LEVAL, Circuit Judge.

The defendants, MasterCard International, Inc. (“MasterCard”), Visa U.S.A., Inc. (“Visa U.S.A.”), and Visa International, Inc. (“Visa International”), appeal from the judgment of the United States District Court for the Southern District of New York (Barbara S. Jones, /.), entered after a non-jury trial, finding that the defendants violated Section 1 of the Sherman Antitrust Act and imposing an injunction. The U.S. Department of Justice (“DOJ”) brought this civil enforcement action challenging the organizational structure of two of the nation’s four major payment card systems. The complaint charged that MasterCard and Visa U.S.A., which are organized as joint ventures owned by their member banking institutions, conspired to restrain trade in two ways: (1) By enacting rules permitting a member-owner of one to function as a director of the other (an arrangement the government described as “dual governance”) (Count I); and (2) by enacting and enforcing “exclusionary rules,” which prohibit their member banks from issuing American Express (“Amex”) or Discover cards (Count II).

After a 34-day trial, the court, in a commendably comprehensive and careful opinion, ruled in the defendants’ favor as to dual governance (Count I). 1 As to Count II, however, the court held that Visa U.S.A. and MasterCard violated the Act by enforcing their respective versions of the exclusionary rule, barring their member banks from issuing Amex or Discover cards. The court further held that Visa International, which owns the Visa brand, licenses it to Visa U.S.A., and exercises certain governance powers over Visa U.S.A., was liable for participating in Visa U.S.A.’s violation. The court ordered the exclusionary rules revoked and permanently enjoined all three defendants from promulgating similar rules in the future. See generally United States v. Visa U.S.A., Inc., 163 F.Supp.2d 322 (S.D.N.Y.2001) (opinion and Proposed Final Judgment); United States v. Visa U.S.A, Inc., 183 F.Supp.2d 613 (S.D.N.Y.2001) (modifications to Proposed Final Judgment).

The defendants brought this appeal. Visa U.S.A. and MasterCard argue that the district court erred in its conclusion that their respective exclusionary rules violate the Sherman Act. Visa International contends there was no adequate basis to hold it liable for Visa U.S.A.’s violation.

For the reasons set forth below, we affirm the judgment.

BACKGROUND

I Description of the General Purpose Payment Card Industry

A The Structure of the Visa and MasterCard Networks

Visa U.S.A. and MasterCard are two of the United States’s four major network systems in the payment card industry, the other two being Amex and Discover. 2 *235 Visa U.S.A. and MasterCard are organized as open joint ventures, owned by the numerous banking institutions that are members of the networks. (Because the vast majority of the members are banks, and because for purposes of this appeal nothing turns on whether members are banks or other types of financial institutions, we refer to the member institutions as “banks.”) MasterCard is owned by its approximately 20,000 member banks; Visa U.S.A. is owned by its approximately 14,-000 member banks. Because MasterCard allows its member banks to issue Visa cards, and Visa U.S.A. likewise allows its members to issue MasterCard cards, many of Visa U.S.A.’s 14,000 members are also members of the MasterCard network. The networks’ operations are conducted primarily by their member banks. While the member banks engage in the card business for profit, MasterCard and Visa U.S.A. themselves operate as non-profit organizations and are largely funded through service and transaction fees paid by their members. Both make a “profit” on these fees, but their business model is not one that strives to maximize earnings at the “network” level. Rather, the two organizations’ capital surpluses are held basically as security accounts, to pay merchants in the event a member bank defaults on a payment obligation.

The member banks of the MasterCard and Visa U.S.A. card networks may function either as “issuers” or “acquirers” or both. A member bank serving as an “issuer” issues cards to cardholders; it serves as the liaison between the network and the individual cardholder. A member bank serving as an “acquirer” acquires the card-paid transactions of a merchant; a particular acquiring bank acts as liaison between the network and those merchants accepting the network’s payment cards with whom it has contracted.

When a consumer uses a Visa card or a MasterCard card to pay for goods or services, the accepting merchant relays the transaction information to the acquiring bank with whom it has contracted. The acquirer processes and packages that information and transmits it to the network (Visa U.S.A. or MasterCard). The network then relays the transaction information to the cardholder’s issuing bank, which approves the transaction if the cardholder has a sufficient credit line. Approval is sent by the issuer to the acquirer, which relays it to the merchant.

Payment requests are sent by the merchant to the acquirer, which forwards the requests to the issuer. The issuer then pays the acquiring bank the amount requested, less what is called an “interchange fee” — typically 1.4%. The acquirer retains an additional fee — approximately .6%. Thus, the issuing bank and the acquirer withold an aggregate of approximately 2% of the amount of the transaction from the merchant. This is known as the “merchant discount.” For a $100 sale, the merchant typically will receive $98, the issuing bank retaining $1.40, while the acquiring bank retains 60 cents.

Both MasterCard and Visa are open joint ventures, meaning that there is no limit to the number of banks that may become members, either as issuers or as acquirers. Any member may serve as both an issuer and as an acquirer. Members agree to abide by their association’s by-laws and other regulations.

A member of either the Visa U.S.A. or MasterCard network may also be a member of the other network. Thus a bank that is a member of Visa U.S.A.’s network and issues Visa cards may also be a mem *236 ber of the MasterCard network and issue MasterCard cards. On the other hand, both MasterCard and Visa U.S.A. have promulgated rules that prohibit their members from issuing American Express or Discover cards. Those rules — Visa’s by-law 2.10(e) and MasterCard’s Competitive Programs Policy (“CPP”) 3 — are the focus of this action, and were held by the district court to violate the Sherman Act.

B The Structure of the American Express and Discover Networks

American Express and Discover, the other two major card systems in the United States, are quite differently organized. They are not joint venture membership associations. Rather, each is a vertically integrated entity, acting for profit, which combines issuing, acquiring, and network functions. (The parties and the District Court occasionally refer to this structure as a “closed loop.”) Amex and Discover deal directly with consumers (by issuing cards), and with merchants (by acquiring and processing transactions). When a consumer makes a purchase with an American Express card, for example, the merchant contacts Amex directly, and if the customer has sufficient credit available, Amex approves the sale. Amex then pays the merchant directly, retaining a percentage — usually 2.73%. (Discover is organized similarly to Amex. Its merchant discount is usually 1.5%.)

Since at least 1995, American Express has sought to change its structure by soliciting banks to issue American Express cards. This effort has been successful outside of the continental United States and abroad, where banks such as Puerto Rico’s Banco Popular have begun issuing Amex-branded cards. In the continental United States, in contrast, Amex has been unsuccessful in its attempt to solicit outside issuers. Because of Visa U.S.A.’s and MasterCard’s exclusionary rules, any bank that undertook to issue Amex-branded cards would be forced to give up issuing both Visa and MasterCard cards — a move no U.S. bank has been willing to make.

C The Relationship Between Visa International and Visa U.S.A.

Visa International is a Delaware corporation organized as a membership association. Its members include both individual banks and “Group Members,” such as Visa U.S.A. and Visa Canada. Group Members (such as Visa U.S.A., described above) are themselves joint ventures. Visa International owns the Visa brand name and licenses that brand to its members. Visa U.S.A. and the other Group Members sub-license the Visa brand to their own issuing members. Visa U.S.A. is the only Visa International member operating in the United States. Thus, all Visa cards issued in the United States are issued by members of the Visa U.S.A. consortium.

*237 Visa International is divided into six geographic regions: USA, Canada, the European Union, Latin America and Caribbean, Asia-Pacific, and Central Europe/Middle East/Africa. Each region is entitled to elect a minimum of two and a maximum of eight representatives to Visa International’s 26-member Board of Directors.

Visa International describes its relationship with its autonomous regional entities as a “federalist system, fashioned after the relationship between individual states and the United States.” VI-17. According to § 15.02 of Visa International’s bylaws, the Visa International Board of Directors has exclusive authority to regulate “purely interregional” matters, while “int-raregional matters” are regulated exclusively by the individual regional boards (subject to overarching Visa International policies, which are decided by the Visa International Board). Intraregional matters “which may have a significant effect on the worldwide Visa program” are regulated by regional boards, “until preempted or regulated by the [International] Board of Directors.” VI-17-18. The power to determine whether a matter is purely in-terregional, purely intraregional, or int-raregional with a potential effect on the worldwide program rests with the Visa International Board of Directors.

II Competition in the General Purpose Payment Card Industry

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. American Express is the largest single card issuer in the United States, as measured by transaction volume. By the same measure, Discover is the fifth largest issuer. The other large issuers are members banks in the Visa and MasterCard networks.

Ill The Challenged Regulations

This appeal concerns the propriety of Visa U.S.A.’s and MasterCard’s so-called “exclusionary” or “exclusivity” rules, which prohibit members of their networks from issuing Amex and Discover cards. The district court concluded that these exclusivity rules are anticompetitive because they restrict the ability of American Express and Discover to compete with Visa and MasterCard in marketing their “network services” to banks. As a result of these exclusionary rules, American Express and Discover have been effectively foreclosed from the business of issuing cards through banks. By reason of the exclusivity rules, a bank choosing to issue Amex or Discover cards would be compelled to forego issuing Visa and MasterCard cards. No United States bank has been willing to give up its membership in the Visa U.S.A. and MasterCard networks in order to issue Amex or Discover cards.

DISCUSSION

Section 1 of the Sherman Antitrust Act prohibits “[e]very contract, combination in the form of trust or otherwise, or conspiracy, in restraint of trade or commerce among the several States.” 15 U.S.C. § 1. For over 100 years, the courts have understood the Sherman Act only to prohibit “unreasonable” restraints on *238 trade. See, e.g., Arizona v. Maricopa County Med. Soc’y., 457 U.S. 332, 342-43, 102 S.Ct. 2466, 73 L.Ed.2d 48 (1982) (citing United States v. Joint Traffic Ass’n., 171 U.S. 505, 19 S.Ct. 25, 43 L.Ed. 259 (1898)). Certain arrangements, such as price fixing and market division, are considered unreasonable per se, but most other restraints are evaluated case by case, under the “rule of reason.” See, e.g., Id., at 343-44, 102 S.Ct. 2466. The principal question in a rule of reason case is often whether the anticompetitive effects of a restraint are outweighed by some procompetitive justification. See, e.g., Clorox Co. v. Sterling Winthrop, Inc., 117 F.3d 50, 56 (2d Cir.1997). The practices challenged in this case are properly analyzed under the rule of reason, as neither Visa U.S.A. nor MasterCard has restricted trade in a manner that constitutes a per se violation.

For the government to prevail in a rule of reason case under Section 1, the district court concluded, and the parties do not argue otherwise, that the following must be shown: As an initial matter, the government must demonstrate that the defendant conspirators have “market power” in a particular market for goods or services. 4 Next, the government must demonstrate that within the relevant market, the defendants’ actions have had substantial adverse effects on competition, such as increases in price, or decreases in output or quality. See, e.g., Atlantic Richfield Co. v. USA Petroleum Co., 495 U.S. 328, 110 S.Ct. 1884, 109 L.Ed.2d 333 (1990). Once that initial burden is met, the burden of production shifts to the defendants, who must provide a procompetitive justification for the challenged restraint. Capital Imaging Assocs., P.C. v. Mohawk Valley Medical Assocs., 996 F.2d 537, 543 (2d Cir.1993). If the defendants do so, the government must prove either that the challenged restraint is not reasonably necessary to achieve the defendants’ procom-petitive justifications, or that those objectives may be achieved in a manner less restrictive of free competition. Bhan v. NME Hosps., Inc., 929 F.2d 1404, 1413 (9th Cir.1991).

We review the district court’s conclusions of law de novo. Sheet Metal Div. v. Local 38 of Sheet Metal Workers Int’l Ass’n, 208 F.3d 18, 22 (2d Cir.2000). Findings of fact are to be upheld unless clearly erroneous. Anderson v. City of Bessemer City, 470 U.S. 564, 573-74, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985).

I Relevant Markets and Market Power

The district court determined, and we agree, that this case involves two interrelated, but separate, product markets: (1) what the court called the general purpose card market, consisting of the market for charge cards and credit cards, and (2) the *239 network services market for general purpose cards.

A distinct product market comprises products that are considered by-consumers to be “reasonabl[y] interchan-geab[le]” with what the defendant sells. Eastman Kodak Co. v. Image Tech’l Servs., Inc., 504 U.S. 451, 482, 112 S.Ct. 2072, 119 L.Ed.2d 265 (1992); United States v. E.I. du Pont de Nemours & Co., 351 U.S. 377, 404, 76 S.Ct. 994, 100 L.Ed. 1264 (1956). After hearing substantial expert testimony, the district court found as a matter of fact that other forms of payment — such as cash, checks, debit cards, and proprietary cards (e.g. the Sears or Macy’s cards) — are not considered by most consumers to be reasonable substitutes for general purpose credit or charge cards. Visa U.S.A., 163 F.Supp.2d, at 335-38. As the government’s expert witness explained, based on empirical analysis of consumer preferences, if prices for general purpose payment cards were to rise significantly, cardholders would likely pay the increased fees, rather than abandon their cards in favor of other forms of payment. Id. Thus, general purpose payment cards constitute a distinct market, separate from the market for such other payment alternatives. We find no reason to doubt the court’s conclusion.

Further, we agree with the district court that the four payment card networks compete with one another in a market for “network services.” Id. at 338-39. General purpose card networks, Judge Jones explained, “provide the infrastructure and mechanisms through which general purpose card transactions are conducted, including the authorization, settlement, and clearance of transactions.” Id. at 338. 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. Issuing banks purchase network services from MasterCard and/or Visa U.S.A., and those two brands compete with Amex and Discover for the banks’ business. Networks also compete for merchants, because the price merchants pay for acceptance of payment cards (the merchant discount) is affected by the size of the interchange fee, which is set by the network.

The district court found, on the basis of expert testimony, that there are no products reasonably interchangeable, in the eyes of issuers or merchants, with the network services provided by the four major brands. Id. This was a reasonable finding: (1) Network-level costs are so high that banks and merchants cannot provide these services for themselves, and (2) issuance and acceptance of credit and charge cards is so profitable (and network service fees so negligible in comparison) that even a large increase in network fees would not provide a rational financial incentive to abandon the business of issuing or accepting payment cards.

We agree with the district court’s finding that Visa U.S.A. and MasterCard, jointly and separately, have power within the market for network services. Market power has been defined by the Supreme Court to mean the “power to control prices or exclude competition.” du Pont, 351 U.S. at 391, 76 S.Ct. 994. NCAA, at 109 n. 38, 104 S.Ct. 2948. Such power may be proven through evidence of specific conduct undertaken by the defendant that indicates he has the power to affect price or exclude competition. KMB Warehouse Distribs., Inc. v. Walker Mfg. Co., 61 F.3d 123, 129 (2d Cir.1995). Alternatively, market power may be presumed if the defendant controls a large enough share of the relevant market. Id. Judge *240 Jones based her finding of market power first on the fact that merchants testified that they could not refuse to accept payment by Visa or MasterCard, even if faced with significant price increases, because of customer preference. Visa U.S.A., 163 F.Supp.2d, at 340. Indeed, despite recent increases in both networks’ interchange fees, no merchant had discontinued acceptance of their cards. Id. In addition, the court inferred market power from the defendants’ large shares of a highly concentrated market: In 1999, Visa U.S.A. members accounted for approximately 47% of the dollar volume of credit and charge card transactions, while MasterCard members accounted for approximately 26%. Id. at 341 — 42. (American Express accounted for 20%; Discover, for 6%.)

The evidence relied on by the district court was sufficient to sustain a finding of market power. In addition, Amex, despite repeated recent attempts, has been unable to persuade any issuing banks in the continental United States to utilize its network services because the exclusivity rule would require such issuing banks to give up membership in the Visa and MasterCard consortiums, and banks are unwilling to do so. In short, Visa U.S.A. and MasterCard have demonstrated their power in the network services market by effectively precluding their largest competitor from successfully soliciting any bank as a customer for its network services and brand.

II Harms to Competition

As noted, to sustain a challenge under § 1 of the Sherman Act, the government must prove that the defendants’ conduct has adversely affected competition. The district court found that Visa U.S.A. and MasterCard’s exclusionary rules harm competition by “reducing overall card output and available card features,” as well as by decreasing network services output and stunting price competition. We cannot say that these conclusions were erroneous.

The most persuasive evidence of harm to competition is the total exclusion of American Express and Discover from a segment of the market for network services. As noted, there are only four major payment card network providers in the United States. While competition among (and within) these networks is robust at the issuing level (where 20,000 separate issuers compete to provide products to consumers), at the network level (where four major networks seek to sell their technical, infrastructure, and financial services to issuer banks) competition has been seriously damaged by the defendants’ exclusionary rules. As the district court noted, “[i]t is largely undisputed that the exclusionary rules have resulted in the failure of Visa and MasterCard member banks to become issuers of American Express and Discover-branded cards.” Id. at 383. The district court cited evidence that three major U.S. issuer banks — Banco Popular, Advanta, and Bank One — would have contracted with American Express to issue Amex cards in the United States but for the exclusionary rules. Id. at 383-87. In addition, Banco Popular has contracted with Amex to issue its cards in Puerto Rico, where no exclusionary rules apply. Id. at 383-84.

As a result, then, of the challenged policies, only two rival networks are effectively able to compete for the business of issuer banks. Testimony at trial revealed that Visa U.S.A. and MasterCard “pay millions of dollars in incentive payments in the form of discounts from the price for network services to selected issuing banks to compete for their business and [that] the banks play Visa and MasterCard against [each] other to obtain lower net prices and higher value for card network services.” Id. at 382. With only two viable competitors, however, such price and product competition is necessarily limited. Trial testimony strongly indicated that *241 price competition and innovation in services would be enhanced if four competitors, rather than only two, were able to compete in this manner for issuing banks. Id. Indeed, the district court found, based on testimony from Visa U.S.A. and MasterCard executives, that both defendants would “respond to ... greater network competition by offering new and better products and services.” Id. at 396. MasterCard’s former CEO, for example, testified that MasterCard would be forced to “speed up” development of a premium card product were Amex cards issued through MasterCard member banks. Id.

In foreign countries, where Visa International rather than Visa U.S.A. operates the Visa network, and no exclusionary rule applies, Amex has succeeded in convincing banks that issue Visa cards also to issue Amex cards. This has caused Visa International to “proactively strengthen” its product offerings to member banks abroad. Id. at 396-97. In addition, an internal Visa International memorandum cautions that Visa U.S.A. would have to compete more vigorously for market share if Amex were permitted to partner with its member banks: “To date, AmEx has been precluded from partnering with U.S. banks, although that situation could change. Since bank partners could significantly increase [Amex’s] acceptance and cards, Visa needs to monitor the situation and counter with competitive products that meet banks[’] needs.” Id. at 397.

The district court also found that product innovation and output has been stunted by the challenged policies. By excluding Amex and Discover from the market for outside card issuers, Visa U.S.A. and MasterCard effectively deny consumers access to products that could be offered only by a network in partnership with individual banks. Such products include cards that are able to link “to transaction accounts, to asset management accounts, to sale of mortgages or other financial products that [banks] offer[ ].” Id. at 396.

We find no error in the district court’s finding that competition has been harmed by the defendants’ exclusionary rules.

Ill The Defendants’ Arguments

Defendants argue on appeal that the district court erred in two ways: (1) by finding that the exclusionary rules harm competition, when they in fact disadvantage only individual competitors; and (2) by failing to recognize that any adverse effects on competition are outweighed by the substantial procompetitive benefits of exclusivity.

A Harms to Competition

First, the defendants argue that the district court erred by mistaking harm to a competitor for harm to competition. They cite the familiar formula that the “antitrust laws protect competition, not competitors.” Clorox Co. v. Sterling Winthrop, Inc., 117 F.3d 50, 57 (2d Cir.1997). (MC 17) Visa U.S.A. contends, for example, that “[t]he decision and remedy in this case will not benefit consumer welfare. Instead, virtually the sole beneficiary will be AmEx which hopes to gain not by offering lower prices or better products but largely by undermining its major brand competitors.” Brief for Appellant Visa U.S.A. at 19-20.

Defendants contend the exclusionary rules are akin to “exclusive distributorship” arrangements, which we have held are “presumptively legal.” Elec. Communications Corp. v. Toshiba Am. Consumer Prods., Inc., 129 F.3d 240, 245 (2d Cir.1997) (citing Oreck Corp. v. Whirlpool Corp., 579 F.2d 126, 131 (2d Cir.1978) (in banc)). We find this argument unpersuasive.

*242 Defendants are certainly correct that the proper inquiry is whether there has been an “actual adverse effect on competition as a whole in the relevant market.” KMB Warehouse, 61 F.3d at 127 (citations and internal quotation marks omitted). We have held that competition is not adversely affected if, despite an exclusive dealership arrangement, “competitors can reach the ultimate consumer of the product by employing existing or potential alternative channels of distribution.” CDC Techs., Inc. v. IDEXX Labs., Inc., 186 F.3d 74, 80 (2d Cir.1999) (quoting Omega Envt’l, Inc. v. Gilbarco, Inc., 127 F.3d 1157, 1163 (9th Cir.1997)) (internal quotation marks omitted).

The defendants argue that the harms identified by the district court as stemming from their exclusionary rules— that the types of cards that consumers can get from their banks are limited and [that] banks are prevented from combining their particular issuing skills with the AmEx brand — are not harms to Amex’s ability to compete as a network (or Discover’s), but rather harms to its distributive capacity, in much the same way Pepsi-Cola’s distributive capacity might be limited by an exclusive arrangement between Coca-Cola and its truckers. For an exclusive dealership arrangement to cause a harm to competition (and overcome the presumption of legality), it must prevent competitors from getting their products to consumers at all. CDC Techs., 186 F.3d at 80 (citing Gilbarco, 127 F.3d at 1163). There is no question, the defendants argue, that Amex and Discover can get their products to consumers, as evidenced by the fact that they are respectively the largest and fifth largest issuers of payment cards in the United States.

The analogy to an exclusive arrangement between Coca-Cola and its truckers is not persuasive. The basic flaw in the analogy is that it depicts Visa U.S.A. (or MasterCard) as a single entity (like Coca-Cola) demanding a restrictive provision in its contract with a supplier of services to it. Visa U.S.A. and MasterCard, however, are not single entities; they are consortiums of competitors. They are owned and effectively operated by some 20,000 banks, which compete with one another in the issuance of payment cards and the acquiring of merchants’ transactions. These 20,000 banks set the policies of Visa U.S.A. and MasterCard. These competitors have agreed to abide by a restrictive exclusivity provision to the effect that in order to share the benefits of their association by having the right to issue Visa or MasterCard cards, they must agree not to compete by issuing cards of Amex or Discover. The restrictive provision is a horizontal restraint adopted by 20,000 competitors.

The analogy proposed by the defendants would be more pertinent if Coca-Cola, Pepsi-Cola, and several other leading sellers of soft drinks joined together to form an association to contract for trucking services and exacted of contracting truckers a commitment not to carry for any soft drink maker that was not a part of the consortium. Even then the analogy would lack the feature here presented that the restraint imposed by the consortium members is on themselves. Each has agreed not to compete with the others in a manner which the consortium considers harmful to its combined interests. Far from being “presumptively legal,” such arrangements are exemplars of the type of anti-competitive behavior prohibited by the Sherman Act. See, e.g., NCAA v. Bd. of Regents, 468 U.S. 85, 99, 104 S.Ct. 2948, 82 L.Ed.2d 70 (1984) (“[M]ember institutions have created a horizontal restraint — an agreement among competitors on the way in which they will compete with one anoth *243 er.”); Fraser v. Major League Soccer, L.L.C., 284 F.3d 47, 57 (1st Cir.2002) (league acting in a horizontal capacity when board acts to control competition among members); Capital Imaging Assocs., P.C. v. Mohawk Valley Medical Assocs., 996 F.2d 537, 545 (2d Cir.1993) (horizontal analysis when HMO board excluded radiology practice group to “insulate” HMO’s member radiologists “from increased competition”); Rothery Storage & Van Co. v. Atlas Van Lines, Inc., 792 F.2d 210, 214 (D.C.Cir.1986) (horizontal restraint because “all of these legally separate corporations agreed to a policy that restricted competition”); NASL v. NFL, 670 F.2d 1249, 1252 (2d Cir.1982) (NFL bylaw banning cross-ownership of other professional sports league teams is a horizontal restraint).

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.

Without doubt the exclusionary rules in question harm competitors. The fact that they harm competitors does not, however, mean that they do not also harm competition. We find no fault with the district court’s finding that the exclusion of Amex and Discover from the ability to market their cards and programs to banks has harmed competition in the market for network services, and that Visa U.S.A. and MasterCard would be impelled to design and market their products more competitively if the banks to which they sell their services were free to purchase network services from Amex and Discover. Nor do we fault the district court’s determination that certain types of products combining unique features of cards offered by Amex and Discover with the advantages of linkage to cardholders’ bank accounts would likely become available. The district court was justified in finding harm to competition.

B Procompetitive Justifications

The defendants argue that even if the exclusionary rules do harm competition, those harms are outweighed by the policies’ substantial procompetitive effects. The defendants assert that the principal benefit of the exclusionary rules is to promote “cohesion” within the MasterCard and Visa U.S.A. networks, so that those networks may compete effectively in the marketplace. Thus, the defendants argue, the exclusionary rules are ancillary to legitimate, procompetitive business strategies. The district court found that the exclusionary rules are not necessary to accomplish that goal, and that in any event the anticompetitive effects outweigh the procompetitive. We believe the court’s finding was reasonable.

The district court found no evidence to suggest that allowing member banks to issue cards of rival networks would endanger cohesion in a manner adverse to the competitive process. Visa U.S.A., 163 F.Supp.2d at 402-06. MasterCard members have long been permitted to issue Visa cards, and vice versa, without such consequences. Moreover, as the district court noted, there is no evidence that the defendants’ network cohesion has been harmed overseas, where, in the absence of exclusionary rules, Amex has contracted with Visa and MasterCard member banks to issue Amex-branded payment cards. Id. at 407.

In sum, the defendants have failed to show that the anticompetitive effects of their exclusionary rules are outweighed by procompetitive benefits.

*244 IV Visa International

The district court held that Visa International was liable for violation of the Sherman Act. It ruled that “because Visa International not only had the power to preempt Visa U.S.A.’s exclusionary rule, but also provided affirmative encouragement for the illegal bylaw, Visa International was in part responsible for the illegal rule.” Visa U.S.A., 183 F.Supp.2d at 617. The conclusion that Visa International is liable was based on the district court’s factual finding that Visa International had provided affirmative encouragement. We cannot say that this finding was clearly erroneous or unsupported by the evidence. Nor do we believe, in the specific circumstances presented, that affirmative encouragement was an insufficient legal basis on which to premise liability. 5

CONCLUSION

The judgment of the district court is Affirmed.

Notes

. The government did not appeal from this ruling.

. The four major systems each issue credit and charge cards. A charge card requires that the balance be paid in full at the end of every billing cycle. A credit card allows customers to pay only a portion of the monthly *235 balance, charging interest on the unpaid balance.

. Visa U.S.A.'s by-law 2.10(e), passed in 1991, states,

The membership of any Member shall automatically terminate in the event it, or its parent, subsidiary or affiliate, issues, directly or indirectly, Discover Cards, or American Express Cards, or any other card deemed competitive by the Board of Directors. E-2897; SPA 97.

MasterCard’s CPP, passed in 1996, provides that

With the exception of participation in Visa, which is essentially owned by the same member entities, and several preexisting programs to the extent individual members participate ... members of MasterCard may not participate either as issuers or acquirers in competitive general purpose card programs. E-2265; SPA 101.

. Some authorities suggest that the market power requirement is unnecessary. See, e.g., FTC v. Indiana Fed’n of Dentists, 476 U.S. 447, 460, 106 S.Ct. 2009, 90 L.Ed.2d 445 (1986) ("Since the purpose of the inquiries into market definition and market power is to determine whether an arrangement has the potential for genuine adverse effects on competition, proof of actual detrimental effects, such as a reduction of output, can obviate the need for an inquiry into market power, which is but a surrogate for detrimental effects.” (internal quotation marks omitted)); NCAA v. Bd. of Regents, 468 U.S. 85, 110 n. 42, 104 S.Ct. 2948, 82 L.Ed.2d 70 (similar); KMB Warehouse Distribs. v. Walker Mfg. Co., 61 F.3d 123, 128-29 (2d Cir.1995) ("This court has not made a showing of market power a prerequisite for recovery in all § 1 cases.”). Whether market power is a necessary element is of no moment here; the district court found that the defendants had market power in the relevant markets, and as indicated below, we see no reason to question that finding.

. In the briefs, Visa International also challenges its inclusion in the injunction. At oral argument, however, Visa International withdrew this claim, indicating that its principal objection was to the district court’s finding of liability, not to its inclusion in the injunction. Tr. 26-29.