s vertical dealings and overlooked the pro-competitive effects on retail competition — the horizontal plane on which Apple does e-book business. “The district court did not analyze the state of competition between ebook retailers,” as the majority concedes. Op. of Judge Livingston, ante, at 311 (for the Court) (emphasis omitted). Exactly.

Judge Livingston’s opinion succumbs to the same fallacy by declaring the majority’s own per se analysis so overwhelming that full rule-of-reason scrutiny requires no more than a “quick look.” Quick-look analysis is an appropriate tool only when “an observer with even a rudimentary understanding of economics could conclude that the arrangements in question would have an anticompetitive effect.” Cal. Dental Ass’n v. FTC, 526 U.S. 756, 770, 119 S.Ct. 1604, 143 L.Ed.2d 935 (1999). Quick-look analysis is not a tool for cutting corners. Judge Livingston’s opinion justifies quick-look analysis by referring to e-book price increases that form the majority’s earlier argument for the application of the per se rule, see Op. of Judge Livingston, ante, at 330 — price increases that, at any rate, are the expected result when monopolistic below-cost pricing dissipates.

In form and substance, Judge Livingston’s analysis demonstrates that when one starts with a finding of unreasonableness per se, the rule of reason analysis is tainted. It is called confirmation bias. The characterization of Apple’s conduct as “vigilantism” is telling. Op. of Judge Livingston, ante, at 297-98 (for the Court), 332. Use of that word either assumes the conclusion that the conduct is illegal, or else confuses it with self-help (which used to be a virtue). -

III

On this appeal, we have reached no majority as to the rule of reason. Judge Livingston writes for herself alone that, as an alternative to the per se rule, she would also affirm under the rule of reason; without a second judge supporting this conclusion, it is dicta, because our affirmance is based on the per se theory adopted by two judges. Unlike my colleagues, I must address the rule of reason, because my vote to reverse depends on my conclusion that this alternative theory of liability is every bit as untenable as liability per se.

Analysis under the rule of reason— whether conducted in full or by an untainted quick look — compels the conclusion that Apple did not violate § 1 of the Sherman Act. The issue is decided by comparing (a) the restrictive effect of Apple’s dealings with (b) the pro-competitive result of deconcentrating a market that had been dominated by a monopolist and insulated from competition through below-cost pricing.

Under the rule of reason, the initial burden rests with the plaintiffs “to demonstrate the defendants’ challenged behavior had an actual adverse effect on competition as a whole in the relevant market.” Geneva Pharms. Tech. Corp. v. Barr Labs. Inc., 386 F.3d 485, 506-07 (2d Cir.2004) (internal quotation marks omitted). Upon plaintiffs’ showing of such an effect, “the burden shifts to the defendants to offer evidence of the pro-competitive effects of their agreement,” and then “the burden shifts back to the plaintiffs to prove that any legitimate competitive benefits offered by defendants could have been achieved through less restrictive means.” Id. The reasonableness of the restraint then boils down to whether the dominant effect of the agreement is to promote competition or restrain it. Id.

Analysis begins with an accounting of anti-competitive effects. Apple’s vertical conduct consisted of negotiating the terms of its own contracts. Of course, every Contract is a restraint of trade to some extent, see Nat’l Collegiate Athletic Ass’n v. Bd. of Regents of Univ. of Okla., 468 U.S. 85, 98, 104 S.Ct. 2948, 82 L.Ed.2d 70 (1984); so this fact alone is neither here nor there.

The agency agreement that Apple signed with each publisher was innocuous: as the parties agree, each term — including the agency structure, MFN clause, and price caps — is absolutely legal. The district court so found expressly:

The Plaintiffs do not argue, and this Court has not found, that the agency model for distribution of content, or any one of the clauses included in the Agreements, or any of the identified negotiation tactics is inherently illegal. Indeed,. entirely lawful contracts may include an MFN, price caps, or pricing tiers.

Apple I, 952 F.Supp.2d at 698. The main restraint resulting from Apple’s vertical conduct was the shifting of pricing power from e-book retailers to e-book publishers. And this effect operated as a restraint only in the sense that Amazon faced pressure to adopt an agency model and to charge 'prices set by the five publishers, which of course remained in competition with each other, and with the publishers who account for the remaining 52 percent of the industry.

The district court opinion and the plaintiffs’ briefs fixate on the idea that Apple ended Amazon’s $9.99 price for most new releases and bestsellers, and that consumers would have preferred a lower price. But the consumer’s near-term preference for low prices is not an object of antitrust law. See Brooke Grp. Ltd. v. Brown & Williamson Tobacco Corp., 509 U.S. 209, 237, 113 S.Ct. 2578, 125 L.Ed.2d 168 (1993). The district court charts the short-term price developments, treating the end of below-cost pricing as anti-competitive and observing with disapproval the natural tendency for prices to rise to competitive levels. The rule of reason promotes competition; it can be safely assumed that if competition sharpens, prices will take care of themselves.

As to the pro-competitive effects, the rule of reason must take account primarily of the deconcentrating of the e-book retail market. The benefit of increasing the number of firms in a market derives from the “inverse correlation between concentration and competition.” Eleanor M. Fox, Economic Concentration, Efficiencies and Competition: Social Goals and Political Choices, in Industrial Concentration and the Market System 137, 149 (Eleanor M. Fox & James T. Halverson eds., 1979). As the district court found, Apple was weighing its entry into the retail e-book market, and the agency structure was the only way Apple would enter the market. Nobody has proposed — before or since Apple’s entry — any “less restrictive means” by which Apple could have achieved the same competitive benefits. See Geneva Pharms., 386 F.3d at 507 (plaintiffs’ burden to prove viable and less restrictive alternative). Apple’s challenged conduct broke Amazon’s monopoly, immediately deconcentrat-ed the e-book retail market, added a platform for reading e-books, and removed barriers to entry by others. And removal of a barrier to entry reduces for the long term a market’s vulnerability to monopolization. These effects sound in the basic goals of antitrust law. Even if only quick-look analysis were appropriate in this case, these effects would vindicate Apple’s conduct. (Judge Livingston’s opinion discounts this pro-competitive effect by noting the open question whether “below-cost pricing is unlawfully anti-competitive,” thereby suggesting that Apple’s dismantling of the entry barrier could be pro-competitive only if the barrier was itself a Sherman Act violation. Op. of Judge Livingston, ante, at 331-32. But it is no matter whether the insuperable barrier that Apple tore down had been raised lawfully or not.)

Another pro-competitive effect is the encouragement of innovation, a hallmark and benefit of competition. Apple began retailing e-books in conjunction with its release of the iPád, a device that integrated cutting-edge functions and applications, just one of which was the capacity for users to buy and read e-books. It is impossible to know the likely course of innovation, and pro-competitive effects of innovation cannot be measured; nevertheless, the encouragement of innovation must be afforded considerable weight under the rule of reason. See generally 2B Areeda & Hovenkamp, supra, ¶ 407. Apple’s business is not the technology of the clothespin.

The restraint of Apple’s vertical conduct was no more than a slight offset to the competitive benefits that now pervade the relevant market.

How else could the competitive benefits have been realized in this market? In the course of this litigation, three theories have been offered for how Apple could have entered the e-book market on less restrictive terms. Each theory misapprehends the market or the law, or both. The absence of alternative means bespeaks the reasonableness of the measures Apple took.

Theory 1: Apple could have competed with Amazon on Amazon’s terms, using wholesale contracts and below-cost pricing. This was never an option. The district court found as fact that: a new entrant into the e-book retail market “would run the risk of losing money if it tried or was forced to match Amazon’s pricing to remain competitive,” Apple I, 952 F.Supp.2d at 658; Apple was “not willing” to engage in below-cost pricing, id. at 657; and Apple could have avoided this money-losing price structure simply by forgoing entry to the market, see id. at 659. Even if Apple had been willing to adopt below-cost pricing, the result at best would have been duopoly, and the hardening of the existing barrier to entry. Antitrust law disfavors a durable duopoly nearly as much as monopoly itself. See 6 Areeda & Hovenkamp, supra, ¶ 1429.

Theory 2: Apple could have entered the e-book retail market using the wholesale model and charged higher prices than Amazon’s. The district court foreclosed this theory as well; it found that Apple refused to impair its brand by charging “what it considered unrealistically high prices.” Apple I, 952 F.Supp.2d at 659. Even if Apple had been willing to tarnish its brand by offering bad value for money, the notion that customers would actually have bought e-books from Apple at the higher price defies the law of demand. Higher prices may stimulate sales of certain -wines and perfumes — not e-books.

Nor could Apple justify higher prices for the e-books by competing on the basis of its new hardware, the iPad, because there is inter-operability among platforms. And if Apple had attempted to pursue this hardware-based competition by programming its iPad to run the iBookstore but to reject Amazon’s Kindle application, Apple might have been exposed to an entirely different antitrust peril. See United States v. Microsoft Corp., 253 F.3d 34, 50-80 (D.C.Cir.2001) (en banc); Google Android, No. 40099 (Eur. Comm’n Apr. 15, 2015) (antitrust proceedings brought by European Commissioner for Competition against Google for favoring Google’s own applications on mobile devices that use Google’s operating system).

Theory 3: Apple could have asked the Department of Justice to act against Amazon’s monopoly. Counsel for the United States actually proposed this at oral argument. At the. same time, however, he conceded that the Department of Justice had already “noticed” Amazon’s e-book pricing and had chosen not to challenge it because the government “regarded it as good for consumers.” Any request from Apple would therefore have been futile. True, Apple could not have known that the Antitrust Division would have adopted the position that below-cost pricing is not a concern of antitrust policy: who could have guessed that the government would adopt a policy that is- primitive as a matter of antitrust doctrine and illiterate as a matter of economics? Nevertheless, hindsight reveals that government antitrust enforcement against Amazon was not an option.

More fundamentally, litigation is not a market alternative. This observation has especial force in markets that are undergoing rapid technological advance, where the competitive half-life of a product is considerably more brief than the span of antitrust litigation. A requirement that potential market entrants litigate instead of enter the market on restrictive (but legal and reasonable) terms, would license monopoly for the duration.

Apple took steps to compete with a monopolist and open the market to more entrants, generating only minor competitive restraints in the process. Its conduct was eminently reasonable; no one has suggested a viable alternative. “What could be more perverse than an antitrust doctrine that discouraged new entry into highly concentrated markets?” In re Text Messaging Antitrust Litig., 782 F.3d 867, 874 (7th Cir.2015).

Application of the rule of reason easily absolves Apple of antitrust liability. That is why at oral argument the government analogized this case to a drug conspiracy, in which every player is a criminal — at every level, on every axis, whether big or small, whether new entrant or recidivist. The government found the analogy useful — and necessary — because in an all-criminal industry there is no justification or harbor under a rule of reason.

IV

Because T see no antitrust violation, I need not consider Apple’s separate challenge to the injunction itself. My eol-leagues, for their own good reasons, do not reach that challenge either. Yet the injunction and its shortcomings bear upon the institutional interest of the courts; and Apple’s challenge deserves some response. In my view, the injunction warps the role of a neutral, court-appointed referee into that of an adversary party, with predictable consequences.

The monitor is an arm of the district court, and owes loyalty in that direction only. See Fed.R.Civ.P. 53(a). But the injunction redirects the loyalty of the monitor to Apple’s chief adversary in the litigation, the Department of Justice. Under the injunction, the DOJ recommends the monitor (Injunction ¶ VI(A)), approves the monitor’s fees (id. ¶ VI(I)), and mediates disputes between the monitor and Apple (id. HITVI(E), (H)). Thus the injunction first creates a neutral fact-finding office, and then gives an adversary the ability to decide who holds the office, how much he gets paid (out of the other side’s pocket), and how broadly he may reach and inquire. Reciprocally, the monitor is directed to inform the government if he “discovers or receives evidence that suggests” further antitrust violations, whether or not related to this litigation. (Id. HVI(F).) This is a device that must misfire.

As events have happened (and were seemingly fore-ordained) the monitor has reason to look to the DOJ with gratitude and loyalty. The DOJ recommended Michael Bromwich as monitor, and the district court appointed him. United States v. Apple Inc., 787 F.3d 131, 134-35, 2015 WL 3405534, at *2 (2d Cir. May 28, 2015). Without a meaningful cap on his fee, Bromwich proposed that defendant Apple compensate him at $1,265 per horn* — an eye-popping rate for service as an agent of a court. Id. at 136, 2015 WL 3405534 at *3. (Because Bromwich lacks antitrust expertise, he proposed to add an actual antitrust lawyer to the team at $1,025 an hour. Id.) When Apple challenged that tariff as unreasonable, Bromwich explained that the injunction gave Apple no standing to object: “the fees and expenses to be paid to the monitor and his team are not set by Apple; they are set by the monitor, with approval reserved for the DOJ and the Plaintiff States.” Id. (quoting Bromwich). Bromwich was right, which is telling: the injunction contemplated no role for the judge.

Once the Department of Justice selected him and approved his hourly fee, Bromwich drew up his own mandate. Although the injunction' contemplated that the monitor would check sufficiency of an antitrust policy that Apple was to prepare in 90 days (and Apple’s compliance with it), Bromwich started his inquiry immediately on his appointment; he multiplied interviews, document inspections, and discontents; he demanded to interview Apple executives without the presence of Apple’s chosen counsel; and he took aim at the competitive culture of the corporation generally — a culture that is obviously aggressive, but just as obviously no business of the courts. See id. at 134-36, 140-41, 2015 WL 3405534 at *2-3, *7.

Having thus been selected by an adversary party, paid at a rate approved by the adversary party, and directed to look to the adversary party for the mediation of disputes, Bromwich was (in every respect important to a lawyer) retained and run by the adversary. Apple had an unenviable choice: it could accept scrutiny by a lawyer whose incentives were corrupted by the injunction that created his office, or attack the fee and the widening scope of inquiry, thereby sharpening the confrontations created by the mechanics of the injunction

A magistrate judge has cut Bromwich’s hourly fee. Id. at 139 n. 4, 2015 WL 3405534 at *6 n. 4. And a panel of this Court has construed narrowly the scope of the monitor’s inquiries. Id. at 136-38, 2015 WL 3405534 at *4. But the structural defect of the injunction remains: allowing an arm of the court to serve as agent of an adversary party. It would take strong stuff for a lawyer to transcend the worldly incentives of this injunction: unlimited work at the (now cut) rate of $1,000 an hour, paid by a solvent party that may expect retaliation for protesting, in order to perform a monitorship subject to extension by the court for reasons that will be influenced by input from the monitor himself.

An injunction that thus blurs the lines of the adversary system does no good for the reputation of the- courts. 
      
      . The factual background presented here is drawn from the district court’s factual findings or from undisputed material in the record before the district court. Because this Court reviews the district court's factual findings for "clear error,” we must assess whether "its view of the evidence is plausible in light of the entire record.” Cosme v. Henderson, 287 F.3d 152, 158 (2d Cir.2002). In light of this obligation, the dissent is wrong to suggest that citations to the record are inappropriate or misleading. When a fact comes from the district court's opinion, we cite that opinion; when one comes from the record, we cite the joint appendix ("J.A.”).
     
      
      . Citing one example, the district court referenced a fall 2009 email in which Hachette’s Young informed his colleágue Nourry of Simon & Schuster’s windowing plans, advising "Completely confidentially, Carolyn [Reidy] has told me that they [Simon & Schuster] are delaying the new Stephen King, with his full support, but will not be announcing this until the day after Labor Day.” Apple, 952 F.Supp.2d at 652 (first and second alterations in original) (internal quotation marks omitted). The district court went on to observe that Young, "Understanding the impropriety of this exchange of confidential information with a competitor, ... advised Nourry that 'it would be prudent for you to double delete this from your email files when you return to your office.’ ” Id.
      
     
      
      . Notably, the possibility of an agency arrangement was first mentioned by Hachette and HarperCollins as a way "to fix Amazon pricing.” J.A. 346.
     
      
      . Cue testified at trial that his reference to "solv[ing] the Amazon issue” denoted the proposal to price ebooks in the iBookstore above $9.99, and was not a reference to raising prices across the industry or wresting control over pricing from Amazon. In this and other respects, the district court found Cue’s testimony to be "not credible” — a determination that, on this record, is in no manner erroneous, much less clearly so. Id. at 661 n. 19. As the district court put it, "Apple’s pitch to the Publishers was — from beginning to end — a vision for a new industry-wide price schedule.” Id.
      
     
      
      . As one HarperCollins executive put it, the "upshot” of moving to the agency model and adopting price caps was that “Apple would control price and that price would be standard across the industry." Apple, 952 F.Supp.2d at 670 (internal quotation marks omitted).
     
      
      . Although Cue denied discussing the MFN that night, the district court found this testimony not credible in light of Cue’s deposition testimony and his contemporaneous email to Jobs that Sargent had “legal concerns over the price-matching.” Apple, 952 F.Supp.2d at 672 n. 38 .(internal quotation marks omitted). This determination was not clearly erroneous.
     
      
      . Indeed, on the morning of January 21, Apple’s initial deadline for the publishers to commit to agency, Simon & Schuster’s Reidy emailed Cue to get “an update on your progress in herding us cats.” J.A. 543.
     
      
      . On January 29, Simon & Schuster’s general counsel wrote to Reidy that she "[could not] believe that Jobs made [this] statement,” which she considered “[i]ncredibly stupid.” J.A. 638.
     
      
      . As the district court found, ”[s]even months was no random period — it was the number of months for which, titles were designated New Release titles under the Apple Agreement and restrained by the Apple price caps and MFN.” Apple, 952 F.Supp.2d at 679.
     
      
      .At trial, Cue claimed he had no advance knowledge of Sargent’s plan to go to Seattle, but the district court found this testimony to be incredible. Sargent had emailed Cue about his trip days before the meeting took place. Moreover, on January 28, the day of the meeting, Jobs told his biographer that the Publisher Defendants "went to Amazon and said, 'You’re going to sign an agency contract or we’re not going to give you the books.’ ” Apple, 952 F.Supp.2d at 678 n. 47. The district court’s assessment of Cue's credibility was not clearly erroneous.
     
      
      . As the district court noted, Macmillan had executed its Contract with Apple a week earlier, so that "the only final agency terms still under discussion were with Amazon.” Apple, 952 F.Supp.2d at 681 n. 52.
     
      
      . Eventually, the Publisher Defendants negotiated agency agreements with Barnes & Noble, and later Google. Random House also adopted the agency model, and joined the iBookstore, in early 2011.
     
      
      . The five Publisher Defendants accounted for 48.8% of all retail trade ebook sales in the United States during the first quarter of 2010.
     
      
      . A weighted average price controls for the fact that different ebooks sell in different quantities by dividing the total price that consumers paid for ebooks by the total number of ebooks sold.
     
      
      . In this sense, the ''hub-and-spoke” metaphor is somewhat inaccurate — the plaintiff must also prove the existence of a “rim” to the wheel in the form of an agreement among the horizontal competitors. See Dickson v. Microsoft Corp., 309 F.3d 193, 203-04 (4th Cir.2002).
     
      
      . Apple's argument on appeal that it did not. have sufficient market power to coordinate the Publisher Defendants is beside the point. Market power may afford one means by which a company can coerce others to comply with its wishes, but brute force is not the only way to foster an agreement. Here, both Apple and the Publisher Defendants understood that Apple was in a position to “solve” the publishers' “Amazon problem” by helping them eliminate what they saw as a mortal threat to their businesses — namely, the $9.99 price point.
     
      
      . Apple endeavors to draw the district court’s factfinding into doubt by asserting, erroneously, that the “bedrock of the court's entire decision” hinges on its supposed determination that Apple, knowing that the publishers had been coordinating beforehand, joined a preexisting conspiracy to raise prices at its initial meetings with the Publisher Defendants — a proposition that, it says, is unsupported by the record. The district court, however, did not find that Apple joined an ongoing conspiracy in late 2009, but merely observed that Apple went into its initial meetings with the understanding that the Publisher Defendants disliked, and were trying to fight, Amazon's $9.99 pricing, and so would be receptive to the news that Apple was open to higher prices. See Apple, 952 F.Supp.2d at 703. These findings were amply supported and help explain how the agreement among Apple and the Publisher Defendants thereafter emerged.
     
      
      . Apple takes issue with the district court's conclusion that Apple was aware of, and facilitated, communication between the Publisher Defendants. But the district court found that Cue believed Reidy was a “leader” in the publishing industry and that, on at least two occasions toward the end of the negotiating period, Cue called a recalcitrant executive, who then spoke to Reidy before agreeing to Apple’s terms. See Apple, 952 F.Supp.2d at 659-60; J.A. 2019-20. Reidy herself adverted to Cue’s role in "herding us cats.” J.A. 543. Moreover, the publishing executives frequently denied having any conversations about Apple during this period, despite strong documentary and phone record evidence to the contrary. The district court found that these denials lacked credibility and "strongly supported] a finding of consciousness of guilt.” Apple, 952 F.Supp.2d at 693 n. 59. This view of the facts is not clearly erroneous.
     
      
      
        . Nor does our holding remotely suggest that price caps are always unlawful, which they are not. See State Oil Co. v. Khan, 522 U.S. 3, 118 S.Ct. 275, 139 L.Ed.2d 199 (1997) (holding that vertical maximum price-fixing agreements should be analyzed under the rule of reason). Apple required price caps because it knew that once the Publisher Defendants moved on Amazon to seize control over ebook prices, they would raise them. Apple wanted to ensure that the Publisher Defendants set "realistic prices” that reflected the lower costs of producing ebooks. J.A. 359. The Publisher Defendants and Apple understood that these caps would become the "standard across the industry.” J.A. 573. The price negotiations therefore reflected a common understanding that prices would rise, but a difference of opinion among the co-conspirators over how high they could reasonably go. See United States v. Andreas, 216 F.3d 645, 680 (7th Cir.2000) (“The need to negotiate spme details of the conspiracy with the cartel members ... does not strip a defendant of the organizer role.”).
     
      
      . Since Leegin, the Sixth Circuit has acknowledged that plaintiffs can "establish[] a per se violation [of the Sherman Act] under the hub and spoke theory.” Total Benefits Planning Agency, Inc. v. Anthem Blue Cross & Blue Shield, 552 F.3d 430, 435 n. 3 (6th Cir.2008). To the extent that the Third Circuit decided otherwise in Toledo Mack Sales & Serv., Inc. v. Mack Trucks, Inc., 530 F.3d 204, 225 (3d Cir.2008), its more recent opinions cast doubt on that decision. In In re Insurance Brokerage Antitrust Litigation, for example, the court noted that "hub-and-spoke conspiracies” have "a long history in antitrust jurisprudence,” and cited Total Benefits for the position that "[t]he critical issue for establishing a per se violation with the hub and spoke system is how the spokes are connected to each other.” 618 F.3d 300, 327 (3d Cir.2010) (internal quotation marks omitted). The court also acknowledged that "[t]he anti-competitive danger inherent” in alleged horizontal collusion “is not necessarily mitigated by the fact that” a broker at a different level of the market structure "managed the details of each bid, nor by the likelihood that the horizontal collusion would not have occurred without the broker’s involvement.” Id. at 338. The panel in Insurance Brokerage, however, had no occasion to revisit Toledo Mack because the plaintiffs had failed to establish a horizontal agreement — the "rim” in the hub- and-spokes conspiracy. Id. at 362.
     
      
      . Significantly, the Publisher Defendants are all major producers of new releases and New York Times bestsellers, and they collectively increased prices in those categories. Those prices remained high notwithstanding the influx of new publishers and low-cost ebooks, to the detriment of consumers interested in that segment of the market. See 42nd Parallel N. v. E St. Denim Co., 286 F.3d 401, 405-06 (7th Cir.2002) (“The key inquiry in a market power analysis is whether the defendant has the ability to raise prices without losing its business.” (internal quotation marks omitted)); K.M.B. Warehouse Distribs., Inc. v. Walker 
        
        Mfg. Co., 61 F.3d 123, 128-29 (2d Cir.1995); cf. U.S. Dep’t of Justice & Fed. Trade Comm’n, Horizontal Merger Guidelines § 6.1 (2010) (noting that, "[i]n differentiated product industries, some products can be very close substitutes ... while other products are more distant substitutes”).
     
      
      . While the dissent accuses us of supposing that "competition should be genteel, lawyer-designed, and fair under sporting rules,” Dissenting Op. at 342, it is the dissent’s position that would have ebook consumers subsidize Apple’s entry into the market by paying more for ebooks so that Apple would not have to compete on price.
     
      
      . A prediction that consumers would have paid more to read ebooks on the iPad than on the Kindle because of the iPad’s improved reading experience or other attractive features does not somehow suggest that ebooks are "Veblen goods [or] Giffen goods.” Dissenting Op. at -- n. 7. The dissent also suggests that Apple could not have depended on the iPad’s hardware advantages as part of a strategy to charge more than.Amazon because antitrust law would have required it to open up the iPad to a Kindle app. Id. at 352. But for a unilateral refusal to deal to be unlawful, the defendant must have monopoly power, which Apple plainly did not. See, e.g., United States v. Microsoft Corp., 253 F.3d 34, 51 (D.C.Cir.2001) (en banc) ("While merely possessing monopoly power is not itself an antitrust violation, it is a necessary element of a monopolization charge.” (citation omitted)); Elhauge, supra, at 268 ("A firm that lacks dominant market power ... can unilaterally choose with whom they deal without fear of antitrust liability.”); see also Trinko, 540 U.S. at 408, 124 S.Ct. 872 ("Under certain circumstances, a refusal to cooperate with rivals can constitute anticompetitive conduct and violate § 2. We have been very cautious in recognizing such exceptions, because of the uncertain virtue of forced sharing and the difficulty of identifying and remedying anticompetitive conduct by a single firm.”).
     
      
      . Apple sought to introduce expert testimony from Dr. Michelle Burtis, which it believed would link continued long-term growth and price changes to its launch of the iBookstore. However, the district court excluded this testimony on the grounds that Dr. Burtis "did not offer any scientifically sound analysis of the cause for this purported price decline or seek to control for the factors that may have led to it.” Apple, 952 F.Supp.2d at 694 n. 61. This was no abuse of discretion. See Zerega Ave. Realty, 571 F.3d at 212-13. "[T]he proponent of expert testimony has the burden of establishing by a preponderance of the evidence” that the expert’s opinion is based on sufficient facts, is the product of reliable principles and methods, and applies those principles and methods reliably to the facts at hand. United States v. Williams, 506 F.3d 151, 160 (2d Cir.2007); see Fed.R.Evid. 702. Dr. Burtis merely compared the average ebook prices from the two years before Apple’s entry into the market with the average prices two years after. She did not account for the rapid growth and change in that industry or explain the process she used to determine whether Apple's agency agreements were responsible for lower prices. See Gen. Elec. Co. v. Joiner, 522 U.S. 136, 146, 118 S.Ct. 512, 139 L.Ed.2d 508 (1997); United States v. Dukagjini, 326 F.3d 45, 54 (2d Cir.2003). The district court therefore acted well within its discretion in excluding Dr. Burtis’s testimony.
     
      
      . Macmillan also contends that the injunc-tive order broadens the restrictions imposed by its consent decree because the decree allows the company to set certain limits on price discounts, which it can no longer set for ebooks sold by Apple.
     
      
      . Apple also argues that the district court’s decision to appoint a Procedure 53 and separation-of-powers principles. Apple devoted only two conclusory sentences to these three separate facial challenges to the district court’s authority. We therefore deem the arguments forfeited and do not consider them. Frank v. United States, 78 F.3d 815, 833 (2d Cir.1996) ("Issues not sufficiently argued are in general deemed waived and will not be considered on appeal.”), vacated on other grounds, 521 U.S. 1114, 117 S.Ct. 2501, 138 L.Ed.2d 1007 (1997); Zhang v. Gonzales, 426 F.3d 540, 545 n. 7 (2d Cir.2005). We also note that, following Rule 53’s amendment in 2003, the Advisory Committee stated that ”[r]eliance on a master” appointed under that Rule "is appropriate when a complex decree requires complex policing, particularly when a party has proved resistant or intransigent,” and that both the Supreme Court and this Court have approved such appointments. Fed.R.Civ.P. 53 advisory committee’s note (2003 Amendments) (citing Local 28 of the Sheet Metal Workers’ Int’l Ass'n v. E.E.O.C., 478 U.S. 421, 481-82, 106 S.Ct. 3019, 92 L.Ed.2d 344 (1986)); see also Republic of the Philippines v. N.Y. Land Co., 852 F.2d 33, 36-37 (2d Cir.1988) (collecting cases). In light of this background, it would be inappropriate to excuse Apple’s failure to argue and for this panel to entertain its facial challenges to the district court’s authority on the scant briefing before us.
      Judge Jacobs, who sat on a separate panel of this Court that considered an as-applied challenge to the monitor's conduct, contends that "the injunction warps the role of a neutral, court-appointed referee into that of an adversary party.” Dissenting Op. at 353. Whatever the merits of this argument, it is not properly before us on this appeal. Here, Apple has asserted only (and without argumentation of any sort) that appointing a monitor, in general, violates the Sherman Act, Rule 53, and separation-of-powers principles. The dissent’s position eschews that broad facial challenge and instead focuses on the conduct of the monitor in this particular case, drawing entirely on a record not before this panel, but presented to a separate panel in another appeal. See United States v. Apple Inc., 787 F.3d 131, 2015 WL 3405534 (2d Cir.2015). We do not believe it is proper to resolve this appeal with reference to arguments that Apple has failed to make.
     
      
      . The parties did not dispute this market definition. Apple I, 952 F.Supp.2d at 694 n. 60.
     
      
      . While the district court did not use the label "barrier to entry,” its findings of fact made the point clearly. In finding that a new entrant to e-book retail in 2009 "would run the risk of losing money if it tried or was forced to match Amazon’s pricing to remain competitive,” Apple I, 952 F.Supp.2d at 658, the district court left no doubt that the effect of Amazon’s below-cost pricing regime was to "impede entry and protect existing market power” — the basic operation of a barrier to entry, 2B Areeda & Hovenkamp, supra, ¶ 420c, at 78.
      The majority disputes whether there was any barrier to entry under Amazon's below-cost pricing regime, because at least one competitor attempted to join the market. See Op. of Judge Livingston, ante, at 299 (for the Court), 333. Even if that entrant had any chance of success (nobody contends that it sold a meaningful number of e-books, or made any money, or reduced Amazon’s mammoth market share to less than 90 percent), that fact need not imply ease of entry because "a barrier may protect a market incumbent without completely excluding entry.” 2B Areeda & Hovenkamp, supra, ¶ 420a, at 73.
     
      
      .The cases are cited by the majority in this order: Klor’s, Inc. v. Broadway-Hale Stores, Inc., 359 U.S. 207, 79 S.Ct. 705, 3 L.Ed.2d 741 (1959); United States v. General Motors Corp., 384 U.S. 127, 86 S.Ct. 1321, 16 L.Ed.2d 415 (1966); Toys “R" Us, Inc. v. FTC, 221 F.3d 928 (7th Cir.2000); Denny's Marina, Inc. v. Renfro Productions, Inc., 8 F.3d 1217 (7th Cir.1993); United States v. MMR Corp., 907 F.2d 489 (5th Cir.1990); Business Electronics Corp. v. Sharp Electronics Corp., 485 U.S. 717, 108 S.Ct. 1515, 99 L.Ed.2d 808 (1988); NYNEX Corp. v. Discon, Inc., 525 U.S. 128, 119 S.Ct. 493, 142 L.Ed.2d 510 (1998).
      Just as unhelpfully, the majority cites dicta from a Sixth Circuit case affirming the dismissal of a lawsuit that alleged a hub-and-spokes conspiracy. See Total Benefits Planning Agency, Inc. v. Anthem Blue Cross & Blue Shield, 552 F.3d 430 (6th Cir.2008). The majority cites the case as if its holding supports the continued legitimacy of the hub-and-spokes theory after Leegin, a flawed interpretation given the Sixth Circuit's disposition on the hub-and-spokes claim. Id. at 435 (holding that plaintiffs inadequately alleged a horizontal conspiracy and that, after Leegin, "all vertical price restraints are to be judged under the rule-of-reason standard” (emphasis added)).
     
      
      .The Third Circuit analyzed a network of restraints, including a conspiracy among insurance brokers, a conspiracy among insurers, and agreements that connected the brokers and insurers. The court explained Leegin s impact this way:
      Under the Supreme Court's jurisprudence, virtually all vertical agreements now receive a traditional rule-of-reason analysis. See Leegin, 551 U.S. 877, 127 S.Ct. 2705. In the factual context of this case, a horizontal agreement means ... an agreement among either the brokers or the insurers in the global conspiracy. Agreements between brokers and insurers, on the other hand, are vertical and would have to be analyzed under the traditional rule of reason.
      
        In re Ins. Brokerage Antitrust Litig., 618 F.3d 300, 318-19 (3d Cir.2010) (internal citation and footnote omitted).
     
      
      . Generally speaking, entry barriers permit monopolization and monopoly power allows a firm to erect entry barriers. See, e.g., Port Dock & Stone Corp. v. Oldcastle Ne., Inc., 507 F.3d 117, 125 (2d Cir.2007); United States v. Microsoft Corp., 253 F.3d 34, 82 (D.C.Cir.2001) (en banc); see also Mobil Oil Corp. v. Fed. Power Comm'n, 417 U.S. 283, 302 n. 23, 94 S.Ct. 2328, 41 L.Ed.2d 72 (1974). Each is less likely to arise when the other is absent from a market.
     
      
      . Amazons's below-cost prices also threatened the market for hard-copy books, see Apple I, 952 F.Supp.2d at 649, and thus the royalties of authors, who may well consider that they have some role in this industry.
     
      
      . In economic terms, e-books are subject to the law of demand and therefore have negative price elasticity of demand. See generally N. Gregory Mankiw, Principles of Economics 67 (6th ed.2012). E-books are neither Veblen goods nor Giffen goods, nor do they have perfectly inelastic demand. See id. at 92-93, 453-54, 835; Laurie Simon Bagwell & B. Douglas Bernheim, Veblen Effects in a Theory of Conspicuous Consumption, 86 Am. Econ. Rev. 349 (1996).
     