author: WESLEY, Circuit Judge:

text:
    UNITED STATES of America, State of Maryland, State of Missouri, State of Vermont, State of Utah, State of Arizona, State of New Hampshire, State of Connecticut, State of Iowa, State of Michigan, State of Ohio, State of Texas, State of Illinois, State of Tennessee, State of Montana, State of Nebraska, State of Idaho, State of Rhode Island, Plaintiffs-Appellees, State of Hawaii, Plaintiff, v. AMERICAN EXPRESS COMPANY, American Express Travel Related Services Company, Inc., Defendants-Appellants, Mastercard International Incorporated, Visa Inc., Defendants, CVS Health, Inc., Meijer, Inc., Publix Super Markets, Inc., Raley’s, Supervalu, Inc., Ahold U.S.A., Inc., Albertsons LLC, The Great Atlantic & Pacific Tea Company, Inc., H.E. Butt Grocery Co., Hyvee, Inc., The Kroger Co., Safeway Inc., Walgreen Co., Rite-Aid Corp., Bi-Lo LLC, Home Depot USA, Inc., 7-Eleven, Inc., Academy, Ltd., dba Academy Sports + Outdoors, Alimentation Couche-Tard Inc., Amazon.com, Inc., American Eagle Outfitters, Inc., Ashley Furniture Industries Inc., Barnes & Noble, Inc., Barnes & Noble College Booksellers, LLC, Beall’s, Inc., Best Buy Co., Inc., Boscovs, Inc., Brookshire Grocery Company, Buc-ee’s Ltd, The Buckle, Inc., The Childrens Place Retail Stores, Inc., Coborns Incorporated, Cracker Barrel Old Country Store, Inc., D’Agostino Supermarkets, Inc., Davids Bridal, Inc., DBD, Inc., Davids Bridal Canada Inc., Dillard’s, Inc., Drury Hotels Company, LLC, Express LLC, Fleet and Farm of Green Bay, Fleet Wholesale Supply Co. Inc., Foot Locker, Inc., The Gap, Inc., HMSHost Corporation, IKEA North America Services, LLC, Kwik Trip, Inc., Lowe’s Companies, Inc., Marathon Petroleum Company LP, Martin’s Super Markets, Inc., Michaels Stores, Inc., Mills E-Commerce Enterprises, Inc., Mills Fleet Farm, Inc., Mills Motor, Inc., Mills Auto Enterprises, Inc., Willmar Motors, LLC, Mills Auto Enterprises, Inc., Mills Auto Center, Inc., Brainerd Lively Auto, LLC, Fleet and Farm of Menomonie, Inc., Fleet and Farm of Manitowoc, Inc., Fleet and Farm of Plymouth, Inc., Fleet and Farm Supply Co. of West Bend, Inc., Fleet and Farm of Waupaca, Inc., Fleet Wholesale Supply of Fergus Falls, Inc., Fleet and Farm of Alexandria, Inc., National Association of Convenience Stores, National Grocers Association, National Restaurant Association, Official Payments Corporation, Pacific Sunwear of California, Inc., P.C. Richard & Son, Inc., Panda Restaurant Group, Inc., PeTSmart, Inc., RaceTrac Petroleum, Inc., Recreational Equipment, Inc., Republic Services, Inc., Retail Industry Leaders Association, Sears Holdings Corporation, Speedway LLC, Stein Mart, Inc., Swarovski U.S. Holding Limited, Wal-Mart Stores Inc,, Whole Foods Market Group, Inc., Whole Foods Market California, Inc., Mrs. Gooch’s Natural Food Markets, Inc., Whole Food Company, Whole Foods Market Pacific Northwest, Inc., WFM-WO, Inc., WFM Northern Nevada, Inc., WFM Hawaii, Inc., WFM Southern Nevada, Inc., Whole Foods Market, Rocky Mountain/Southwest, L.P., The William Carter Company, Yum! Brands, Inc., Southwest Airlines Co. Movants.
    Docket No. 15-1672
    August Term, 2015
    United States Court of Appeals, Second Circuit.
    Argued: December 17, 2015
    Decided: September 26, 2016

      Evan R. Chester, Cravath, Swaine & Moore LLP, New York, NY (Peter T. Bar-bur, Kevin J. Orsini, Cravath,‘Swaine & Moore LLP; Donald L. Flexner, Philip C. Korologos, Eric J. Brenner, Boies, Schiller & Flexner LLP, on the brief), for Defendants-Appellants American Express Company and American Express Travel Related Services Company, Inc.
    Nickolai G. Levin, Attorney, U.S. Department of Justice, Antitrust Division, Washington, D.C. (Sonia K. Pffaffenroth, Deputy Assistant Attorney General, Craig W. Conrath, Mark H. Hamer, Andrew J. Ewalt, Kristen C. Limarzi, Robert B. Nicholson, James J. Fredricks, Daniel E. Haar, Attorneys, U.S. Department of Justice, Antitrust Division; Mike DeWine, Ohio Attorney General, Mitchell L. Gentile, Assistant Ohio Attorney General, on the brief), for Plaintiffs-Appellees the United States, et al.
    Before: WINTER, WESLEY, and DRONEY, Circuit Judges.

      . This opinion pertains exclusively, to credit cards. Though Amex argued before the District Court that the relevant market should include debit cards and other alternative payment types as well as a proposed submarket comprising payment-card services provided to travel and entertainment ("T & E”) merchants, Amex has abandoned this argument on appeal.

   WESLEY, Circuit Judge:

Defendants-Appellants American Express Company and American Express Travel Related Services Company, Inc. (collectively, “American Express” or “Amex”) appeal from a decision of the United States District Court for the Eastern District of New York (Garaufís, J.) dated February 19, 2015, finding that Amex unreasonably restrained trade in violation of § 1 of the Sherman Act, 15 U.S.C. § 1, by entering into- agreements containing nondiscriminatory provisions (“NDPs”) barring merchants from (1) offering customers any discounts or nonmon-etary incentives to use credit cards less costly for merchants to accept, (2) expressing preferences for any card, or (3) disclosing information about the costs of different cards to merchants who accept them. See United States v. Am. Express Co., 88 F.Supp.3d 143 (E.D.N.Y. 2015). In addition to holding Amex liable for violating § 1, the District Court permanently enjoined Amex from enforcing its NDPs, See Order Entering Permanent Injunction as to the American Express Defs., United States v. Am. Express Co., No, 10-cv-4496 (NGGXRER), 2015 WL 1966362 (E.D.N.Y. Apr. 30, 2015), ECF No. 683.

For the reasons that follow, we REVERSE and REMAND with instructions to'enter judgment in favor of Amex.

I. BACKGROUND

A, Credit-Card Industry—A General Overview

Since its inception in the 1950s, the credit-card industry has generated untold efficiencies to travel, retail sales, and the purchase of goods and services by millions of United States consumers. Every card transaction necessarily involves a multitude of economic ácts and actors. The end users—the cardholder and a merchant— rely on those acts and actors to provide essential, interdependent services. Take, for example, a cardholder who pulls into a gas station to refuel her car. The cardholder takes out her credit card—for which she pays an annual fee while also receiving frequent flyer miles on her favorite airline for every dollar spent—inserts the card into the credit-card slot on the gas pump, and fills her tank with gas. Her credit card is immediately charged for the transaction, and the station owner receives payment quickly—minus a fee.

The simple transaction of gassing up a car by use of a credit card is enabled by a complex industry involving various commercial structures performing various essential functions. Responsibility for issuing cards and paying retailers for sales using them, extending credit to the cardholders, and collecting amounts due from them can be vested in one firm or in a multiplicity of firms engaged in a division of specified functions and connected in a network by contractual arrangements.

Retailers will not accept credit-card purchases without a guarantee of quick reimbursement. Returning to the customer at the gas pump, it would limit credit-card use if the gas station had to have a reimbursement contract with the particular entity that issued the card to the car owner. The establishment of an umbrella network of individual firms—usually banks—that both issue cards and contract with merchants allows the gas buyer to have a card issued by Bank A, while the gas station has a reimbursement contract with Bank B. Bank A and Bank B in turns have an arrangement in which Bank A reimburses Bank B for the purchase of gas and bills the consumer..In the lingo of the industry, Bank A is the issuer and Bank B is the acquirer. Typically, banks in the network both issue and acquire, and consumers need only find a retailer that accepts a card owned by the consumer and not worry about whether the retailer deals with the card issuer.

From the cardholders’ perspective, many cardholders may find convenience in carrying and using more than one card. Cards come with varying fees and offer benefits with different values to different consumers.. Some cards offer airline miles, others points towards hotel stays or cash back rewards while’ others offer both rewards benefits and enhanced security.

The benefits of a particular card to a consumer are also largely affected by its acceptability among those who sell goods or services to consumers. Widespread acceptance of a card among sellers in turn depends heavily upon widespread acceptance among the consumers targeted by each seller. Retail sellers get the benefits not-only of increased trade because of consumer convenience, but also of not having to choose between limited .cash-only sales and extending credit to consumers. Extensions of credit are administratively costly and commercially risky. However, sellers must cover some of the costs of a credit card’s attracting customers, including efforts to build the prestige attached to certain cards, carrying out all the tasks of extending credit, and bearing responsibility for the ■ risks of extending credit to individual consumers.

In the end, both the credit-card industry and those who sell goods and services target the same group of consumers, albeit in the guise, respectively, of cardholders and purchasers of goods and services.

B. The “Two-Sided Market”

The functions provided by the credit-card industry are highly interdependent and, - at the cardholder/merchant-acceptance level, result in what has been called a “two-sided market.” The cardholder and the merchant both depend upon widespread acceptance of a card. That is, cardholders benefit from holding a card only if that card is accepted by a wide range of merchants, and merchants benefit from accepting a card only if a sufficient number of cardholders use it.

The interdependency that causes price changes on one side can result in demand changes on the other side. If a merchant finds that a network’s fees to accept a particular card exceed the benefit that the merchant gains by accepting that card, then the merchant likely will choose not to accept the card. On the other side, if a cardholder finds that too few merchants accept a particular card, then the cardholder likely will not want to use that card in the first place. Accordingly, in order to succeed, a credit-card network must “find an effective method for balancing the prices on the two sides of the market.” This can be a difficult task since cardholders’ and merchants’ respective interests are often in tension: merchants prefer lower network fees, but cardholders desire better services, benefits, and rewards that are ultimately funded by those fees.

To balance the two sides of its platform, a two-sided market typically charges different prices that reflect the unique demands of the consumers on each side. Within the credit-card industry, cardholders are generally less willing to pay to use a certain card than merchants are to accept that same card, and thus a network may charge its cardholders a lower fee than it charges merchants. Because merchants care about card usage while cardholders care about card acceptance, it may even make sense for a network to charge only merchants for usage while charging cardholders only for access to the card in the first place.

C. Historical Development of the Credit-Card Industry

The modern payment-card industry began in 1949 with the “Diner’s Club,” a joint venture between' two individuals who used a small sum of start-up capital to register fourteen New York restaurants for participation. Diner’s Club initially charged participating restaurants seven percent of the total tab and gave cards away to diners for free. This model was so successful that by its first anniversary, Diner’s Club boasted a membership of over 330 U.S. restaurants, hotels, and nightclubs. At that point, though it had begun charging a membership fee to its 42,000 cardholders, Diner’s Club was earning over three quarters of its revenue from the merchant side of its platform.

Amex, which had long been a major player in the travel and entertainment (“T & E”) business, entered the payment-card industry in the early 1950s already having acquired consumers on both sides of the platform. Thanks to this established position, Amex was initially able to set its cardholder fee higher than the Diner’s Club cardholder fee and thereby cultivate a prestigious, upscale image of “exclu-siv[ity].” Amex then attracted merchants by setting its merchant fee slightly lower than the contemporary Diner’s Club merchant fees.

Despite Amex’s initial success in getting both sides on board its platform, it had no previous experience extending credit and thus struggled for some time to become profitable. In the early 1960s, Amex was able to alleviate this problem by increasing cardholder fees and pressuring cardholders to make timely payments. Amex first turned a profit in 1962 and by 1966 was the volume leader in the payment-card industry.

In the meantime, Visa and MasterCard entered the market, opting to pursue slightly different pricing strategies than any of the payment-card companies that came before. The predecessors of Visa, MasterCard, and other similar networks entered the market in the mid-1960s as banking cooperatives that collaborated on a card brand to pool the merchants that individual member banks of the cooperative had signed up on their respective cards. Following several years of nationwide experimentation with various types of cooperative card systems, the enactment of federal usury laws, and numerous antitrust lawsuits against the new payment-card associations, Visa and MasterCard emerged as the two national associations that “[j]ust about every bank in the card field” became “convinced” they must join.

D. Credit Cards Today

Credit-card transaction volume in the United States is shared primarily by four networks: Visa (45%), American Express (26.4%), MasterCard (23.3%), and Discover (5.3%). Visa and MasterCard operate cooperative or “open-loop” systems that involve as many as five distinct actors, including the network, cardholder, merchant, issuer, and acquirer. On one side of the platform, the issuer acts as an intermediary between the network and the cardholder. On the other side of the platform, the acquirer typically acts as an intermediary between the network and the merchant. The issuer and acquirer are typically banks.

When a cardholder uses his or her card to make a purchase, the transaction information is sent immediately to the acquirer, who discharges the cardholder’s obligations by paying the merchant the funds owed on the transaction. As the price for handling this transaction, the acquirer charges the merchant a merchant-discount fee. The amount of the merchant-discount fee is determined in large part by the interchange fee, which is paid by the acquirer to the issuer as the price for handling its transactions with the cardholder. The optimal interchange fee depends on several factors, including “the split of total costs between issuer and acquirer, the demand elasticities for both types of users, and the intensity of competition in both the issuing and acquiring markets.”

The merchant discount is typically a percentage discount rate multiplied by the purchase price. The bulk of the merchant discount is the interchange fee, the rate of which varies according to (1) the merchant’s industry, and (2) the cardholder’s chosen card product. Because Visa and MasterCard use interchange fees to fund cardholder rewards, such as cash back or airline miles, high rewards cards are generally subject to higher interchange rates and thus cost more for merchants to accept. Visa and MasterCard do not directly set the interchange fee, but “they influence these prices by implementing interchange fees that flow from the acquiring bank (where the merchant’s account is credited) to the card-issuing bank (where the consumer’s account is debited).”

In contrast to Visa and MasterCard, Amex is a proprietary network that operates a “closed-loop” system. Within this closed loop, Amex acts not only as the middleman network but also as both the issuer and acquirer for the vast majority of transactions involving its cards. Therefore, in most cases, Amex maintains direct relationships with both its cardholders and merchants by “provid[ing] issuing services to cardholders, acquiring- and processing services to merchants, and network services to both sides of the platform in order to facilitate the use and acceptance of its payment cards.” Special App. 16. The Amex system is sometimes referred to as a “three-party system because the network (ie., Amex itself) serves as the only intermediary between the cardholder and merchant.

Within its closed-loop system, Amex directly sets the interchange fee so as to maximize profit. Setting the interchange fee also allows Amex to set the accompanying merchant-discount fee and cardholder benefits directly. Amex charges a single discount rate for all Amex card products, meaning that, regardless of whether a cardholder uses Amex’s highest rewards card or its lowest, the merchant still must pay the same fee in order to accept the Amex card.

Unlike Visa and MasterCard, which run “lend-eentric” models deriving more than half their revenues from interest charged to cardholders for unpaid balances on the cardholder’s charges for a given billing .period, Amex runs a “spend-centric” model whose revenues are primarily dependent on merchant-discount fees. This model is critical to Amex’s merchant value proposition, which is that merchants who accept Amex gain access to “marquqe” cardholders who tend to spend more on both, an annual and per-transaction basis than customers using alternative payment methods. Amex’s model is also critical to its cardholder value proposition, which features a robust rewards program and numerous other benefits, including customer service, fraud protection, and purchase and return protection.

Both merchants and cardholders engage in “multihoming,” meaning that both cardholders and merchants may choose to use or accept several different cards, Multi-homing tends to lower prices by functioning essentially as an availability of substitutes. This downward pricing pressure “is not entirely a free lunch” for all consumers, however, because increased multihom-ing on one side of the platform allows the card network to charge more to consumers on the other side, for whom fewer substitutes might be available. A cardholder often has more choices of payment method than a merchant has the ability to accept, and thus the cardholder may simply opt not to own cards that charge membership fees or offer relatively few cardholder benefits. Largely due to ■ multihoming, not all merchants or all cardholders use all payment-card networks. Approximately three million of the total nine million U.S. merchant locations that accept credit cards— that is, roughly one out of every three—do not accept Amex cards.

E. Competition Within The Credit-Card Industry

The credit-card industry continues to be characterized by formidable barriers to entry. These barriers arise because of the nature of the industry and the requirements a network must fulfill before entering it. A network in the credit-card industry must be prepared to issue huge amounts of credit, and thus the network itself must have access to huge amounts of money. The network’s credit must of course be rock solid because merchants will not deal with an issuer without absolute certainty that the issuer will meet its obligations. As the District Court recognized, potential new entrants also face a “chicken and egg problem” wherein “a firm attempting entry into the [payment-card] network market would struggle to convince merchants to join a network without a significant population of cardholders and, in turn, would also struggle to convince cardholders to carry a card associated with a network that is accepted at few merchants.” Am. Express Co., 88 F.Supp.3d at 190.

Throughout the 1960s and 1970s, Visa, MasterCard, and Amex competed fiercely with one another for consumers on both sides of their platforms. Amex sought to keep up with Visa and MasterCard by expanding outward from the T & E market to include “everyday-spend” merchants such as gas stations, supermarkets, and pharmacies. It also sought to increase both its merchant and cardholder value propositions by introducing its membership-rewards program for cardholders and developing new technologies to better leverage the advantages of its closed-loop system for merchants.

In the 1980s, this competition led Visa and MasterCard to adopt exclusionary rules preventing member institutions from issuing card products on the Amex or Discover networks. Visa and MasterCard also ran campaigns highlighting Amex’s smaller merchant-acceptance network, consumers’ resulting perceptions of the utility and value of Amex’s card products, and Amex’s higher- merchant-discount rates. These campaigns, which included the “It’s Everywhere You Want To Be” and “We Prefer Visa” initiatives, were remarkably effective, leading Amex’s overall share of payment-card charge volume to dip from about 25% in 1990 to 20% in 1995.

Amex responded to Visa’s and MasterCard’s exclusionary rules and campaigns by strengthening contractual restraints designed to control how merchants treat Amex cardholders at the point of sale. These restraints, known as non-discriminatory provisions (“NDPs”), had existed in Amex’s card-acceptance agreements in some form or another since the 1950s, but Amex tightened them considerably in the late 1980s and early 1990s to ensure that merchants could not state a preference for any payment-card network other than Amex.

Amex’s standard NDPs are contained in section 3.2 of Amex’s Merchant Regulations. The NDPs provide that a merchant who accepts Amex cards may not engage in the following behaviors:

• indicate or imply that [it] prefer[s], directly or indirectly, any Other Payment Products over [Amex’s] Card,
• try to dissuade Cardmembers from using the Card,
• criticize or mischaracterize the Card or any of [Amex’s] services or programs,
• try to persuade or prompt Cardmem-bers to use any Other Payment Products or any other method of payment (e.g., payment by check),
• impose any restrictions, conditions, disadvantages or fees when the Card is accepted that are not imposed equally on all Other Payment Products, except for electronic funds transfer, or cash and check,
• engage, in activities that harm [Amex’s] business or the American Express Brand (or both), or
• promote any Other Payment- Products (except [the ■ merchant’s] own private label card that' [it] issue[s] for use solely at [the merchant’s] Establishments) more actively than [it] pro-motets] [Amex’s] -Card.

App. 923. Annex actively monitors for noncompliance with its NDPs via oversight of the merchant’s client manager at Amex and the merchant’s charge volume, random on-site visits, and cardholder complaints and reports.

Amex designs its NDPs to curb merchant steering and thus preserve what it refers to as “welcome acceptance,” a term describing cardholders’ enjoyment of “a frictionless and consistent point-of-sale experience when using their American Express cards.” Am. Express Co., 88 F.Supp.3d at 225 (internal quotation marks omitted). Although merchants across various industries regularly try to “steer” their customers toward certain purchasing decisions via strategic product placement, discounts, and other deals, steering within the credit-card industry can be harmful insofar as it interferes with a network’s ability to balance its two-sided net price. Accordingly, Amex’s NDPs (and other networks’ similar restraints) aim to increase cardholders’ certainty as to whether its cards will be accepted and on what terms. Certainty that Amex cards will be accepted makes the network more attractive to cardholders—and, in turn, cardholders’ use of the Amex network makes its cards more attractive for merchants to accept.

F. Procedural History of This Case

On October 4, 2010, the United States Government and seventeen Plaintiff States (collectively, “Plaintiffs”) sued Amex, Visa, and MasterCard for unreasonably restraining trade in violation of § l. Plaintiffs. alleged in their complaint that absent the anti-steering provisions contained in each networks’ respective merchant agreements—including Amex’s NDPs—mer-chants would be able to use steering “at the point of sale to foster competition on price and terms among sellers of network services” by encouraging customers to use less expensive or otherwise preferred cards. App. 136. The complaint alleged further that Amex, Visa, and MasterCard used anti-steering provisions to .suppress interbrand competition by blocking competition from rival networks and. removing incentives for networks to reduce card fees. See App. 128,148-49.

In 2011, Visa and MasterCard entered into consent judgments and voluntarily rescinded their anti-steering provisions. Amex, however, proceeded to a seven-week bench trial in the United States District Court for the Eastern District of New York in the summer of 2014. After trial, the District Court concluded that Plaintiffs had “shown by the preponderance of the evidence that Amex’s NDPs violate the U.S. antitrust laws” and that “[Amex’s] NDPs create an environment in which there is nothing to offset credit-card networks’ incentives—including American Express’s incentive—to charge merchants inflated prices for their services.” Am. Express Co., 88 F.Supp.3d at 150. In reaching this conclusion, the District Court made the following findings:

1) Relevant Market: A payment-card network sits at the center of a two-sided platform that “comprises at least two separate, yet deeply interrelated, markets: a -market for card issuance, in which Amex and Discover compete with thousands of Visa- and MasterCard-issuing banks; and a network services market, in which Visa, Mastercard, Amex, and Discover compete to sell acceptance services.” Id. at 151, Despite the two-sided nature of the platform, however, the relevant market for antitrust analysis in this case is only the market for “network services.” Id. (citing United States v. Visa USA, Inc., 344 F.3d 229 (2d Cir. 2003)).
2) Market Power: “American Express possesses sufficient market power in the network services market to harm competition, as evidenced by its significant market share, the market’s highly concentrated nature and high barriers to entry, and the insistence of Defendants’ cardholder base on using their American Express cards— insistence that prevents most merchants from dropping acceptance of American Express when faced with price increases or similar conduct.” Id. '
3) Anticompetitive Effects: “Plaintiffs have proven that American Express’s NDPs have caused actual anticompet-itive effects on interbrand competition. By preventing merchants from steering additional charge volume to their least expensive network, for example, the NDPs short-circuit the ordinary price-setting mechanism in the network services market by removing the competitive ‘reward’ for networks offering merchants a lower price for acceptance services. The result is an absence of price competition among American Express and its rival-networks.” Id.

In conjunction with its liability determination, the District Court permanently enjoined Amex from enforcing its NDPs for a period of ten years.

Amex timely appealed.

II. DISCUSSION

On appeal from a bench trial, this Court reviews a district court’s findings of fact for clear error and its conclusions of law de novo. Beck Chevrolet Co. v. Gen. Motors LLC, 787 F.3d 663, 672 (2d Cir. 2015). “The application of law to undisputed facts is also subject to de novo review.” Id. (citing Deegan v. City of Ithaca, 444 F.3d 135, 141 (2d Cir. 2006)). A finding of fact is clearly erroneous when, “although there is evidence to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed.” Anderson v. City of Bessemer City, N.C., 470 U.S. 564, 573, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985) (internal quotation marks omitted).

A. Governing Law

Section 1 of the Sherman Act prohibits “[ejvery contract ... in restraint of trade or commerce among the several States.” 15 U.S.C. § 1. “To prove a § 1 violation, a plaintiff must demonstrate: (1) a combination or. some form of concerted action between at least two legally distinct economic entities that (2) unreasonably restrains trade.” Geneva Pharms. Tech. Corp. v. Barr Labs. Inc., 386 F.3d 485, 506 (2d Cir. 2004). Though the Sherman Act could be read literally to strike down virtually every contract that exists, the Supreme Court has recognized repeatedly that “the Sherman Act was intended to prohibit only unreasonable restraints of trade.” 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) (emphasis added).

The Sherman Act aims to “protect[ ] competition as a whole in the .relevant market, not the individual competitors within that market.” Tops Mkts., Inc. v. Quality Mkts., Inc., 142 F.3d 90, 96 (2d Cir. 1998). Disputes between business competitors thus are not the proper subjects of antitrust actions. .¿tee Capital Imaging Assocs., P.C. v. Mohawk Valley Med. Assocs., Inc., 996 F.2d 537, 543 (2d Cir. 1993). This limitation, in addition to supporting judicial economy, is based on the antitrust principle that “[pjrocompetitive or efficiency-enhancing aspects of practices that nominally violate the antitrust laws may cause serious harm to individuals, but this kind of harm is the essence of competition and should play no role in the definition of antitrust damages.” Atl. Richfield Co. v. USA Petroleum Co., 495 U.S. 328, 344, 110 S.Ct. 1884, 109 L.Ed.2d 333 (1990) (internal quotation marks omitted).

To determine whether a practice unreasonably restrains trade in violation of the Sherman Act, courts apply one of two rules designed to provide guidance in forming judgments about the competitive significance of challenged restraints. See Leegin Creative Leather Prods., Inc. v. PSKS, Inc., 551 U.S. 877, 885-87, 127 S.Ct. 2705, 168 L.Ed.2d 623 (2007). Under the per se rule, certain practices, e.g., horizontal price-fixing or market division with no purpose other than to limit competition, are entitled to a conclusive presumption of unreasonableness and thus considered per se illegal. See Bogan v. Hodgkins, 166 F.3d 509, 514 (2d Cir. 1999) (citing Arizona v. Maricopa Cty. Med. Soc’y, 457 U.S. 382, 344, 102 S.Ct. 2466, 73 L.Ed.2d 48 (1982)). All other practices are analyzed under the rule of reason. See id.; see also Leegin, 551 U.S. at 885, 127 S.Ct. 2705 (“The rule of reason is the accepted standard for testing whether a practice restrains trade in violation of § 1.”).

“Agreements within the scope of § 1 may be either ‘horizontal,’ i.e., ‘agreements] between competitors at the same level of the market structure,’ or ‘vertical,’ i.e., ‘combinations of persons at different levels of the market structure, e.g., manufacturers and distributors.’ ” Anderson News, L.L.C. v. Am. Media, Inc., 680 F.3d 162, 182 (2d Cir. 2012) (quoting United States v. Topco Assocs., Inc., 405 U.S. 596, 608, 92 S.Ct. 1126, 31 L.Ed.2d 515 (1972)). “Restraints imposed by agreement between competitors have traditionally been denominated as horizontal restraints, and those imposed by agreement between firms at different levels of distribution as vertical restraints.” Bus. Elecs. Corp. v. Sharp Elecs. Corp., 485 U.S. 717, 730, 108 S.Ct. 1515, 99 L.Ed.2d 808 (1988). Vertical restraints “are generally judged under the rule of reason.” Anderson News, at 183, (internal quotation marks omitted); see also Leegin, 551 U.S. at 907, 127 S.Ct. 2705 (“Vertical price restraints are to be judged according to the rule of reason.”); Cont’l T.V., Inc. v. GTE Sylvania Inc., 433 U.S. 36, 59, 97 S.Ct. 2549, 53 L.Ed.2d 568 (1977) (“When anticompetitive effects are shown to result from particular vertical restrictions they can be adequately policed under the rule of reason, the standard traditionally applied for the majority of anticompetitive practices challenged under [§ ] 1 of the Act.”).

Courts apply the rule of reason using a three-step burden-shifting framework. First, a plaintiff bears the initial burden of demonstrating that a defendant’s challenged behavior “had an actual adverse effect on competition as a whole in the relevant market.” Capital Imaging, 996 F.2d at 543. Examples of actual anti-competitive effects include reduced output, decreased quality, and supracompetitive pricing. See Tops Mkts., 142 F.3d at 96; Capital Imaging, 996 F.2d at 546-47.

If the plaintiff cannot establish anticompetitive effects directly by showing an actual adverse effect on competition as a whole within the relevant market, he or she nevertheless may establish anticom-petitive effects indirectly by showing that the defendant has “sufficient market power to cause an adverse effect on competition.” Tops Mkts., 142 F.3d at 96; see also K.M.B. Warehouse Distribs., Inc. v. Walker Mfg. Co., 61 F.3d 123, 129 (2d Cir. 1995) (“ ‘[W]here the plaintiff is unable to demonstrate [an actual advei'se effect on competition,] ... it must at least establish that defendants possess the requisite market power’ and thus the capacity to inhibit competition market-wide.” (quoting Capital Imaging, 996 F.2d at 546)). Because “[m]arket power is but a ‘surrogate for detrimental effects,’ ” Tops Mkts., 142 F.3d at 96 (quoting FTC v. Ind. Fed’n of Dentists, 476 U.S. 447, 461, 106 S.Ct. 2009, 90 L.Ed.2d 446 (1986)), “[a] plaintiff seeking to use market power as a proxy for adverse effect must show market power, plus some other ground for believing that the challenged behavior could harm competition in the market, such as the inherent anticompetitive nature of the defendant’s behavior or the structure of the interbrand market,” id. at 97.

Once the plaintiff satisfies its initial burden to prove anticompetitive effects, the burden shifts to the defendant to offer evidence of any procompetitive effects of thé restraint at issue. See Geneva Pharms., 386 F.3d at 507. If the defendant can provide such proof, then “the burden shifts back to the plaintifft ] to prove that any legitimate competitive benefits offered by defendant ] could have been achieved through less restrictive means.” Id. (citing Capital Imaging, 996 F.2d at 543).

Courts must be careful to avoid confusing healthy competition with the anticompetitive exercise of market power. “Adverse” effects among different sellers “can actually enhance market-wide competition by fostering vertical efficiency and maintaining the desired quality of a product.” K.M.B., 61 F.3d at 127-28. Further, when output expands at the same time that prices increase, “rising prices are equally consistent with growing product demand” as with anticompetitive behavior. Brooke Grp. Ltd. v. Brown & Williamson Tobacco Corp., 509 U.S. 209, 237, 113 S.Ct. 2578, 125 L.Ed.2d 168 (1993). “Under these conditions, a [fact-finder] may not infer competitive injury from price and output data absent some evidence that tends to prove that output was restricted or prices were above a competitive level.” Id.

“Ultimately, it remains for the factfinder to weigh the harms and benefits of the challenged behavior.” Capital Imaging, 996 F,2d at 543. To prevail on a § 1 claim, a plaintiff must show more than just an adverse effect on competition among different sellers of the same product. See K.M.B., 61 F.3d at 127. “The overarching standard is whether defendants’ actions diminish overall competition, and hence consumer welfare.” Id.' (emphasis added) (internal quotation marks omitted).

B. Analysis

At the outset, all parties and the District Court agree that Amex’s NDPs are a vertical restraint, meaning that they result from agreements setting terms between buyers and sellers. See Appellant’s Br. at 2 (“The NDPs are non-price vertical restraints that prevent merchants—which also function as distributors of Amex’s product—from reaping the benefits of accepting Amex cards while simultaneously damaging Amex’s brand and Amex’s relationship with its cardholders.”); Appellee’s Br. at 50 (“Amex’s NDPs- are vertical restraints because Amex and the merchants are at ‘different levels of distribution,’ and because the imposition of Amex’s NDPs was not alleged to be the product of a ‘horizontal’ agreement with any of its [credit-card] network rivals.”); Am. Express Co., 88 F.Supp.3d at 167 (“As non-price vertical restraints between firms at different levels of production—namely, between the network and its merchant-consumers—American Express’s NDPs are properly analyzed under the rule of reason.”).

We agree that the NDPs are a vertical restraint. The challenged agreements are between Amex and merchants, rather than laterally among competing networks. The Plaintiffs’ claim in this case is premised upon Amex’s use of NDPs as a condition of a merchant or provider accepting Amex cards from consumers purchasing the merchants’ goods dr services; some merchants wish to attract Amex cardholders but then déal only on Visa’s and MasterCard’s terms.

Many verti'cál restraints by a product-creator are imposed on market intermediaries to induce those dealing with the ultimate consumer to promote the particular product. Resale price maintenance, for example, induces retailers to advertise or otherwise promote a product without fear that a firm without promotion expenses will undercut the price of the goods. See Leegin, 551 U.S. at 892-93, 127 S.Ct. 2705. Exclusive dealerships achieve a similar result. It is primarily for this reason that legal and economic scholars often view vertical restraints as having procompetitive effects.

1. Market Definition .

■ The District Court’s definition of the relevant market in this case is fatal to its conclusion that-Amex violated § 1. The District Court concluded that Plaintiffs proved that Amex’s “NDPs have caused and continue to cause actual harm to competition in the network services market” by showing that the NDPs “sever the essential link between the price and sales of network services by denying merchants the opportunity to influence their customers’ payment decisions and thereby shift spending to less expensive cards.” Am. Express Co., 88 F.Supp.3d at 207. In the District Court’s view, “the NDPs short-circuit the ordinary price-setting mechanism in the network services market by removing the competitive ‘reward’ for networks offering merchants a lower price for acceptance services.” Id. at 151 (emphasis added).

This Court defines the relevant market “as all products ‘reasonably interchangeable by consumers for the same purposes.’ ” Geneva Pharms., 386 F.3d at 496 (quoting United States v. E. I. du Pont de Nemours & Co., 351 U.S. 377, 395, 76 S.Ct. 994, 100 L.Ed. 1264 (1956)). “Market definition is a deeply fact-intensive inquiry,” Todd v. Exxon Corp., 275 F.3d 191, 199 (2d Cir. 2001) (Sotomayor, /.), because its purpose is “to identify the market participants and competitive pressures that restrain an individual firm’s ability to raise prices' or restrict output,”’ Geneva Pharms., 386 F.3d at 496. The proper market definition thus can be determined “only after a factual inquiry into the ‘commercial realities’ faced by consumers.” Eastman Kodak Co. v. Image Tech. Servs., Inc., 504 U.S. 451, 482, 112 S.Ct. 2072, 119 L.Ed.2d 265 (1992) (quoting United States v. Grinnell Corp., 384 U.S. 563, 572, 86 S.Ct. 1698, 16 L.Ed.2d 778 (1966). “The basic principle is that the relevant market definition must encompass the realities of competition.” Balaklaw v. Lovell, 14 F.3d 793, 799 (2d Cir. 1994) (internal quotation marks omitted)).

The District Court erred in excluding the market for cardholders from its relevant market definition. The District Court expressly “decline[d] to ... collaps[e] the issuance and network services markets into a single platform-wide market for transactions” on the ground that it “takes the concept of two-sidedness too far.” Am. Express Co., 88 F.Supp.3d at 172, 173. Instead, the District Court focused on Amex’s NDPs “[a]s non-price vertical restraints between firms at different levels of production—namely, between the network and its merchant-consumers.” Id: at 167. It then defined the relevant market as one for “network services,” meaning the market for “core enabling functions provided by networks, which allow merchants to capture, authorize, and settle transactions for customers who elect to pay with their credit or charge card.” Id. at 171 (emphasis added).

The District Court erred in patterning its relevant market inquiry largely after that undertaken by this Court in Visa. Visa called for analysis of the relevant product market to determine whether Visa’s and MasterCard’s exclusionary rules were agreements restraining trade in violation of the Sherman Act. See Visa, 344 F.3d at 237-40; United States v. Visa U.S.A., Inc., 163 F.Supp.2d 322, 335-40 (S.D.N.Y. 2001). The exclusionary rules at issue prohibited Visa’s and MasterCard’s thousands of member banks from issuing cards on the Amex or Discover networks, thereby resulting in “the total exclusion of American Express and Discover from a segment of the market for network services.” Visa, 344 F.3d at 240.

In Visa, this Court defined the relevant market as the market for payment-card “network services,” in which the sellers are the four major payment-card networks and the buyers are both card issuers and merchants:

[T]he four payment card networks compete with one another in a market for network services. General purpose card networks .., provide the infrastructure and mechanisms through which general purpose card transactions are conducted, including the authorization, settlement, and clearance of transactions. Whereas in the market for general purpose cards, the issuers are the sellers, and cardholders are the buyers, in the market for general purpose card network services, the four networks themselves are the sellers, and the issuers of cards and merchants are the buyers.

Id. at 239 (emphasis added) (citations and internal quotation marks omitted). This Court then found that the exclusionary rules were anticompetitive because they “decreas[ed] network services output and stunt[ed] price competition” by precluding Amex’s and Discovers participation in the relevant market. Id. at 240-41; see also id. at 243 (“In the market for network services, where the four networks are sellers and issuing banks and merchants are buyers, the exclusionary rules enforced by Visa U.S.A. and MasterCard have absolutely prevented Amex and Discover from selling their products at all.” (bolded emphasis added)).

In Visa, the horizontal restraint in the market for network services had an anti-competitive effect not only in that market but also in the market for cardholders’ obtaining the general purpose cards. Visa’s discussion of the market for network services as separate from the market for general purpose cards was, therefore, consistent with antitrust principles. Separating the two markets here—analyzing the effect of Amex’s vertical restraints on the market for network services while ignoring their effect on the market for general purpose cards—ignores the two markets’ interdependence. Separating the two markets .allows legitimate competitive activities in the market for general , purposes to be penalized no matter how output-expanding such activities may be. The relevant market in this case is not the same as the relevant market in Visa because the two-sided platform at issue here is a single firm operating: within the broader “network services” industry at issue in Visa. The relationship between the two consumer sides of a platform that provide network services is not the same as the relationship between the various platforms competing with one another within the network-services industry. Unlike the contested conduct in this case, the contested conduct in Visa occurred not among' different sides of the same network platform, but rather between the platforms themselves.

Moreover, the vertical restraints at issue in this case are markedly different from the horizontal restraints that were at issue in Visa. In contrast to Amex’s NDPs, the Visa panel understood the Visa and MasterCard exclusionary rules at issue not as vertical restraints, but rather as a “horizontal restraint adopted by 20,000 competitors.” Visa, 344 F.3d at 242. Amex’s NDPs, unlike Visa’s and MasterCard’s exclusion-axy rules, are agreements between Amex and its merchants, not agreements between competing payment-card networks.

The Visa panel thus did not conduct a rule-of-reason analysis to determine whether vertical restraints were inhibiting competition on one particular side of a two-sided platform. Instead, the Visa panel conducted a rule-of-reason analysis to determine whether horizontal restraints were inhibiting competition on one particular level of competition contained within a two-sided platform:

Competition in the payment card industry takes place at the “network” level, as well as at the “issuing” and “acquiring” levels. At the network level, the four ' brands compete with■ one another to establish brand loyalty in favor of the Visa, MasterCard, Amex, or Discover card. At the issuing level, approximately twenty thousand banks that issue Visa and MasterCard cards to customers compete with one another and with Amex and Discover. Unlike the network services market, which has only four major participants, approximately 20,000 entities compete for customers in the issuing market, and no single participant is dominant.

Visa, 344 F.3d at 237 (emphases added). Consequently, Visa does not provide the template for resolution of this case.

To define the relevant market, this Court often applies a “hypothetical monopolist test” (“HMT”) asking whether a hypothetical monopolist acting within the proposed market “would be ‘substantially constrainfed]’ from increasing prices by the ability of customers to switch' to other producers.” Todd, 275 F.3d at 202 (alteration in original) (quoting AD/SAT, Div. of Skylight, Inc. v. Associated Press, 181 F.3d 216, 228 (2d Cir. 1999)). Under the HMT, “‘[a] market is any grouping of sales whose sellers, if unified by a hypothetical cartel or merger, could profitably raise prices significantly above the competitive level. If the sales of other producers substantially constrain the price-increasing ability of the hypothetical cartel, these others are part of the market.’ ” AD/SAT, 181 F.3d at 228 (emphasis omitted) (quoting 2A Phillip E. Areeda et al., Antitrust Law ¶ 533, at 169).

The Court implements the HMT by imagining that a hypothetical monopolist has imposed a small but significant non-transitory increase in price (“SSNIP”) within the proposed market. If the hypothetical monopolist can impose this SSNIP without losing so many sales to other products as to render the SSNIP unprofitable, then the proposed market is the relevant market. By contrast, if consumers are able and inclined to switch away from the products in the proposed market in sufficiently high numbers to render the SSNIP unprofitable, then the proposed market definition is likely too narrow and should be expanded.

The District Court'also erred in its application of the HMT. As an initial matter, the District Court did not apply the HMT to define the relevant market but instead employed it only to exclude debit cards from the market it had already defined in a conclusory manner, ie., the market for network services. Furthermore, even 'had the District Court not defined the relevant market prematurely, its HMT analysis failed to quantify the change in cardholder behavior resulting from decreased merchant demand to use the hypothetical monopolist’s network for credit-card transactions.

The District Court found that “there is limited direct quantitative evidence in the record from which the court might make a definitive calculation of either merchants’ or cardholders’ sensitivity to pricing changes in the network services market.” Id. at 179. Instead of balancing hypothetical effects on merchant behavior against hypothetical effects on cardholder behavior, however, the District Court considered cardholder behavior only with respect to a merchant’s decision to join a payment-card network in the first place. Nee id. (finding it “highly unlikely that" merchant' attrition resulting from [a hypothetical monopolist’s imposition of a SSNIP in the proposed product market] would be sufficient to render it unprofitable, given the high rates of credit-insistent spend merchants would place at risk by switching away from credit card acceptance”).

A proper application of the HMT in this case would not have merely assumed that a decrease in quantity of network services demanded by merchants facing a SSNIP would be too small to render the aceompa-nying price increase unprofitable. The District Court instead should have considered the extent to which even a low level of merchant attrition might cause some cardholders to switch to alternative forms of payment. Application of the HMT to a two-sided market must consider the feedback effects inherent on the platform by accounting for the reduction in cardholders’ demand for cards (or card transactions) that would accompany any degree of merchant attrition.

Although the District Court claimed that it “accounted] for the two-sided features of the credit-card industry in its market definition inquiry,” it expressly declined “to define the relevant product market to encompass the entire multi-sided platform.” Am. Express Co., 88 F.Supp.3d at 174. This was error because the price charged to merchants necessarily affects cardholder demand, which in turn has a feedback effect on merchant demand (and thus influences the price charged to merchants). In order to retain cardholders, a network may need to increase cardholder benefits—or, viewed another way, “decrease prices” to cardholders. This may call for an increase in merchant fees to fund the increased cardholder rewards. ■ If an increase in merchant fees leads to merchant attrition high enough to render the increased merchant fees unprofitable for the network, then the network will not raise merchant fees and consequently will not increase cardholder rewards. This, in turn, may cause the network to lose cardholders.

2. Market Power

“Market power is the power to force a purchaser to do something that he would not do in a competitive market.” Eastman Kodak, 504 U.S. at 464, 112 S.Ct. 2072 (internal quotation marks omitted); see also E. I. du Pont de Nemours & Co., 351 U.S. at 391, 76 S.Ct, 994 (“[Market] power is the power to control prices or exclude competition.”). It may be shown directly “by evidence of specific conduct indicating the defendant’s power to control prices or exclude competition.” KM.B., 61 F.3d at 129 (internal quotation marks omitted). If no direct evidence exists, market power may be inferred based on market share. See Todd, 275 F.3d at 199 (“One traditional way to demonstrate market power is by defining the relevant product market and showing defendants’ percentage share’ of that market.”).

The District Court found that, regardless of whether Plaintiffs had proven anti-competitive effects directly, they had successfully discharged their burden under the rule of reason indirectly by showing that Amex possesses sufficient market power to affect competition adversely in the relevant market. See Am. Express Co., 88 F.Supp.3d at 187. Based on the record, the District Court found that Amex, which “accounted for 26.4% of [credit] card purchase volume in the United States” as of 2013, “is the second largest [credit] card network when measured by charge volume.” Id. at 188. It found further that “charge volume is the most direct measure of output in this particular market, and is also the primary determinant of the remuneration networks receive from merchants in exchange for network services.” Id. at 189.

Ultimately, the District Court concluded that Amex “enjoy[s] significant market share in a highly concentrated market with high barriers to entry, and [is] able to exercise uncommon leverage over [its] merchant-consumers due to the amplifying effect of cardholder insistence and derived demand.” Id. at 188. To reach this conclusion, the District Court engaged in an extensive analysis of Amex’s pricing practices, including its Value Recapture (‘VR”) initiative conducted between 2005 and 2010, its ability to price discriminate between various industry segments, and its policy of charging merchants a premium over its competitors’ rates. Id. at 195-98. The District Court’s finding of market power rested primarily on its analysis of the VR initiatives and its assessment of cardholder insistence. See id. at 188 (highlighting “the amplifying effect of cardholder insistence and derived demand” and the price increases imposed during the VR initiatives while finding that “Plaintiffs’ other pricing arguments are less persuasive, and are ultimately unnecessary to the court’s finding that American Express possesses market power”). ■

Amex’s VR initiatives comprised “a series of targeted price increases in certain industry segments between 2005 and 2010, with the stated purpose of better aligning its prices with the value it perceived as being delivered to both cardholders and merchants.” Id. at 195-96.- The VR initiatives collectively “comprised at least twenty separate price increases accomplished through a combination of increased discount rates, new or increased per transaction fees, and reduced side payments to merchants.” Id. at 196. These increases “were imposed on an industry-specific basis, with several merchant segments—typically those with relatively high rates of cardholder insistence—targeted for multiple rounds of price hikes.” Id.

Analyzing the evidence before it, the District Court found that “American Express’s ability to impose significant price increases during its Value Recapture initiatives between 2005 and 2010 without any meaningful merchant attrition is compelling evidence of [Amex’s] power in the network service market.” Id. at 198. Emphasizing that it was “unaware of any large merchant in the United States that elected to cancel its acceptance of Amex cards in response to the Value Recapture price increases,” id. at 197, the District Court concluded that the “ability to profitably impose such price increases across a broad swath of its merchant base with little or no meaningful buyer attrition is compelling proof of [market] power,” id. at 196.

The District Court erred in its evaluation of the Value Recapture program by failing to recognize that increased demand on the cardholder side of the platform expands value on the merchant side. In other words, the District Court did not acknowledge that increases in merchant fees are a concomitant of a successful investment in creating output and value. In order to remain competitive on the cardholder side of the platform, a payment-card network might need to increase cardholder rewards—or, in other words, cut prices to cardholders. This, in turn, might diminish the network’s profitability from the hypothetical price increase. If the network chose in that situation not to increase cardholder rewards, then merchant attrition likely would continue increasing as a result of the reduction in cardholders. Over time, the reduction in transactions could make the hypothetical price increase unprofitable.

The District Court erred in concluding that “increases in merchant pricing are properly viewed as changes to the net price charged across Amex’s integrated platform,” Am. Express Co., 88 F.Supp.3d at 196 (emphasis added), because merchant pricing is only one half of the pertinent equation. The District Court heard testimony that “[p]ayments made to obtain or retain co-brand partnerships ,., benefit the issuing side of Amex’s business by opening new channels for acquiring cardholders.” Id. at 203. It expressly declined to factor that evidence into its VR analysis, however, on the basis that those benefits did not accrue on the merchant side of the platform. See id. at 203-04 (declining to use benefits to cardholders “to offset the price paid by those .companies for network services in their capacity as Amex-accept-ing merchants” (emphasis added)). Because the two sides of the platform cannot be considered in isolation, it was error for the District Court to discard evidence of “ ‘two-sided price’ calculations ... intended to capture the all-in price charged to merchants and consumers across Defendants’ entire platform.” Id. at 203.

More problematically, the District Court’s finding of market power was premised in large part on “cardholder insistence,” a term it used to describe “the segment of Amex’s cardholder base who insist on paying with their Amex cards and who would shop elsewhere or spend less if unable to use their cards of choice.” Id. at 191. The District Court noted that Amex’s “26.4% share of a highly concentrated market with significant barriers to entry” likely would not suffice to prove market power alone “were it not for the amplifying effect of cardholder insistence,” Id. at 190-91. Amex’s “highly insistent or loyal cardholder base [was] critical to the court’s finding of market power” because, in the District Court’s view, “cardholder insistence effectively prevents merchants from dropping American Express.” Id. at 191-92.

It was error for the District Court to have relied on cardholder insistence as support for its finding of market power. Cardholder insistence results not from market power, but instead from competitive benefits on the cardholder side of the platform and the concomitant competitive benefits to merchants who choose to accept Amex cards. As Plaintiffs’ own expert explained, an increase in the value of cardholder rewards—which attracts customer loyalty—is “equivalent to a price decrease” to the cardholder, and thus it brings down the net price across the entire platform. App. 919. A firm that can attract customer loyalty only by reducing its prices does not have the power to increase prices unilaterally.

Cardholder insistence is exactly what makes it worthwhile for merchants to accept Amex cards—and thus cardholder insistence is exactly what makes it worthwhile for merchants to pay the relatively high fees that Amex charges. The District Court found specifically that a significant source of Amex cardholder insistence is its cardholder rewards: “Cardholder insistence is derived from a variety of sources. First, and perhaps most importantly, cardholders are incentivized to use their Amex cards by the robust rewards programs offered by the network.” Am. Express Co., 88 F.Supp.3d at 191; see also id. at 191 n.25 (quoting Plaintiffs’ expert’s testimony that Amex’s “very attractive rewards program” is “the big source of insistence” for most Amex cardholders (internal quotation marks omitted); id. at 191 (“Amex’s industry-leading corporate card program ... drives a significant degree of insistent spending....”). Further, the District Court found that Amex’s cardholder insistence and “current market share would dissipate if the company were to stop investing in those programs that make its product valuable to cardholders.” Id. at 195. That Amex might not enjoy market power without continuing investment in cardholder benefits indicates, if anything, a lack of market power; evidence showing that Amex must compete on price in order to attract consumers does not show that Amex has the power to increase prices to supracompetitive levels.

The District Court’s finding that cardholder insistence “effectively prevents merchants from dropping American Express,” id. at 192, ignores the fact that roughly one-third of credit card-accepting merchants in the United States currently do not accept Amex. As explained by the economist amici, “[t]here is no meaningful economic difference between ‘dropping American Express’ ... and a decision not to accept American Express in the first place.” Econ. Amicus Br. 7. A merchant chooses whether or not to accept a particular credit card based on an individualized assessment of the various costs and benefits associated with accepting that card. Because different merchants face different costs and benefits, they can—and in fact do—reach different conclusions about whether or not to accept that card. A single merchant running a pool supply store in a small town, for example, very well might choose not to accept Amex because the products he sells, such as pool toys and cleaning supplies, do not generate enough profit to justify paying the relatively high fees he would be charged to accept Amex cards. By contrast, a major home appliance outlet is more likely to pay Amex’s merchant fees because it sells higher-ticket items that cardholders may wish to purchase using their Amex cards. For his or her part, the cardholder may be more likely to purchase a high-ticket item from a merchant who accepts Amex because this purchase will yield relatively high cardholder rewards and benefits—but it is less likely that the cardholder will insist on using Amex for small purchases, like pool cleaning supplies, that yield fewer cardholder rewards. In this way, cardholder insistence is precisely what makes accepting Amex cards worthwhile for those merchants that do.

The NDPs prevent a merchant from seeking high-end clientele by advertising acceptance of Amex cards but then, at the critical point of sale, offering that clientele a discounted price for not using the Amex card.' In this case, we see no monopolistic danger in this purpose. Amex has a legitimate interest in seeing that cardholders who take advantage of amenities offered to Amex cardholders simply by virtue of owning the card are not enticed to use their Visa or MasterCard by card-connected discounts from merchants. For example, Amex'does not-want a cardholder who takes ample advantage of such amenities—■ and prestige—when travelling to be talked into accepting a discount at the point of purchase of lawn furniture by paying with Visa or MasterCard.

We conclude that, so long as Amex’s market share is derived from cardholder satisfaction, there is no reason to intervene and disturb the present functioning of the payment-card industry. Whatever market power Amex has appears, on this record, to be based on its rewards programs and perceived prestige, ie., Amex cardholders regard the card as'cheaper than competing Visa and MasterCard cards. The NDPs protect that program and that prestige. Outlawing the NDPs would appear to reduce this protection—and likely with the result of increasing the market shares of Visa and MasterCard.

3. Actual Adverse Effect on Competition

The District Court’s erroneous market definition caused its anticompetitive effects finding to come up short, for it failed to consider the two-sided net price accounting for the effects of the NDPs on both merchants and cardholders. Though acknowledging that it had no “empirical evidence that the NDPs have resulted in a higher two-sided price,” id, at 215, the District Court nevertheless maintained that Plaintiffs had provided sufficient circumstantial evidence and expert testimony to support the conclusion that the NDPs had anticompetitive effects on the market as a whole. This finding hinged on the District Court’s conclusion that “[p]roof of anticompetitive -harm to merchants, the primary consumers of Amei-ican Express’s network services, is sufficient to discharge Plaintiffs’ burden in this case.” Id. at 208 (emphasis added).

This analysis erroneously elevated the interests of merchants above those of cardholders. Under the direct method of proving by the rule of reason that Amex violated § 1, Plaintiffs bore the initial burden to show that Amex’s NDPs have “an actual adverse effect on competition as a whole in the relevant market.” K.M.B., 61 F.3d at 127 (emphasis added) (internal quotation marks omitted). Here, the market as a whole includes both cardholders and merchants, who comprise distinct yet equally important and interdependent sets of consumers sitting op either side of the payment-card platform. The NDPs simultaneously affect competition for merchants and cardholders by protecting the critically important revenue that Amex receives from its relatively high merchant fees. The revenue earned from merchant fees funds cardholder benefits, and cardholder benefits in turn attract cardholders. A reduction in revenue that Amex earns from merchant fees may decrease the optimal level of cardholder benefits, which in turn may reduce the intensity of competition among payment-card networks on the cardholder side of the market.

By attracting cardholders, Amex delivers a significant benefit to merchants: Amex cardholders. Amex cardholders are considered “marquee buyers” within the payment-card industry; they tend not only to be more affluent than cardholders on competitor networks, but they also spend more on average per transaction than other cardholders and do so more often. See Am. Express Co., 88 F.Supp.3d at 200-01. Even if Amex cardholders were not marquee buyers, however, merchants still would benefit from Amex’s NDPs insofar as those NDPs help attract cardholders.

The District Court fairly observed that Amex’s “price increases were not wholly offset by additional rewards expenditures or otherwise passed through to cardholders.” Id. at 215. Indeed, evidence on the record suggests—and Amex conceded at oral argument—that not all of Amex’s gains from increased merchant fees are passed along to cardholders in the form of rewards. Even so, the fact remains that “the evidentiary record does not include a reliable measure of the two-sided price charged by American Express that correctly or appropriately accounts for the network’s expenses on the cardholder side of the platform.” Id. at 199 n.30. A finding that not every dime of merchant fees is passed along to cardholders says nothing about other expenses that Amex faces, let alone whether its profit margin is abnormally high.

Because the NDPs affect competition for cardholders as well as merchants, the Plaintiffs’ initial burden was to show that the NDPs made all Amex consumers on both sides of the platform—ie., both merchants and cardholders—worse off overall. Plaintiffs’ argument that the language “as a whole” means only that they were required to show harm to competition in general (rather than to only a single competitor) is unavailing. See Pis.’ Br. 69-70. Whether the NDPs had pro-competitive effects on cardholders—let alone whether any alleged procompetitive effects on cardholders outweigh “anticompetitive” effects on merchants—has no bearing on whether Plaintiffs carried their initial burden under the rule-of-reason analysis to show anti-competitive effects on the relevant market “as a whole.” See K.M.B., 61 F.3d at 127. It was not Amex’s burden to disprove anti-competitive effects; it was Plaintiffs’ burden to prove them.

Plaintiffs might have met their initial burden under the rule of reason by showing either that cardholders engaged in fewer credit-card transactions (ie., reduced output), that card services were worse than they might otherwise have been (ie., decreased quality), or that Amex’s pricing was set above competitive levels within the credit-card industry (i.e., supracompetitive pricing). At trial, however, they offered no such proof. .To the contrary, the evidence presented at trial suggested that industry-wide transaction volume has substantially increased and card services have significantly improved in quality. At oral argument, Plaintiffs conceded that credit-card networks are offering more and better cardholder benefits than ever before, including enhanced fraud-protection services, airline miles, and cash-back rewards. Increased investment in cardholder rewards has accompanied a dramatic increase in transaction volume across the entire credit-card industry: in 2013, total combined transaction volume from all four major payment networks represented approximately $2.4 trillion, marking an eight-percent increase from 2012 and a thirty-percent increase from 2008. See App. 2428.

This evidence of increased output is not only indicative of a thriving market for credit-card services but is also consistent with evidence that Amex’s differentiated closed-loop model, supported by its NDPs, has increased rather than decreased competition overall within the credit-card industry. The District Court thus erred by “inferring] competitive injury from price and output data absent some evidence that tends to prove that output was restricted or prices were above a competitive level.” Brooke Grp. Ltd., 509 U.S. at 237, 113 S.Ct. 2578.

Without evidence of the net price affecting consumers on both sides of the platform, the District Court could not have properly concluded that a reduction in the merchant-discount fee would benefit the two-sided platform overall. Because Plaintiffs-provided neither “a reliable measure of American Express’s per transaction margins,” Am. Express Co., 88 F.Supp.3d at 198, nor “a reliable measure of American Express’s two-sided price that appropriately accounts for the value or cost of the rewards paid to cardholders,” id. at 215, they failed to meet their burden to show anticompetitive effects directly.

CONCLUSION

The District Court erred here in focusing entirely on the interests of merchants while discounting the interests of cardholders. This approach does not advance overall consumer satisfaction. Though merchants may desire lower fees, those fees are necessary to maintaining cardholder satisfaction—and if a particular merchant finds that the cost of Amex fees outweighs the benefit it gains by accepting Amex cards, then the merchant can choose to not accept Amex cards. Indeed, many merchants have already made and continue to make this choice.

Plaintiffs bore the burden in this case to prove net harm to Amex consumers as a whole—that is, both cardholders and merchants—by showing that Amex’s nondiscriminatory provisions have reduced the quality or quantity of credit-card purchases. Given the District Court’s explicit finding that neither party provided reliable evidence of Amex’s costs or profit margins accounting for consumers on both sides of the platform, and given evidence showing that the quality and output of credit cards across the entire industry continues to increase, we conclude that Plaintiffs failed to carry their burden to prove a § 1 violation. Accordingly, we REVERSE and REMAND the case with instructions to enter judgment in favor of Amex.

ADDENDUM

Figure 1

The basic functions of as many as five distinct actors comprising the Visa and MasterCard cooperative, open-loop systems.

Figure 2

The basic relationships and interactions between actors in the Visa and MasterCard cooperative, open-loop networks.

Figure 3

The basic functions of the three actors in the American Express proprietary, closed-loop system.

Figure 4

The basic relationships and interactions between the actors in the proprietary, closed-loop American Express system.

Figure 5,

The relationship of the markets at issue in Visa and the markets at issue in this case can be visualized this way:

[Editor’s Note: The preceding image contains the reference for footnote]

      . Almost all credit-card companies employ umbrella networks: As the reader will soon see, Amex is the exception.

      . See Lapo Filistrucchi et al., Market Definition in Two-Sided Markets: Theory and Practice 5 (Tilburg Law School Legal Studies Research Paper Series No. 09/2013), available at http://papers.ssrn.com/sol3/papers.cfm? abstract_id=2240850 (hereinafter Filistrucchi et al. (2013)); David S. Evans, The Antitrust Economics of Multi-Sided Platform Markets, 20 Yale J. on Reg. 325, 328 (2003). Two-sided markets were first clearly identified' in the early 2000s. by economists Jean-Charles Ro-chet and Jean Tiróle, a 2014 Nobel laureate. Rochet and Tiróle formally defined the concept as follows:
      [A] market is two-sided if the platform can affect the volume of transactions by charging more to one side of the market and reducing the price paid by the other side by ' an equal amount;' in othér words, the price structure matters, and platforms must design it so as to bring both sides on board.
      Jean-Charles Rochet & Jean Tiróle, Two-Sided Markets: A Progress Report, 37 RAND J. Econ. 645, 664-65 (2006).

        .See Jean-Charles Rochet & Jean Tiróle, An Economic Analysis of the Determination of Interchange Fees in Payment Card Systems, 2 Rev, Network Econ. 69, 71 (2003), available at https://www.researchgate.nel/publication/ 24049673_AmEconomic_Analysis_.of_the_ Determmatiori_of_Interchange_Fees_in_ Payment_Card_Systems.

      . See id. at 72; see also Benjamin Klein et al., Competition in Two-Sided Markets: The. Antitrust Economics of Payment Card Interchange Fees, 73 Antitrust L.J. 571, 580 (2006) (hereinafter Klein et al. (2006)) (''[T]he value of a payment system'to consumers increases with the number of merchants that accept the card and the value of a payment system to merchants increases with consumer use of the card.”).

      . See David S. Evans & Michael Noel, Defining Antitrust Markets When Firms Operate Two-Sided Platforms, 2005 Colum. Bus. L. Rev. 667, 695 (2005).

      . Rochet & Tiróle, Interchange Fees, supra note 4, at 72.

      . See id. at 73.

      . See Klein et al., supra note 5, at 573-74 (explaining that merchants typically bear a larger fraction of the total costs of a payment-card system than do cardholders "not due to payment card system market power over merchants, but because demand sensitivity generally is much greater on the cardholder side of the market than on the merchant side of the market”).

      . See Evans & Noel, supra note 6, at 682; see also id. at 668 ("Empirical surveys of industries based on [two-sided platforms] find many examples of prices that are low, or even negative, so that customers on one side are incentivized to participate in the platform.”).

      . See David S. Evans, Some Empirical As-pecto of Multi-Sided Platfom Industries, 2 Rev. Network Econ. 191 (2003), reprinted in Davis S. Evans & Richard Schmalensee, The Industrial Organization of Markets with Two-Sided Platforms, Competition Policy International (Spring 2007), reprinted in Platform Economics: Essays on Multi-Sided Businesses 1, 282 (David S. Evans ed. 2011). Prior to 1950, payment cards were issued only by retailers for use in their stores. Then and now, these "store cards” operate as one-sided markets because they are distributed to only a single set of consumers: cardholders. See id. at 283.

      . Amex originally formed in 1850 as an express mail company. See David S. Evans & Richard Schmalensee, More than Money, in Paying with Plastic (3d ed. 2012), reprinted in Platform Economics, supra note 11, at 282, 285-86.

      . Evans, Empirical Aspects, supra note 11, at 42-43 (internal quotation marks omitted).

      . See id. at 42-43.

      . See Evans & Schmalensee, More than Money, supra note 11, at 286. Relying on the parties’ written submissions and expert testimony offered at trial, the District Court explained the basics of credit as follows:
      Credit cards enable cardholders to make purchases at participating merchants by accessing a line of credit extended to the cardholder by the issuer of that card. Cardholders are invoiced for purchases typically once per month and often have a grace period during which payment may be made. The delay between a purchase event and the cardholder’s deadline for paying the bill on which that purchase appears is referred to as the "float,” and it enables cardholders to temporarily defer payment on their purchases at no additional cost (i.e., without paying interest).

        Am. Express Co., 88 F.Supp.3d at 153 (citations omitted).

      . See Evans & Schmalensee, More than Money, supra note 11, at 286-87.

      . See id. at 288.

      . See David S. Evans & Richard Schmalen-see, Interchange Fees and Their Regulation (May 2005), reprinted in Platform Economics, supra note 11, at 314, 325.

      . Evans & Schmalensee, More than Money, supra note 11, at 290 (internal quotation . marks omitted).

      . The facts in this and the following sections are drawn largely from the District Court’s Findings of Fact, much of which was taken from the parties’Joint Statement of Undisputed Fact, see Parties' Stipulated Statements of Fact, Am. Express Co., No. 10-cv-4496 (NGG)(RER) (filed June 6, 2014), ECF No. 447-1 (hereinafter "Jt. Stmt.”), and none of which are in dispute.

      . The parties stipulated that these percentage figures were accurate as of 2013.

      . For a graphical depiction of this system, see infra Addendum Figure 1.

      . For a diagram outlining the allocation of fees between the parties involved in this system, see infra Addendum Figure 2.

      . Rochet & Tiróle, Interchange Fees, supra note 4, at 75 (emphases omitted).

      . Klein et al., supra note 5, at 572.

      . For a graphical depiction of this system, see infra Addendum Figure 3.

      . Amex occasionally uses third-party banks as issuers. At the present time, nine third-party banks issue Amex cards, accounting for roughly one percent of Amex’s total U.S. charge volume per year.

      . For a diagram outlining the allocation of fees between the parties involved in this system, see infra Addendum Figure 2.

      . Rochet & Tirole, Interchange Fees, supra note 4, at 72.

      . See Klein et al., supra note 5, at 590-91.

      . “Marquee buyers” are defined as certain customers on one side of a two-sided market who are "extremely valuable to customers on the other side of the market.” Evans, Empirical Aspects, supra note 11, at 37. The existence of marquee buyers “tends to reduce the price to all buyers and increase[] it to sellers.” Id. (identifying Amex as an example of a company that benefits from marquee buyers insofar as these buyers allow Amex “to charge a relatively high merchant discount as compared to other card brands, especially for their corporate card, because merchants view[] the American Express business clientele as extremely attractive.”).

      . See Evans & Noel, supra note 6, at 690.

      . See Evans, Antitrust Economics, supra note 5, at 346.

      . Id. at 347.

      . Diner’s Club floundered during this time, in part because it failed to keep up with newly emerging competition from the bank card associations. Today, Diner’s Club has shrunk to almost nothing in the United States. See Evans & Schmalensee, More than Money, supra note 11, at 287.

      . The District Court found that ‘‘[b]y retaining end-to-end control of all spending data on its network, American Express is able to sell its merchants information on and analysis of its cardholders’ spending behaviors, allowing the merchant to engage in more effective targeted marketing or identify new locations for geographic expansion, among other applications.” Am. Express Co., 88 F.Supp.3d at 159.

      .These exclusionary rules were the subject of the litigation in United States v. Visa U.S.A., Inc., 344 F.3d 229 (2d Cir. 2003).

      . In accordance with the Durbin- Amendment, Amex’s NDPs do not prevent merchants from offering discounts or otherwise steering customers to use cash, check, debit, or auto- ' mated clearing house ("ACH”) transfers. Plaintiffs in this litigation have not challenged the NDPs insofar as they prohibit merchants from imposing fees when accepting Amex cards that are not “imposed equally on all Other Payment Products,” nor have Plaintiffs challenged the NDPs to the extent that they prohibit merchants from "mischaracter-iz[ing]” the Card or "engag[ing] in activities that harm [Amex’s] business or the American Express Brand (or both).” See Am. Compl. ¶ 28, ECF Dkt, No. 53 (quoting Amex’s Standard NDPs).

      . Not all merchants are bound by Amex’s ■ standard NDPs. Certain merchants, including Sears, Crate & Barrel, Home Depot, and Hilton Hotels & Resorts, have negotiated the right to steer toward their private label or co-brand cards. Even these merchants, however, remain subject to restrictions on whether and how they can influence a customer's payment-card choice at the point of sale.

      . The seventeen states are Maryland, Missouri, Vermont, Utah, Arizona, New Hampshire, Connecticut, Iowa, Michigan, Ohio, Texas, Illinois, Tennessee, Montana, Nebraska, Idaho, and Rhode Island. Though Hawaii was originally an eighteenth Plaintiff State, it stipulated to the dismissal of its claims without prejudice before trial,

      . Though the Supreme Court once suggested in a footnote, that vertical price restraints might warrant differential treatment under the law from vertical non-price restraints, see Continental T.V., Inc. v. GTE Sylvania Inc., 433 U.S. 36, 51 n.18, 97 S.Ct. 2549, 53 L.Ed.2d 568 (1977), it later clarified that there is "little economic justification” for any differential treatment, Leegin, 551 U.S. at 904, 127 S.Ct. 2705. Accordingly, both vertical price restraints and vertical non-price restraints are analyzed under the rule of reason.

      . Both the Plaintiffs and the District Court flagged alleged distinctions between the NDPs and other vertical restraints, see Am. Express Co., 88 F.Supp.3d at 168; Appellee’s Br. at 50-51, in apparent attempts to recast the vertical restraints as horizontal. We have never drawn this type of distinction between any varieties of vertical restraints and decline to do so here. Moreover, because we apply the rule of reason to both vertical and horizontal restraints, see supra note 41 and accompanying text, we find that any such distinction is without meaningful difference to the antitrust analysis in this case.

      . See, e.g., Richard A. Posner, Vertical Restraints and Antitrust Policy, 72 U. Chi. L Rev. 229, 250 (2005) ("Another name for [loyalty] might be low transaction costs and customer inertia, which might be another name for economizing on transaction costs.”); Benjamin Klein, Andres V. Lerner, Kevin M. Murphy, Lacey L. Piache, Competition in Two-Sided Markets: The Antitrust Economics of Payment Card Interchange Fees, 73 Antitrust L.J. 571, 574 (2006) ("Letting merchants who have agreed to accept a payment card and display the payment system's symbol decide which of the system’s cards to accept and which to reject would impose a significant cost on the payment system's brand name by undermining consumer expectations of guaranteed acceptance.... Such demands would impose an externality on the entire payment card system, and eventually lead some merchants to drop acceptance of the payment system's cards.”).

      . For a graphical depiction of the salient differences, see infra App. Figure 5.

      . We note briefly that the District Court apparently did not use its own relevant market definition when analyzing both anticompeti-tive effects and market power. The District Court defined “network services” as no more than the services provided by a payment-card platform "to facilitate the use and acceptance of its payment cards.” Am. Express Co., 88 F.Supp.3d at 157. It then recognized explicitly that the network fee comprises only one part of the full merchant-discount rate subtracted from the merchant's profit at the point-of-sale. See id. at 157 (“[T]he merchant discount fee is primarily comprised of three elements: a percentage interchange fee, an acquirer fee, and a network fee.”). These findings notwithstanding, the District Court analyzed anticompetitive effects with respect to the full merchant-discount rate, not simply the fees associated with "network services.” See, e.g., id. at 215 (finding that "American Express’s merchant restraints have allowed all four networks to raise their swipe fees more easily and more profitably than would have been possible were merchants permitted to influence their customers' payment decisions”); id. at 219 (concluding that removal of Amex’s NDPs would "result in lower swipe fees charged to merchants”). We need not decide here whether this inconsistency constitutes error because, in any event, the District Court defined the relevant market incorrectly.

      . Plaintiffs’ own expert, Dr. Michael Katz, recognized that an increase in the value of cardholder rewards is "equivalent to a price decrease” to cardholders. App. 919.

      , Amex argues that its 26.4% market share "is a red flag that counsels against a finding [of] market power” because “no court in any circuit has ever found that a firm violated Section 1 with a share of the relevant market below 30 percent absent proof of horizontal collusion, and courts in this Circuit have recognized that ‘firms with market shares of less than 30% are presumptively incapable of exercising market power.' ” Amex Br. 70 (quoting Commercial Data Servers, Inc. v. Int’l Bus. Machs. Corp., 262 F.Supp.2d 50, 74 (S.D.N.Y. 2003) (internal quotation marks omitted) (collecting cases)). The District Court rejected this argument in a footnote stating that “[m]arket share is but one factor considered when attempting to approximate a defendant firm’s power in a relevant market, and that a firm's share falls below some arbitrary threshold cannot disprove allegations of market power without reference to the other competitive dynamics at play.” Id. at 189 n.23. Though we agree with the District Court that market share is "one factor” relevant to market power analysis, we decline to establish any strict threshold of market share sufficient to establish a § 1 violation.

      . The District Court found that the price discrimination evidence was of "limited probative value” because Plaintiffs did not provide any reliable measure of ■ Amex's per-transaction margins across its industry groups. Am. Express Co., 88 F.Supp.3d at 198. Similarly, although the District Court received evidence of merchant pricing premiums, it concluded ultimately that "given the absence of clarity with respect to whether Amex maintains a premium in today's market and whether such premium is or has been justified by the network’s differentiated value propositions, the court finds Plaintiffs’ evidence of Amex’s pricing premium to be of limited utility in the present market power analysis,” id. at 202.

      . See supra note 46.

      . For similar reasons, a doctor may choose to not accept American Express from her patients for co-payments. The high cost of merchant fees from American Express may cut in to the doctor's profit margins, and the doctor has little concern about “marquee buyers.” Her patients come to her because they think she is a good doctor—and even if her patients would prefer some frequent flyer miles from using a credit card for the co-payment they won’t switch doctors just for the miles.

      . One of die ironies of this case is that the government, which usually worries about oli-gopolists engaging in-indirect collusion leading to pricing’ similarities, seeks relief in this case that might drive the three cards to greater similarities. Indeed, the differences between the major payment cards have narrowed over time, as one might expect from healthy competition. The relief sought by the government in this case could even increase market concentration by reducing Amex’s share to Visa’s and MasterCard’s benefit.

      . The District Court also concluded that Plaintiffs offered sufficient proof of harm on the cardholder side of the market in the form of higher retail prices. This conclusion is erroneous, ■ as it fails to take into account offsetting benefits to cardholders in the form of rewards and other services.

      . See supra note 31.

      . See Klein et al, supra note 4, at 580 (explaining that “the value of a payment system to [cardholders] increases with the number of merchants that accept the card and the value of a payment system to merchants increases with [cardholder] use of the card.'T

      . Amex argues on appeal that the District Court’s liability determination and injunction each separately violate the rule of Colgate, which states that " 'the [Sherman Act] does not restrict the long recognized right of [a] trader or manufacturer ... freely to exercise his own independent discretion as to parties with whom he will deal.’ ” In re Adderall XR Antitrust Litig., 754 F.3d 128, 134 (2d Cir. 2014) (first and second alterations in original) (quoting United States v. Colgate & Co., 250 U.S. 300, 307, 39 S.Ct. 465, 63 L.Ed. 992 (1919); see also Monsanto Co. v. Spray-Rite Serv. Corp., 465 U.S. 752, 761, 104 S.Ct. 1464, 79 L.Ed.2d 775 (1984) ("A manufacturer of course generally has a right to deal, or refuse to deal, with whomever it likes, as long as it does so independently.”). We need not decide this question, however, because we have already determined that the liability determination should be reversed.

      . Rochet & Tiróle, Interchange Fees, supra note 3, at 74.

      . Rochet & Tiróle, Interchange Fees, supra note 3, at 72;

      . This Court recognized in Visa that "[n]et-worlcs also compete for merchants”—but because this bore on its analysis only insofar as it relied on merchant testimony that merchants could not afford to discontinue accepting Visa or MasterCard, see Visa, 344 F.3d at 239-40, merchants have been omitted from the ''buyers” column of this table for the sake of simplicity.