The provision of payment-clearing services is a big business for banks and other payment intermediaries. About $75 in U.S. payments is processed each year per $1 of U.S. gross domestic product, which translates into more than 90 billion payments valued in excess of $1,000 trillion per year. Estimates indicate that intermediating payment transactions accounts for about 38% of the largest U.S. banking companies' total operating revenues. In light of banks' significant role as payment intermediaries, Lacker and Weinberg suggest that more work should be done on "payment economics." Most of the work surveyed by Lacker and Weinberg examines large-value, or wholesale, payment systems-such as the U.S. Clearing House Interbank Payment System or the Fedwire system-from central-planning perspectives of monetary economists. Thus, much payment-economics work focuses on funds-market and various liquidity-, credit-, and systemic-risk issues germane to monetary theory and policy. This orientation perhaps helps to explain the employment of overlapping-generations models in the study of payment flows in overnight and intraday funds markets. Only a handful of studies relating to payment issues of acute concern to central banks employ an industrial organization perspective.
Nevertheless, industrial organization research is more relevant to regulation and antitrust issues confronted in retail payment systems, such as bank card payment networks, which over the years have been subjected to a variety of lawsuits, legal regulations, and antitrust actions. On the legal and regulatory front, most attention has been placed on interchange fees. In 1979, National Bancard Association unsuccessfully challenged in U.S. courts the existence of interchange fees, which a payment network charges an issuing bank on behalf of an acquiring bank. A few years ago, the Reserve Bank of Australia banned no-surcharge rules and began regulating interchange fees. In Denmark, interchange fees on domestic card payments are prohibited; in Sweden and the Netherlands, no-surcharge rules requiring retailers accepting a payment network's cards not to provide discounts for cash use are illegal; and in the European Union, the European Commission recently intervened to bring down interchange fees. On the antitrust front, U.S. payment card networks have faced Department of Justice challenges to restrictions on issuers and to a proposed merger between acquirers. Payment card networks have also confronted private lawsuits challenging the legality of "Honor All Cards" rules requiring retailers that honor a network's credit cards to accept its debit cards as well.
This article reviews and evaluates the public policy implications of recent studies that have sought to apply analysis of network externalities and the theory of two-sided markets to card payment networks. These studies reach mixed conclusions about the efficacy of regulating the fee structure of card payment networks. They provide support, however, for antitrust challenges of certain restrictive rules that some card payment networks have attempted to impose.
2. Two-Sided Markets and Network Externalities
Most analyses of credit card networks are based on the concept of two-sided markets. As shown in Figure 1, in a two-sided market, one or more platforms facilitate dealings between end users. In the case of a card-payment network, the network itself-for instance, Visa, MasterCard, Discover, or American Express-constitutes the platform. Network owners, which may or may not include banks, are platform providers. End users are retailers and cardholders.
Figure 1: A Two-Sided Card Payment Network
Figure 1 depicts a card network that may charge end users usage fees (uc and ur) and membership fees (mc and mr). Let's suppose for the time being-see discussion of membership fees below-that the card network platform assesses usage fees only, in which case a cardholder pays a per-dollar fee (uc) for each dollar of payments the network transmits to a retailer on behalf of the cardholder. From each dollar transmitted to the retailer, the network also deducts a usage fee equal to (ur). The total per-unit usage charge to end users, therefore, is (u = uc + ur).
If the overall transactions volume handled by the card network platform were to depend solely on this total price-that is, if changes in (uc) and (ur) with u unchanged had no effect on transactions volumes-then the market would only be one-sided. In this instance, only the overall price would influence end users. The network platform providers could vary that price without generating unbalanced reactions on the part of end users. In a two-sided market, however, variations in (uc) and (ur) bring about a change in the aggregate transactions volume even if the overall price u remains unchanged. Thus, changing the relative price structure alters total network activity. The network platform providers must specify a price structure that balances this asymmetry of price effects on the two sides of the market.
In the bank payment card industry, users' valuations of access to a given payment network vary with the number of other end users. For example, when more people opt to use cards issued by a particular network, an incumbent cardholder benefits from the fact that the expanded number of cardholders raises the likelihood that retailers will choose to accept the network's card. Hence, payment services provided by card networks are subject to network externalities, or third-party spillover effects.
Hayashi suggests that a key reason that retailers accept payment cards is transactional benefits in the form of sales that otherwise would not take place. In an analysis of retailers' motivations in accepting credit card payments, Chakravorti and To discuss an additional incentive, which is that accepting credit cards permits merchants to close current sales with illiquid consumers rather than confronting uncertainty regarding future sales. Rochet and Tirole argue that merchants' recognition of actual and anticipated sales expansions arising from network benefits to customers also internalizes those benefits, which expose merchants as well to network externalities. Merchants accept a payment platform's cards as long as fees are less than the internalized benefits.
Network externalities impinge on the balancing act that card payment networks must perform in developing their price structures. As discussed by Rochet and Tirole, the Coase theorem indicates that parties should be able use contracts internalizing usage externalities to attain a social optimum if property rights are clearly defined and if there is neither transaction cost nor asymmetric information. Transaction costs and constraints established by networks or policymakers that impede such welfare-improving contractual agreements, they suggest, accounts for the two-sidedness of the price structure of card payment networks.
Why do networks often charge membership fees as well as usage fees? It is well known from the literature on price discriminating two-part tariffs that including access fees can efficiently enable the recouping of fixed costs, which for issuers include marketing and advertising expenses and for acquirers include expenses in developing and maintaining payment-clearing systems. Membership fees such as those depicted in Figure 1 reflect the application of two-part tariffs within the overall pricing structure of card payment networks. In addition, Rochet and Tirole suggest that if cross-subsidization is part of an optimal pricing structure, portions of end-user surpluses can be captured via access prices such as membership fees. Recently, Armstrong has also provided an analysis of two-sided markets in which flat membership charges can assist in balancing externalities confronting end users.
3. Multiple Levels of Participation and Pricing Structures in Card Payment Networks
As explained by Schmalensee, fee structures of a card payment network depend on whether the network is proprietary-that is, operated as a profit-maximizing "closed network," as in the case of the American Express network-or cooperative-that is, operated by an association of coordinating institutions, such as Visa's "open network." The basic two-sided structure depicted in Figure 1 is most applicable to a unitary proprietary network that engages in all issuing and acquiring activity on its own behalf. An alternative proprietary system is a non-unitary system in which the network contracts with other parties, such as selected institutions that do some of the issuing and/or acquiring. In contrast, in a cooperative card payment network, independent institutions establish a contractual arrangement for coordinating card payments via the network.
Figure 2: Competing Card Payment Networks
Figure 2 provides a stylized depiction of co-existing card-payment networks. The figure displays two institutions, Bank i and Bank j, which are members of two networks. For simplicity, the figure shows Bank i as an issuer with respect to both card network platforms and displays, and Bank j as a payment acquirer with respect to the two platforms. Some banks perform both roles in cooperative networks, although increasingly banks that operate as acquirers contract with third parties to process payments.
As in Figure 1, banks potentially charge membership and usage fees to cardholders and retailers. The two networks depicted in Figure 2 also may charge banks the fees b1 and b2, which denote membership and/or usage fees and the fees f1 and f2, which denote interbank fees-the interchange fees that the network collects from issuing banks on behalf of acquiring banks. Baxter provided the first formal analysis of interchange fees within a bank payment-clearing association, which he showed must take into account the two-sided nature of the payment transactions. In Baxter's model with perfectly competitive net-issuing and net-acquiring banks, the association is indifferent about levels of the interchange fee-a result sometimes called "interchange-fee neutrality."
Schmalensee and Rochet and Tirole point out that imperfect competition yields considerably more scope for variation in pricing structures across card payment networks. Studies of networks' pricing structures often presume low search costs and little product differentiation on the acquiring side, which researchers often offer as support for assuming perfectly competitive behavior among acquirers, even though Evans and Schmalensee document increased concentration among acquirers. In contrast, such studies presume that search costs and the scope for product differentiation are greater on the issuing side, thereby resulting in some market power for issuers.
Some studies assume that rival card payment networks process a volume of transactions that is either arbitrarily fixed or essentially predetermined via an exogenously specified distribution of consumer transaction choices. In the context of a model in which issuers have no incentive to operate as acquirers, Rochet and Tirole conclude that the interchange fee that maximizes overall social welfare is never higher than the profit-maximizing level in the absence of other pricing complications such as surcharges for purchases with cash instead of cards. They find that in the absence of such surcharges, the profit- and output-maximizing interchange fees coincide, a situation in which a socially inefficient overprovision of payment cards can occur. When card surcharges are allowed, Rochet and Tirole's framework indicates that there can be an underprovision of payment cards, resulting in ambiguous welfare effects.
In the context of a framework in which retailers' benefits from network participation are heterogeneous, Wright shows that the welfare-maximizing interchange fee must balance the differing externalities faced by cardholders and retailers, with the profit-maximizing aggregate usage level typically lying below the socially optimal level. Wright separately finds that the welfare effects of imposing a "one-price policy" prohibiting surcharges for card purchases depends on the degree of market power possessed by retailers. Retailers possessing market power and the capability to impose surcharges will set prices to extract surplus from cardholders, thereby reducing revenues accruing to issuers. In the absence of retailer market power, however, a one-price policy results in a bifurcation of the retailing market into cash-only and card-only segments.
Schmalensee also studies the functioning of a single card payment platform in the context of a basic usage-pricing framework. He finds that a single unitary proprietary platform maximizing its own private value establishes a set of fees that generate the smallest transaction volume. Essentially, a unitary proprietary platform acts as a profit-maximizing monopoly and establishes a fee structure that restrains output of transaction services to the profit-maximizing level. A cooperative system, in contrast, aims to attain an output objective while covering operating costs; hence, it spreads payment volumes across the separate net-issuing and net-acquiring groups utilizing the payment network.
Within Schmalensee's single-network framework, which abstracts from banks' interactions with cardholders and presumes fixed weights in network decision-making by issuing or acquiring banks, the optimal interchange fee can be decomposed into two parts. One part depends on the difference between demand elasticities across cardholders and retailers. The other part depends on the difference in costs faced by issuers and acquirers. Schmalansee concludes that a cooperative platform typically will set a pricing structure that yields, relative to unitary and non-unitary proprietary platforms, the highest volume of payment transactions. Double-marginalization (or double-monopoly-markup) problems confront both cooperative and non-unitary networks, with the latter producing a volume of payment transactions that is intermediate between the volumes forthcoming from cooperative and unitary proprietary networks.
Eisenmann et al. contemplate governance issues faced by two-sided platforms including providers responsible for serving as users' primary point of contact, as sponsors determining who may participate in a platform-intermediated network, and as developers of its technological workings-much as banks do in card payment networks such as Visa and MasterCard. Eisenmann et al. argue that over time, two-sided networks tend to evolve into hybrids of proprietary and cooperative structures. In the long run, they conclude, such networks naturally gravitate toward centralized control over platform technology via closed sponsorship of a platform and shared responsibility for serving end users via open platform services. This could help explain why the American Express and Discover networks have recently sought to encourage participation by banks.
Bolt and Tieman study a model of a monopoly two-sided platform such as that depicted in Figure 1, and thus ignore interchange fees. In addition, they abstract from membership fees. In this simplified setting, they show that under the socially optimal pricing structure, the monopoly platform fails to cover its operating costs. As a consequence, they conclude, network externalities faced by the card payment platform create a second-best pricing problem analogous to that faced by a natural monopoly, in which first-best, allocatively efficient pricing generates negative economic profits. A possible consequence, Bolt and Tieman suggest, is a card payment network pricing structure that includes cross-subsidization schemes, higher interchange fees, and no-surcharge rules preventing retailer participants from giving discounts to customers who pay with cash.
When platform providers compete for end users, as in Figure 2, the range of pricing-structure complexities broadens considerably. Nearly all work analyzing such competitive, two-sided-network settings has appeared very recently. In these settings, end users can "multihome": Cardholders can participate in more than one network by utilizing more than one payment card, or retailers can accept cards from more than one network.
Rochet and Tirole briefly touch on the impacts of cardholder multihoming in competing payment systems. They contend that if one network seeks to undercut another by setting a slightly lower interchange fee, then retailers have an incentive to respond by accepting the former system's card and rejecting the card of the other system. The result is a potential reduction in welfare compared with the monopoly case.
In a more general framework, Rochet and Tirole examine a model that extends the setting in Figure 1 to the case of more than one platform competing for the same end users, in which "buyers" (cardholders in the payment-network context) utilize the services of differentiated platforms that either are profit-maximizing firms or non-profit associations. Rochet and Tirole include buyers and sellers of different types, with a network platform competing to obtain "marquee buyers"-cardholders that generate a particularly high surplus to retailers-from another platform while taking into account "captive buyers" that remain loyal to their initial platform choice. Other things being equal, the presence of marquee buyers naturally raises the seller price, but the presence of capital buyers skews the pricing structure to the benefit of sellers. Naturally, an increase in predisposition to multihoming on the part of buyers also is beneficial to sellers. These results could be sensitive, however, to Rochet and Tirole's assumption of no fixed membership fees, which Armstrong suggests could complicate joint determination of pricing structures in competing two-sided markets. Rochet and Tirole find that under some circumstances interchange fees could be lower and total market surplus greater in a monopoly setting than when two networks compete.
Cabral suggests, however, that Rochet and Tirole's ambiguous welfare results regarding monopoly versus competition among two-sided networks does not necessarily rule out the existence of other more-than-offsetting welfare losses that might arise from the existence of a monopoly network. A recent analysis by Chakravorti and Roson studies a variety of interactions between payment networks, including duopoly and cartel behavior with or without symmetry of the networks' payment instruments (such as credit cards offered by one platform and debit cards on another). Within their framework, which includes some simplifying assumptions such as monopolistic retailers, Chakravorti and Roson find that competition unambiguously raises the welfare of end users, although not generally uniformly, even in the case of symmetric competition.
Guthrie and Wright seek to classify the wide array of equilibrium pricing structures that can emerge from competition between two card identical payment platforms facing potentially multihoming cardholders and retailers. Guthrie and Wright find that either both networks set the same structure of fees with at least one side of end users (cardholders or retailers) multihoming, or only one network survives and attracts the exclusive participation of all end users. Guthrie and Wright conclude that in a setting with homogeneous retailers, competition between networks cannot boost fees charged to retailers. They argue that if retailers are more realistically heterogeneous, platform competition can yield higher fees for retailers, thus leading to higher interchange fees. The fee structure can be further biased against retailers if consumers choose a preferred card to hold and thereby benefit from platform competition that focuses on attracting cardholders rather than retailers. In contrast, if retailers know that cardholders always hold multiple cards, retailers can "steer" cardholders to their preferred network, resulting in platform competition focusing on attracting retailers, to the retailers' benefit.
Ambrus and Argenziano analyze a model of two-sided network competition. They allow for heterogeneous consumer valuations of external benefits, which results in equilibrium outcomes that include multiple networks. Equilibrium network configurations entail differentiation of network products and asymmetric pricing structures across networks. In the context of payment card networks, these conclusions suggest that sufficient heterogeneities across cardholder and merchant end users could yield a stable outcome with card networks offering differentiated payment services-as observed at present.
4. Regulatory and Antitrust Issues in Card Payment Networks
Is the common European practice of regulating interchange fees and no-surcharge rules appropriate? Should card-payment-network rules be subjected to antitrust scrutiny? There has been some initial work evaluating these regulatory and antitrust issues. Schmalensee, in his analysis of a single card network platform, finds that interchange fees under either cooperative or non-unitary proprietary systems are driven primarily by different weights within the network of net-issuing versus net-acquiring banks. He also finds that the proprietary, private-value maximizing interchange fee may be higher or lower than the output-maximizing fee of cooperative network platform providers. Furthermore, his analysis suggests that a policy action reducing the interchange fee potentially could depress network transactions output. Policy intrusions into the fee-setting process, Schmalensee concludes, could place cooperative networks at a competitive disadvantage with respect to proprietary networks, leading institutions to abandon higher-output cooperative networks in favor of lower-output proprietary networks. Thus, there is no clear economic argument in favor of antitrust policy that interferes in the setting of interchange fees.
Regulators often argue that fees should be purely cost-based. As Rochet and Tirole point out, however, applying this logic would yield the conclusion that governmental fee regulations should be applied to the television industry, newspapers, videogame platform providers, and other two-sided industries. On one hand, Rochet and Tirole question whether retailers actually experience harm as a result of interchange fees and suggest that some perceived harm may result from the fact that heterogeneous retailers internalize customer benefits at different levels. On the other hand, Rochet and Wang analyze a three-stage game with four parties-acquirers, issuers, consumers, and merchants-interacting within a single card network. They examine the role of intensity of issuer competition and conclude that consolidation among issuers could drive up interchange fees to the benefit of issuers and the detriment of merchants and consumers-a theoretical implication that they find receives support from U.S. data. Their model suggests that regulating the interchange fee to a lower level generates a revised pricing structure that, on net, engenders entry of new issuers and boosts the welfare of merchants and consumers. Not addressed by their single-platform framework is whether this result would hold true for competing networks.
Schwartz and Vincent utilize a model with variable transaction volumes to examine the implications of no-surcharge rules, such as those already imposed in some nations and that some observers argue should be adopted in the United States. Schwartz and Vincent suggest that such rules imbalance the fee structure between end users, resulting in harm to retailers. Networks respond by reducing cardholder fees and granting rebates to card users if possible, with cardholder welfare potentially declining if rebates are not feasible. Network profits increase, and overall welfare increases only if there are a sufficiently large number of cash users.
Rochet and Tirole examine effects of an honor-all-cards rule. In their benchmark model based on their earlier study, they find that such a rule not only benefits the multi-card network platform providers that impose it but also allows providers to optimally rebalance externalities across end users. The network then processes larger volumes of both credit and debit payments, resulting in greater social welfare, which implies that the 2003 U.S. court judgment (ruling the application of an honor-all-cards rule to multiple types of cards to be illegal) could be welfare-reducing. Generalizing their framework to allow for heterogeneous retailers, differentiated platforms, and varying substitutability between credit and debit transactions yields the same rebalancing effect on the mutli-card network's pricing structure. Welfare implications become ambiguous in this more general setting.
Emch and Thompson contemplate the application of the Department of Justice merger guidelines to card payment networks. Emch and Thompson show that it is possible that monopolization of a two-sided market considerably raises the prices charged to cardholders but not retailers, or vice versa. They derive price markup formulas for fees charged to end users and propose applying the guidelines' standard test for a "small but significant and non-transitory increase in price" that might result from a proposed merger to the sum of the prices the network charges to both groups of end users. White notes, however, that the pricing relationships derived by Emch and Thompson hinge their assumption of fixed proportions. He also concludes that their results likely depend on the simple two-sided framework they utilize, which more readily apply to proprietary networks than to open card associations.
Sun and Tse (2007) seek to examine the impacts of multihoming by applying a differential game analysis to both monopolistic and competing payment networks. They conclude that when end users engage in multihoming, networks can co-exist. The steady-state market shares of competing networks can, however, diverge considerably depending on participants' multihoming propensities. Sun and Tse also argue that network distributors, such as card issuers, play a crucial role in maintaining and expanding a network. Sun and Tse's analysis provides some measure of support for the Department of Justice's actions charging Visa and MasterCard with antitrust violations for their rules forbidding banks from becoming issuers of American Express and Discover cards.
Whereas monetary-theoretic frameworks of analysis emphasize how the nature of payments can complicate a monetary equilibrium, the industrial organization approach takes as given the monetary system in which payment networks are imbedded. Furthermore, in contrast to monetary-theoretic models of payment systems, the modern industrial organization approach focuses on the two-sided nature of bank card payment network platforms. This approach highlights the importance of two-sided pricing structures constructed with an aim to account for network externalities that differentially affect cardholders and retailers.
So far, this industrial organization approach has yielded several conclusions and policy implications. First, privately and socially optimal pricing structures of two-sided card payment networks entail a complicated balancing of incentives faced by end users confronting network externalities.
Second, platform providers typically will charge cardholders and retailers unbalanced fees. Optimal interchange fees must reflect this asymmetrical pricing structure, so regulation of interchange fees will not necessarily improve overall social welfare, nor will restrictions on payment networks' rules governing surcharges. Fee and rule regulations could well be harmful, although regulations may be more likely to boost the well-being of merchants and consumers when issuers possess market power.
Third, some recent work on decomposing the pricing structure of card payment networks suggests that it may be possible to develop methods of applying current antitrust policy guidelines to card payment networks. Nevertheless, this conclusion must be regarded as tentative given that this initial work is predicated on a number of simplifying assumptions.
Fourth, payment-platform rules requiring retailers to honor debit cards if they accept the network's credit cards are not necessarily anti-competitive. Such rules may be consistent with an aim to effectively balance interests of all end users within a coherent pricing structure. Nevertheless, more work must be done to establish conditions under which honor-all-cards rules are welfare improving rather than welfare reducing.
Finally, rules restricting participation of banks in competing networks may be anti-competitive. Efforts to steer banks away from a competing platform reduce its ability to establish a critical mass of distributors. Rules restricting bank participation in competing networks reduce the likelihood of a multihoming outcome involving multiple rival card payment networks, thereby potentially reducing social welfare.
David VanHoose is Professor of Economics and Lay Professor of Private Enterprise at the Hankamer School of Business at Baylor University. VanHoose also serves as a Senior Research Fellow at Networks Financial Institute, which has supported his work on the topic of his article.
 Charles Kahn and William Roberds, "Why Pay? An Introduction to Payments Economics," Journal of Financial Intermediation 18 (2009): 1-23.
 Lawrence Radecki, "Banks' Payment-driven Revenues," Federal Reserve Bank of New York Economic Policy Review 5 (1999): 53-70.
 Jeffrey Lacker and John Weinberg, "Payment Economics: Studying the Economics of Exchange," Journal of Monetary Economics 50 (2): 381-387 (2003).
 See, e.g., Charles Kahn and William Roberds, "Real-time Gross Settlement and the Costs of Immediacy," Journal of Monetary Economics 47 (2001): 299-319; Antoine Martin, "Optimal Pricing of Intraday Liquidity," Journal of Monetary Economics 51 (2004): 401-424; Joydeep Bhattacharya, Joseph Haslag, and Antoine Martin, Federal Reserve Bank of New York Staff Report No. 281, April 2007; and Cyril Monnet and William Roberds, "Optimal Pricing of Payment Services," Journal of Monetary Economics 55 (2008): 1428-1440.
 David VanHoose, "Central Bank Policy Making in Competing Payment Systems," Atlantic Economic Journal 28 (2000): 117-139; Cornelia Holthausen and Jean-Charles Rochet, "Efficient Pricing of Large Value Interbank Payment Systems," Journal of Money, Credit, and Banking 38 (2006): 1797-1818.
 See Sujit Chakravorti, "Theory of Credit Card Networks: A Survey of the Literature," Review of Network Economics 2 (2003): 50-68.
 See, e.g., Jean-Charles Rochet and Jean Tirole, "Two-sided Markets: A Progress Report," Rand Journal of Economics 37 (2006): 645-667.
 Fumiko Hayashi, "A Puzzle of Card Payment Pricing: Why Are Merchants Still Accepting Card payments?" Review of Network Economics 5 (2006): 144-174.
 Sujit Chakravorti and Ted To, "A Theory of Credit Cards," International Journal of Industrial Organization 25 (2007): 583-595.
 Jean-Charles Rochet and Jean Tirole, "Externalities and Regulation in Card Payment Systems," Review of Network Economics 5 (2006): 1-25.
 Rochet and Tirole, "Two-sided Markets."
 Mark Armstrong, "Competition in Two-Sided Markets," Rand Journal of Economics 37 (2006): 668-691.
 Richard Schmalensee, "Payment Systems and Interchange Fees," Journal of Industrial Economics 50 (2002): 103-122.
 William Baxter, "Bank Interchanges of Transactional Paper: Legal and Economic Perspectives," Journal of Law and Economics 26 (1983): 541-588.
 Schmalensee, "Payment Systems"; Jean-Charles Rochet and Jean Tirole, "Cooperation among Competitors: Some Economics of Payment Card Associations," Rand Journal of Economics 33 (2002): 549-570.
 David Evans and Richard Schmalensee, "Paying with Plastic: The Digital Revolution in Buying and Borrowing," (Cambridge, Massachusetts: MIT Press, 1999).
 Rochet and Tirole, "Cooperation among Competitors"; Wilko Bolt and Alexander Tieman, "Social Welfare and Cost Recovery in Two-sided Markets," Review of Network Economics 5 (2006): 103-117; Julian Wright, "Optimal Card Payment Systems," European Economic Review 47 (2003): 587-612; Julian Wright, "The Determinants of Optimal Interchange Fees in Payment Systems," Journal of Industrial Economics 52 (2004): 1-26.
 Rochet and Tirole, "Cooperation among Competitors."
 Wright, "Optimal Card."
 Wright, "Determinants."
 Shmalensee, "Payment Systems."
 Thomas Eisenmann, Geoffrey Parker, and Marshall Van Alstyne, "Opening Platforms: How, When, and Why?" in Platforms, Markets, and Innovation, ed. Anabelle Bawer (Cheltenham, UK: Edward Elgar, 2008).
 Bolt and Tieman, "Social Welfare."
 Rochet and Tirole, "Cooperation among Competitors."
 Jean-Charles Rochet and Jean Tirole, "Platform Competition in Two-sided Markets," Journal of the European Economic Association 1 (2003): 990-1029.
 Armstrong, "Competition in Two-Sided Markets."
 Luis Cabral, "Market Power and Efficiency in Card Payment Systems: A Comment," Review of Network Economics 5 (2005): 15-25.
 Sujit Chakravorti and Roberto Roson, "Platform Competition in Two-sided Markets: The Case of Payment Networks, Review of Network Economics 5 (2006): 118-140.
 Graeme Guthrie and Julian Wright, "Competing Payment Schemes," Journal of Industrial Economics 55 (2007): 37-67.
 Attila Ambrus and Rossella Argenziano, "Asymmetric Networks in Two-sided Markets," American Economic Journal: Microeconomics 1 (2009): 17-52.
 Schmalensee, "Payment Systems."
 Jean-Charles Rochet and Jean Tirole, "Competition Policy in Two-sided Markets, with a Special Emphasis on Payment Cards," in Handbook of Antitrust Economics, ed. Paulo Buccirossi (Cambridge, Massachusetts: MIT Press, 2008), 543-582
 Rochet and Tirole, "Externalities and Regulation."
 Jean-Charles Rochet and Zhu Wang, "Industry Concentration and Credit Card Pricing Puzzles," unpublished manuscript, Toulouse University and Federal Reserve Bank of Kansas City, 2009.
 Marius Schwartz and Daniel Vincent, "The No Surcharge Rule and Card User Rebates: Vertical Control by a Payment Network," Review of Network Economics 5 (2006): 72-102.
 See, e.g., Nicholas Economides, "Competition Policy Issues in the Consumer Payments Industry," in Moving Money: The Future of Consumer Payments, eds. Robert Litan and Martin Neil Baily (Washington, DC: Brookings Institution Press, 2009), 113-126.
 Schwartz and Vincent, "No Surcharge Rule."
 Jean-Charles Rochet and Jean Tirole, "Tying in Two-sided Markets and the Honor All Cards Rule," working paper, Toulouse University, February 9, 2006.
 Rochet and Tirole, "Cooperation among Competitors."
 Eric Emch and T. Scott Thompson, "Market Definition and Market Power in Payment Card Networks," Review of Network Economics 5 (2006): 45-60. For a detailed discussion of these guidelines, see David VanHoose, "Policy Implications of Endogenous Sunk Fixed Costs in Banking: Has U.S. Antitrust Policy Been on the Wrong Track?" Networks Financial Institute policy brief PB-2008-06, December 2008.
 Lawrence White, "Market Definition and Market Power in Payment Card Networks: Some Comments and Considerations," Review of Network Economics 5 (2006): 61-71.
 Mingchun Sun and Edison Tse, "When Does the Winner Take All in Two-sided Markets?" Review of Network Economics 6 (2007): 16-40.