Full text of Working Papers (Federal Reserve Bank of Chicago) : Platform Competition in Two-Sided Markets : The Case of Payment Networks, Working Paper 2004-09

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

Federal Reserve Bank of Chicago

Platform Competition in
Two-Sided Markets:
The Case of Payment Networks
Sujit Chakravorti and Roberto Roson

WP 2004-09

Platform Competition in Two-Sided Markets:
The Case of Payment Networks
Sujit Chakravorti

Roberto Roson

∗

July 5, 2004

Abstract
In this article, we construct a model to study competing payment networks, where networks offer differentiated products in terms of benefits to
consumers and merchants. We study market equilibria for a variety of market structures: duopolistic competition and cartel, symmetric and asymmetric networks, and alternative assumptions about multihoming and consumer
preferences. We find that competition unambiguously increases consumer
and merchant welfare. We extend this analysis to competition among payment networks providing different payment instruments and find similar results.
JEL Classifications: D43, G21, L13
Key words: two-sided markets, payment systems, network externalities, imperfect competition

∗

Chakravorti: Research Department, Federal Reserve Bank of Chicago, 230 S. LaSalle Street,
Chicago, IL 60604, U.S.A. E-mail: sujit.chakravorti@chi.frb.org. Roson: Economics Department, Universita’ Ca’ Foscari di Venezia, Cannaregio S. Giobbe 873, 30121 Venice,
Italy. E-mail: roson@unive.it. We thank Wilko Bolt, David Evans, Jean-Charles Rochet,
Jean Tirole, Tuomas Takalo and participants at the Economics of Two-Sided Markets conference
held at the University of Toulouse, the Economics of Payments conference held at the Federal Reserve Bank of Atlanta and the 2004 International Industrial Economics conference for comments
on previous drafts. The views expressed are not necessarily those of the Federal Reserve Bank of
Chicago or the Federal Reserve System.

1 Introduction
Two-sided markets are defined as a platform(s) providing goods and services to
two distinct end-users where the platform attempts to set the price for each type
of end-user to “get both sides on board” because the benefits of one type of
end-user increases as the participation of the other type of end-user increases.
Armstrong (2002), Evans (2003), and Rochet and Tirole (2003) suggest various
examples of two-sided markets such as yellow pages (advertisers and users), adobe
acrobat (creators of documents and readers), and television networks (viewers and
advertisers). In this paper, we study an example of a two-sided market–payment
networks (consumer and merchants).
Recently, antitrust authorities and courts in several jurisdictions have investigated the business practices of payment networks. In the United States, the Government sued MasterCard and Visa alleging anticompetitive business practices.
The court ruled that MasterCard and Visa must allow financial institutions to issue competitor network credit cards such as American Express and Discover (see
United States v. Visa U.S.A., Inc. (2001)). In another U.S. case that was settled
out of court, around 5 million U.S. merchants sued the two card associations alleging an illegal tying of the associations offline debit cards and credit cards. The
card associations agreed to unbundle their offline debit card branded product from
their credit card branded product. In Australia, the Reserve Bank of Australia
set rules for the determination of interchange fees, removed no-surcharge restrictions, and reduced barriers for entry to the market for credit card services (see
Reserve Bank of Australia (2002)). The authorities in the European Commission
and the United Kingdom have also investigated the business practices of the card
associations (see European Commission (2002) and Cruickshank (2000)). These
investigations has led to the development of several theoretical models to study
pricing of payment services.
In this paper, we study the pricing strategies of payment networks that maximize the joint profits earned from both types of end-users. Recent investigations
of these markets have focused on the determination of various prices including interchange fees, merchant discounts, and retail prices of goods and services within
a single payment platform (see Chakravorti and Emmons (2003), Chakravorti and
To (2003), Rochet and Tirole (2002), Schmalensee (2002), Schwartz and Vincent
(2002), Wright (2003) and Wright (2004)). 1 Often policy discussions have focused on whether each participant is paying her fair share of the underlying cost
1

For summary of these papers and others, see Chakravorti (2003).

1

of the payment service.
Recently, Guthrie and Wright (2003) and Rochet and Tirole (2003) have investigated pricing decisions by payment networks when there are competing payment platforms. We build upon these two models by considering joint distributions for consumer and merchant benefits from participating on each network. In
other words, each consumer and merchant is assigned a network-specific level
of benefit from participating on each network. Consumers and merchants base
their payment network usage decision on the difference between their individual
network-specific benefit and that network’s participation fee. Our model also differs because we consider the effects of competition on price level and price structure. Unlike Guthrie and Wright, we consider fixed fees instead of per-transaction
fees for consumers.2 We focus on the case where consumers choose to participate
in only one payment network, often referred to in the literature as singlehoming,
and merchants that are able to accept payment products from both networks, often referred to as multihoming. We consider three types of market structures for
payment networks: cartel, non-cooperative duopoly under product differentiation,
and Bertrand duopoly (price competition for homogeneous products). We find
that competition unambiguously improves consumer and merchant welfare while
reducing the profits of payment networks. Competition also affects the price structure. However, at a given price level, the price structure in a competitive duopoly
may not be welfare-efficient.

2 Literature Review
While the literature on network effects is well established (see Farrell and Saloner (1985) and Katz and Shapiro (1985)), this literature ignores how to price
services for two different sets of consumers where each set of consumer benefits from an increased level of participation by the other. Recently, several papers have investigated price structures in two-sided markets with network effects.
Armstrong (2002), Caillaud and Jullien (2001), Jullien (2001), Rochet and Tirole
(2003), and Schiff (2003) explore platform competition for various industries. A
major contribution of this literature is that different types of consumers may not
share equally in the costs of providing the good or service. In some cases, one-type
of end-user may be subsidized. Many of the results depend on the accessibility of
2

Rochet and Tirole (2003) consider fixed fees as an extension of their model but restrict one
side of the market to singlehome.

2

different types of consumers to different platforms, the underlying fee structure,
and their demands for services from a specific platform.
An example of a two-sided market with network effects is the market for payment services. Rochet and Tirole (2004) state that a necessary condition for twosided markets is the failure of Coase theorem. A key observation in the market for
payment services is that the law of one price generally prevails. In other words,
merchants are reluctant to charge different prices based on the underlying cost of
each payment instrument.3 The charging of one-price implies that there is not
complete pass-through of the cost of payment instruments. However, Rochet and
Tirole argue that the failure of Coase theorem is not sufficient for a market to be
two-sided. They state that for a given price level, if the price structure affects the
total volume of transactions on the platform, the market is said to be two-sided.
Several models have shown that the interchange fee is not neutral under one-price
policies and imperfect goods markets (Frankel (1998) and Gans and King (2003)).
Most of the payment network literature has only considered a single payment
platform. Baxter (1983) models a four-party open network consisting of consumers, merchants, and their respective banks.4 Payment providers charge consumers and merchants usage fees. The merchant’s payment provider usually pays
an interchange fee to the consumer’s payment provider. He finds that to balance
the demands for payment services by consumers and merchants, an interchange
fee may be required to compensate the financial institution that serves the group
that benefits less and/or faces higher costs to bring that group on board. Rochet
and Tirole (2002), Wright (2003), and Wright (2004) expand on Baxter by considering the effects of strategic interactions among payment system participants
on the determination of the interchange fee.
Rochet and Tirole (2003) consider platform competition generally and investigate some characteristics of payment markets. First, they provide a general
framework to model platform competition that is applicable to various markets.
Second, they are able to characterize the determinants of price allocation between
end-users. There may be instances where one end-user subsidizes the other. Third,
3

There is a long legal and regulatory history in the United States concerning the
charging of different prices depending on the type of payment instrument used (see
Chakravorti and Shah (2003)). Even in countries, where merchants face no restrictions to impose different prices, few merchants choose to do so (see IMA Market Development AB (2000)
and Vis and Toth (2000)).
4
There are also closed or proprietary networks where one entity serves all consumers and merchants that are members and operates the network. Examples of such networks include American
Express and Discover in the United States.

3

they find that the seller’s price (could be viewed as the merchant discount in the
payment services context) increases with captive buyers (buyers could be viewed
as consumers in the payments context) and decreases when there are marquee
buyers under certain conditions. Similarly, the buyer’s price moves in the opposite direction. Captive buyers prefer to use a certain platform and marquee buyers
are coveted by sellers.
Guthrie and Wright (2003) also model competing payment networks where
merchants use card acceptance as a strategic tool. They assume per-transaction
costs for both consumers and merchants and each network’s benefit is identical to
their competitors. Their main result is that when consumers hold only one card,
competition between payment networks does not result in a lower interchange fee.
However, if some consumers are able to hold more than one card, equilibrium interchange fees are lower if merchants are monopolists. If merchants compete for
customers, merchants are willing to pay higher interchange fees potentially erasing any reduction in interchange fees.
Schiff (2003) explores platform competition in a Cournot duopoly, focusing
on the effects of benefit asymmetry, for the two sides, on the market equilibria. He finds that multiple equilibria may occur for some parameter values. He
also considers the possibility of having “open systems,” where subscribing to a
network gives access to all agents on the other side of the market (independent of
their network affiliations). In his framework, competing platforms have incentives
to make their systems open.5
Our model differs from the existing literature in several ways. First, we focus on competing payment networks that offer payment instruments that have
independent benefits and costs for consumers and merchants. In other models,
consumers and merchants are indifferent between the benefits of each network.
As a result, we are able to compare differences in consumer and merchant preferences to each network’s products. For example, certain consumers may prefer
to pay with one network’s debit card while others may prefer to pay with another
network’s debit card.6 Consumers may prefer one network’s product over another’s based on the types of services offered or the status of being a member. We
also consider competition among different types payment instruments offered by
different networks. Consumers not only choose among networks for a type of pay5

This is equivalent to a special access regime (peering) used, especially, on the Internet. The
economics of peering access is investigated in Little and Wright (2000), and Roson (2003).
6
In the United States, there are two types of debit card networks–signature-based cards that
use credit card networks to process transactions and PIN-based cards that use the ATM networks
to process transactions. These types of transactions have different pricing structures.

4

ment instrument, but also choose among different types of payment instruments.
We consider this case as an extension of our model.
Second, we consider the effects of competition on price level and price structure. Rochet and Tirole (2003) assume a small fixed level of profits for both
issuing and acquiring sides in a non-profit joint-venture network. In reality, in
both credit card and debit card markets, for-profit and non-profit networks coexist. They consider welfare effects of changes in the price structure at a given
price level. Similarly, Guthrie and Wright (2003) consider only welfare effects of
changes in price structure and not of changes in the price level. In most of the
model variants presented in these papers, networks maximize profits by maximizing the volume of transactions. This is important because, in many circumstances,
social welfare maximization also implies maximizing the volume of transactions.
In our model, maximizing profits is not generally the same as maximizing the
volume of transactions, meaning that market prices are not necessarily welfare
optimal.
Third, in our model, each network serves as both issuer and acquirer. Therefore, we do not explicitly model the interchange fee. However, we can implicitly
consider interchange fees if there are differences in the demands of both types
of end-users for the payment services and/or differences in costs to provide these
services to the distinct type of end-users.
Fourth, in our model, consumers pay fixed membership fees and merchants
pay per transaction fees. The introduction of fixed fees may restrict consumers
from multihoming. We will explore the effects of this assumption below.

3 The Model
We construct a one-period model of payment network competition with three
types of agents. There are two payment network operators. There are a large
number of consumers (C) and a large number of merchants (M). Consumers
demand one unit of each good and purchase goods from each merchant.
To focus on the choice of payment instrument, consumers and merchants derive utility based on the type of payment instrument used. There are three payment instruments. Cash is the default payment instrument available to all consumers and merchants at zero cost yielding zero utility for both consumers and
merchants.7 There are two payment networks each offering a payment product
that is associated with positive benefits for most consumers and merchants. These
7

In reality, the cost of cash transactions is not zero and the utility of using cash is not zero. The

5

networks may offer similar products such as different types of credit cards or offer different types of instruments such as credit and debit cards. Each network
provides services to both consumers and merchants directly and must recover the
total cost of providing these services.
The total benefits, obtained by a consumer from being a member of a network,
is given by a per-transaction benefit, hci , multiplied by the number of merchants
accepting the payment product, Dim . For each consumer, per-transaction benefits,
hci , are independently distributed via a cumulative distribution with support [0, τ i ],
where i ∈ {1, 2} is an index referring to the specific payment network. Consumer
benefits may include convenience, extension of short-term and long-term credit,
security, and status.
Unlike Rochet and Tirole (2003) and Guthrie and Wright (2003), we consider
network benefits that are platform-specific. This is a key difference in our model.
We motivate this difference by observing that different card networks provide different benefits to different consumers. For example, charge cards, instruments
where consumers are not allowed to revolve balances, coexist with credit cards,
instruments where consumers are allowed to revolve. The pricing structures differ
between these two instruments as well. Charge cards such as American Express cards have traditionally charged higher fees than Visa and MasterCard cards
where issuers earn revenue from finance charges to revolvers. Another example
is the coexistence of signature-based and PIN-based debit cards where there are
different price structures between these products. In our model, we allow some
consumers to have strong preferences for a given network’s product and allow
other consumers to have weaker preferences so that price structures may affect
usage decisions.
Consumers pay an annual fee, fic , to access the payment system, allowing
them to make an unlimited number of payments. 8 While most U.S. issuers do
not impose annual fees, some credit and debit card issuers that offer additional
enhancements such as frequent-use awards impose annual fees. Generally, most
European issuers impose annual fees.
We assume fic is sufficiently high such that each consumer holds only one
card.9 Utility from card holding is given by the difference between total benekey assumptions here are that cash transactions cost less than any other type of transaction and
that the utility from using cash is less than that of using other payment instruments.
8
Guthrie and Wright (2003) do not consider fixed fees. Rochet and Tirole (2003) consider
fixed fees as a special case of their model. The introduction of fixed fees does not allow for the
consideration of multihoming consumers and merchants in an easily tractable model.
9
Given the marginal cost for card usage is zero and the marginal benefit is positive, consumers

6

fits from all transactions and the fee. Therefore, the total benefit to consumers
increases as merchant acceptance increases. Once a consumer becomes a member of a payment network, we assume the consumer uses that network’s payment
product exclusively with merchants that accept it. In other words, non-cash purchases dominate cash purchases for those consumers that are members of a payment network.
Each merchant is a monopolist selling an unique good.10 Merchant benefits
could include security, convenience, and status. Merchants pay a per-transaction
fee for each transaction, fim , but cannot set different prices based on the payment
instrument used.11 A payment type will be accepted whenever the per-transaction
benefit hm
i (which is drawn randomly from a cumulative distribution function
m
Fi , with support [0, µi ]) exceeds the per-transaction fee. Note that: (1) acceptance choices are independent, and (2) acceptance does not depend on the number
of consumers that are members of that payment network whereas a consumer’s
choice depends on the number of merchants accepting the payment card. 12 There
are three types of merchants. Those that accept neither of the payment network’s
products because the benefit from accepting them is lower than the fee charged.
Other merchants will only accept one of the payment network’s products because
while the net benefit of one network is positive, the other is negative. Finally,
some merchants will accept both non-cash payment products because there are
positive benefits from doing so.
To sum up, utility for the representative consumer, U c , and merchant, U m , can
be expressed as:
U c = max{0, hc1 D1m − f1c , hc2D2m − f2c }

(1)

m
c
m
m
U m = max{0, D1c (hm
1 − f1 )} + max{0, D2 (h2 − f2 )}

(2)

will prefer to use this instrument for all transactions. Similar arguments have been made for check
usage in the United States, see Chakravorti and McHugh (2002).
10
Note that by construction, we ignore business stealing effects. Other models, such as
Guthrie and Wright (2003), have shown that business stealing incentives may allow network operators to charge higher fees to merchants.
11
Pricing restrictions on merchants may take various forms. Non-discrimination pricing polices
prohibit merchants from setting different prices based on the payment instrument used. In the
United States, merchants are allowed to extend discounts for purchases made with non-credit
card payment forms. However, card association rules usually prohibit surcharges for credit card
purchases in most jurisdictions.
12
Clearly, if merchants are restricted to choosing only one payment network, the number of consumers that are members of a payment network would affect the merchants’ choice of networks.

7

where Dic is the number of consumers holding network i’s instrument and D im is
the number of merchants accepting network i’s product. 13
Payment networks face two kinds of costs: a consumer fixed cost, gi , and a
merchant per-transaction cost, ci . Networks maximize the following:
Πi = (fic − gi )Dic + (fim − ci )Dic Dim

(3)

Networks choose simultaneously and non-cooperatively the consumer and merchant fees, taking the other network choices as given (a Nash equilibrium). Timing is as follows:
• Consumer and merchant benefits are randomly drawn;
• Networks maximize profits, by choosing fic and fim ;
• Merchants decide which payment forms to accept;
• Consumers decide which payment option to purchase;
• Transactions are realized.
The number of accepting merchants is determined, on the basis of the distribution function F im :
(4)
Dim = (1 − Fim (fim ))M
Note that merchants accept non-cash payment alternatives as long as their benefits
from doing so are greater than their costs. Because merchants only face pertransaction fees, they need only have one consumer using the network’s product
to accept it as long as the benefit is greater than the cost.
The consumer side of the market is more complicated. To be chosen, a card
has to pass two tests: (1) consumers must derive positive utility, and (2) the utility
derived from this payment form must be higher than the other payment form. The
market shares can be identified as in figure 1, where each consumer is mapped
to a point, whose coordinates (hci Dim , hcj Djm ) express total potential benefits from
using card i or j.
In figure 1, the large rectangle is divided into six parts. Consumers falling
inside the smaller rectangle in the bottom left do not join either payment network,
13

Because we assume that consumers singlehome and always prefer to use non-cash payment
alternatives, we equate membership in a payment network with usage of its product when merchants accept the payment product.

8

Figure 1: Network’s share of consumers

9

as their benefits are smaller than the membership fees of either network. Other
consumers become members of either payment network i if in rectangle B or
payment network j if in rectangle A. When both networks are associated with
positive utility, consumers choose on the basis of relative utility, and the border
between the two market areas is given by the 45 degree segment that splits the
square into triangles C and D. Consumers in area E also choose a network on
the basis of relative utility, but their choice is primarily determined by the number
of accepting merchants. For this reason, only the network offering the highest
consumer surplus (τ Dm − f c ) attracts consumers in an area like E, which is
absent if networks are symmetric and apply equal prices to both consumers and
merchants.
Assuming uniform and independent random variables for consumer benefits
for each payment product, the consumer demand for each network can be written
as:
Dic =

(mi − fic )fjc + .5w2 + (mi − fic − w)w
C
mi mj

(5)

Djc =

(mj − fjc )fic + .5w2 + (mj − fjc − w)w
C
mi mj

(6)

and

where:
w = min(mi − fic , mj − fjc )
mi = τi Dim

mj = τj Djm

Profit Maximization
When choosing the consumer and merchant fees, fic and fim , each payment network maximizes profits, given by equation 3. It may be shown that optimal fees
obey the following principle:
Proposition 1 Profit maximizing fees can be determined on the basis of a “mod-

10

ified Lerner rule” that is:14
pc + f m − c =
where pc =
and:

f c −g
Dm

pc
fm
=
c
m + cm − m c

(7)

is the per-transaction revenue and cost from serving a consumer,
c =

∂Dc pc
∂Dc
1
=
c
c
c
c
∂p D
∂f (f − g)Dc
cm =
m =

∂Dc f m
∂f m Dc

∂Dm f m
∂f m Dm

Proof. Following Rochet and Tirole (2003), substitute into equation 3, and consider the following problem:
max log Πi = log(pci + fim − ci ) + log Dic + log Dim

pci ,fim

(8)

Assuming log-concavity, equation 7 is obtained from simple manipulations of
first-order conditions of the maximization problem 8, observing that:
f c − g ∂Dm
pc m
∂pc
=− m 2
= m
∂f m
(D ) ∂f m
f




Proposition 1 highlights that the problem of setting optimal fees can be decomposed in two parts: the choice of the global price level p ci + fim , and the
problem of balancing the relative prices p ci /fim .
When demand functions are expressed as in equations 4, 5, and 6, the distribution of merchant benefits is uniform in the interval [0, µ], and markets have both
unitary mass, network elasticities are:
14

This result is an adaptation of a finding obtained by Rochet and Tirole (2003), who derive first
order general conditions for profit maximization in a two-sided market. In deriving these conditions, however, they ignore the effect of a variation in network size on the price level. Equation
7 translates the result of Rochet and Tirole for our case, while taking into account the effect of
network size on the consumer price. The result does not depend on specific assumptions about
benefit distributions.

11

fic + w
(fic − g)τi τj Dim Djm Dic
τi fim (fic + w)
τi fim
=
−
cm
i
µi τi τj Dim Djm Dic µi τi2 τj (Dim )2 Djm
fim
m
=
i
µi Dim
ci =

(9)

The Effects of Competition on Prices and Welfare
To see how competition affects the market equilibrium, we now consider two
cases: a duopoly, where each network maximizes its profits, assuming the competitor’s fees as given, and a monopoly, where an hypothetical cartel maximizes
the sum of the two networks’ profits. The difference between the two cases is
given by the fact that a monopolist internalizes any pecuniary externality, that is,
any effect of a price change in the other operator’s profit. In other words, the
cartel maximizes the sum of the two profit functions, as defined in equation 3.
Furthermore, as the following proposition states, pecuniary externalities have an
unambiguous effect on the price level and welfare.
Proposition 2 In the market for payment services defined above, the sum of consumer and merchant prices in duopoly are always lower than in monopoly, so
that competition is always welfare enhancing for both consumers and merchants.
Indeed, lower merchant fees increase merchant welfare and, indirectly, consumer
welfare because of the higher number of accepting merchants. Lower consumer
fees increase consumer welfare and, indirectly, merchant welfare because of the
higher number of consumers in a network.
Proof. Since the number of of subscribing merchants is unaffected by the other
network prices, cross-effects on profits only operate through changes in the consumers’ demand volume:
c
∂Dic
Πi ∂Dic
∂Πi
c
m
m ∂Di
=
(f
−
g)
+
(f
−
c)D
=
>0
i
i
i
∂fjc
∂fjc
∂fjc
Dic ∂fjc
c
∂Dic
Πi ∂Dic ∂Djm
∂Πi
c
m
m ∂Di
=
(f
−
g)
+
(f
−
c)D
=
>0
i
i
i
∂fjm
∂fjm
∂fjm
Dic ∂Djm ∂fjm

12

(10)

where the sign of both relationships is obtained from the definitions of utility 1
and 2.
An increase in both merchant and consumer fees applied by the competitor
network expands the consumer demand. Consequently, the profit of a network
increases if the competitor raises its prices. This is the conventional pecuniary
externality due to competition. The perceived price elasticity of a competitive
network will always be larger than that of a monopolistic cartel, and competition
unambiguously reduces both merchant and consumer fees.


In the model with uniform and independent distributions for consumer and
merchant benefits, cross price derivatives (and elasticities) are, in general, discontinuous, but they can be written in a compact way, using the notation introduced
above:
w
∂Dic
=
C>0
c
∂fj
mi mj
∂Dic
∂Dic ∂mj
=
∂fjm
∂mj ∂fjm



mi − fic − w Dic −τj
−
CM
=
mi mj
mj µj
 c
Di τ j

w = mi − fic

 mj µj CM > 0
=

(11)
(12)


2
c 2

 (mj ) −(fj2) τj CM > 0 w = mj − f c
j
2mi (mj )
µj

Proposition 2 has a simple intuitive explanation. A two-sided network has
two instruments to attract more consumers: the prices applied to consumers and
merchants. Both instruments, however, work to the same direction, expanding
one network and reducing the competitor’s one. Despite the existence of two
price instruments, pecuniary externalities work in the standard way.
This finding, intuitive as it may seem, is actually in sharp contrast with most
recent literature on competition in credit card networks (e.g., Rochet and Tirole
(2002), Guthrie and Wright (2003)), where it is shown that competition may be
harmful for consumers and merchants. The key difference between our approach
and the previous literature is that the latter is based on the (sometimes implicit)
assumption of constant profits of the financial institutions of consumers and merchants and an often zero profit condition for the network itself.
13

If profits are constant for member banks, the main effect of competition is
altering the price balance on the two market sides. However, as we show in the
appendix, the equilibrium price structure is not generally welfare-efficient neither
in competition nor in monopoly. In both cases, it would be possible to achieve
higher aggregate welfare levels by reducing the price on one side, while increasing
the price on the other side, so as to keep global network profits unchanged. The
move from monopoly to competitive duopoly may not help in this sense. However,
if profits are unconstrained, the overall price reduction dominates the effects on
the price structure and welfare unambiguously improve for both sides.
It should be stressed that we retain the existence of two alternative platforms,
even in the monopolistic setting. On the contrary, Schiff (2003) considers a monopoly with a single platform, finding that welfare may improve when switching
from duopolistic competition to monopoly. Prices actually increase, but a single
standard is imposed, which is beneficial in the presence of network externalities.
This result may not hold in our model, however, because we consider networkspecific preferences. Therefore, like in a monopolistic competition model, the
trade-off between economies of scale and “taste for variety ” should be taken into
account.
Symmetric Competition
If networks are perfectly symmetric, equilibrium prices, in all market structures,
must be equal. Guthrie and Wright (2003) consider some cases of symmetric
competition between payment platforms. They focus solely on the price balance
effect of competition, because they consider either a bank association with fixed
margins on the two market sides, or proprietary schemes subject to Bertrand-like
competition, dissipating profits. This implies that, in their model, total revenue is
constant in all market structures.
In our model, market competition reduces total prices and increases merchant
and consumer welfare. However, the price reduction is not, in general, uniform in
the two sub-markets. To see this, consider the effects of a reduction in merchant
and consumer fees on the other network’s demand volume. Figure 2 provides a
graphical illustration of changes in market sizes generated by a reduction of consumer fee, whereas figure 3 provides a representation of the effects of a merchant
fee reduction.
When the consumer fee is reduced in a network, the network’s demand expands because some new customers are convinced to choose this platform. Among
these customers, some were not subscribing to any card before, whereas some others are now switching from the other network.
14

Figure 2: Market share effects of a reduction in a consumer fee

15

Figure 3: Market share effects of a reduction in a merchant fee

16

A reduction in a merchant fee, on the other hand, has an indirect effect on the
other network demand. A reduction in the merchant fee affects the merchant’s
demand, which in turn affects the consumer’s demand: m shifts outward. The
area corresponding to the competing network’s market share does not change, but
the density of the consumers in the rectangle decreases.
Because of this “stretching effect” some consumers, previously associated
with points slightly to the left of the 45 degree segment in figure 3, are now found
to the right of this dividing line, in another market area. 15 These consumers are
switching to the alternative network, not because consumer fees are lower there,
but because there is a larger base of accepting merchants.
In a monopolistic two-sided market, a network operator selects prices to balance the two sides of the market (to get “both sides on board”). Under competition, the competitive pressure may be different in the two sub-markets, and the
price structure, which emerges in equilibrium, depends on the different market
conditions. In other words, competition does not simply drive the prices down,
but also alters the balance of prices.
In our model, a key factor, determining the relative degree of competition
between the two market sides, is given by:
τM
∂m
=
−
∂f m
µ
that is, the factor translating a reduction in f m into an outward shifting of m.
We provide simulations of various equilibria to demonstrate relationships between different market structures. Table 1 presents parameter values, equilibrium
fees, network profits, consumer and merchant demand, and total transaction volumes for a series of symmetric duopolistic and monopolistic market equilibria.
The first four columns give parameter values: customer fixed costs, transaction
costs, upper end of the merchant benefits distribution, upper end of the consumer
benefits distribution. The parameters are not indexed, because they are identical
for both networks. The subsequent four columns give equilibrium values for consumer and merchant fees, their difference, and equilibrium profits. The next three
columns show each network’s demand volume for consumers and merchants and
its total non-cash transactions.
Table 1A shows equilibrium values for each firm under duopolistic Nash competition and table 1B shows equilibrium values of each firm when the two firms
15

Also, some previous non-subscribers, initially in the smaller lower left rectangle, are moved
rightward into the market area.

17

operate as a cartel. The results show that for all parameter values the duopolistic
competition results in lower consumer and merchant fees, higher consumer and
merchant demand and a greater number of total transactions.
There are two cases where either the consumer fee or the merchant fee is zero
(or even negative) in the duopolistic market. 16 As expected from our previous
discussion, this is a consequence of µ  τ , or µ  τ , making one side of the
market significantly more competitive than the other.
Table 1: Symmetric Competition
A: Duopolistic
g
c
0
0
0 0.5
0.2 0
0
0
0
0
0
0

µ τ
1 1
1 1
1 1
2 1
2 1
1 2

fc
.181
.248
.360
0
-.169
.828

fm fc − fm
.236
-.055
.449
-.201
.199
.161
.666
-.666
.732
-.901
0
.828

Π
Dc Dm Dc Dm
.170 .471 .764 .360
.087 .397 .551 .219
.127 .398 .801 .319
.222
.5
.667 .333
.137
.5
.634 .317
.343 .414
1
.414

µ τ
1 1
1 1
1 1
2 1
1 2

fc
.376
.326
.474
.218
1.155

fm fc − fm
.248
.128
.451
-.125
.202
.272
.813
-.595
0
1.155

Π
.211
.096
.141
.302
.385

B: Cartel
g
c
0
0
0 0.5
0.2 0
0
0
0
0

Dc Dm Dc Dm
.375 .752 .282
.324 .549 .178
.324 .798 .259
.433 .594 .257
.333
1
.333

The fee for merchants does not significantly change in the two market structures. However, the fees to consumers changes drastically from the duopoly to
16

The fourth and the fifth rows in table 1A show results for the same set of parameter values.
In one case, consumers fee are constrained to be non-negative, whereas in the other case they can
take negative values. There are examples of negative fees in the United States such as cashback
programs. On the other hand, equilibrium fees in the cartel case are never negative. Also, it is easy
to see that equilibrium merchant fees cannot be negative in any market structure.

18

the cartel. In column 7, we compute the difference between consumer fees and
merchant fees, and we find that the difference increases for all parameter values.
The reason why consumers gain relatively more, in our examples, from market
competition, is explained in the following proposition.
Proposition 3 In the symmetric market with uniform and independent distributions of consumer and merchant benefits, there is more competitive pressure on
the consumer side (higher marginal profits from a fee reduction) if, in the monopolistic equilibrium, either the merchant fee is zero, or:
Mf c
≤ 2µ − τ
Dm

(13)

Proof. Assume fjm > 0. Starting from a symmetric equilibrium, suppose that
either fjc or fjm are marginally decreased. In both cases, w = mi − fic . Using
this value for w in equations 11 and 12, we find that the marginal change in the
consumer demand of the competing network, determining the pecuniary externality on profits (and the relative competitive pressure), is higher for the variation in
consumer fees if:
|

τ M (m − f c )[f c + .5(m − f c )]
∂Dic
m − fc
∂Dic
≥
|
≥
|
|
⇒
∂fjc
∂fjm
m
µ
m2

(14)

where we dropped subscripts, for notational convenience, and we made use of the
definition of demand 5 or 6. Condition 13 is obtained from simple manipulations
of 14.
On the contrary, assume fjm = 0. In this case, the partial derivative of the consumer demand is discontinuous, because all merchants are already subscribing
both networks, and a further reduction in the merchant fee would not bring about
more merchants and, consequently, more consumers. The networks are therefore
competing on one side only (the consumer one), and only consumer fees can decrease.


Observing that consumer fees cannot be negative in the cartel equilibrium, the
following corollary can be immediately derived: 17
If f c = 0 for both networks, all consumers subscribe to one network. Lower fees cannot
increase total consumer demand or profits. On the other hand, negative fees can be observed in the
competitive duopoly, because of the desire to undercut the competitor.
17

19

Corollary 1 A sufficient condition for the consumer fees falling less than merchant fees under competition, if merchant fees remain strictly positive, is :
τ ≥ 2µ

(15)

What is the meaning of τ and µ ? They are both parameters determining the
amplitude of the interval of the (uniform) distribution function of transactional
benefits for consumers (τ ) and merchants (µ).
If the support of a distribution function is larger, there is more differentiation
among agents. When τ ≥ 2µ a marginal change in the consumer fee produces
little effects on the consumer demand, but a marginal change in the merchant fee
produces relatively large variations in the merchant demand. As a consequence,
the duopolistic networks compete more vigorously on the merchant sub-market,
and merchant fees decrease relatively more if condition 15 is met. 18
In the appendix, we look at the resulting price structures and see that they
are not welfare efficient. Furthermore, although competition improves welfare
because of a reduction in total price, the price structure may actually worsen in
terms of welfare.
Asymmetric Competition
Most real markets involve competition between asymmetric players. For example,
debit and credit cards are competing payment instruments, although they differ in
terms of cost structure and services provided to consumers and merchants. Such
competition has been investigated by the courts in the United States and by regulators in other parts of the world. We are not aware of any theoretical models that
have attempted to investigate such competition.
Unfortunately, the analysis of asymmetric competition in the model illustrated
above is very complex, and general analytical results cannot be readily obtained.
Yet, useful insights can be gained through a combination of numerical examples
and a careful inspection of the optimization condition 7, which still hold, in general, under asymmetry.
A simple way to address the issue is to start from a symmetric equilibrium
and consider a marginal change in a specific cost or demand parameter, for one of
the two networks. How will this perturbation of symmetry conditions affect the
market equilibrium? This question can usefully be decomposed into two parts:
(a) how will this change induce different aggregate price levels? (b) how will
18

In our numerical examples, this never occurs.

20

asymmetric conditions affect the balance between relative prices on the two sides
of the market?
The first sub-question has a quite straightforward answer. The model considered here is reminiscent of an asymmetric Hotelling model, and results are similar. In an asymmetric Hotelling duopoly, consumers are evenly distributed along
a [0,1] segment, with one firm located at point 0 and the other one located at point
1+∆. Consumers buy one unit of a good, selecting the firm associated with the
minimum total cost, which is the sum of producer price and transportation cost.
In this case, it can be easily shown that (under full market coverage) prices applied by the first firm (and profits) are an increasing function of the parameter ∆,
whereas the opposite occurs for the competitor. Analogously, in our model any
cost increase, or any positive change in consumer/merchant preferences, will induce higher (aggregate) prices by a firm and a reaction by its competitor, which
lowers its own (aggregate) prices.
In addition, the price balance between the two market sides also changes, because elasticities in equation 7 vary. Rochet and Tirole (2004) notice that this
effect can be explained in the form of a simple “topsy-turvy principle”: a factor
that is conducive to a high price on one side, to the extent that it raises the platform’s margin on that side, tends also to call for a low price on the other side,
as attracting members on that other side becomes more profitable. Because the
relevant cost concept in a two-sided market is the opportunity cost, any time an
additional marginal unit is produced on one side, the network faces a marginal
cost, but it can also raise the price on the other side, as the utility of the other side
agents is increasing.
Coupling this effect with the asymmetric Hotelling one, we can see that any
factor that is conducive to a high price on one side for one network induces: (a)
a lower price on the other side for the same network, (b) a lower price on the
same side for the other network, (c) a higher price on the other side for the other
network. In other words, the networks follow a “reversed strategy” in terms of
price balancing.
Table 2 presents equilibrium prices and demand volumes under asymmetric
duopolistic competition and collusion, for a variety of parameter values. The
cases could be interpreted as simulating (in a rather simplistic way) competition
between a debit card network (network 2) and a credit card network (network 1).
The latter is assumed to have higher customer costs and to provide more benefits
to consumers (such as credit) and potentially, to merchants.
The effects of competition on the asymmetric market are not qualitatively different from the ones obtained under symmetry. This should not come as a surprise,
21

as the sign of pecuniary externalities in equations 11 and 12 were derived for the
general case.
Numerical simulations confirm that relative prices, both in competition and in
collusion, move in opposite directions, when parameter values for one network
are changed from the symmetric benchmark. In all circumstances, when fees on
one side of the market are lowered by a network, the other network reacts by lowering fees on the opposite market side.

22

Table 2: Asymmetric Competition
A. Duopoly
Network 1
g
0.1
0.1
0.1
0.1

c
µ
τ
fc
fm fc − fm
0
1 1.1 .328 .176
.152
0.5 1 1.1 .397 .372
.025
0 1.1 1.1 .285 .235
.050
0.5 1.1 1.1 .363 .434
-.071

Π
Dc Dm Dc Dm
.153 .410 .824 .338
.068 .312 .628 .196
.158 .427 .786 .336
.075 .335 .605 .203

Network 2
τ
fc
fm fc − fm
1.0 .190 .255
-.065
1 .249 .461
-.212
1 .188 .250
-.062
1 .249 .459
-.210

Π
Dc Dm Dc Dm
.189 .496 .745 .370
.096 .420 .539 .226
.184 .489 .750 .367
.093 .412 .541 .223

c
µ
τ
fc
fm fc − fm
0
1 1.1 .522 .177
.345
0.5 1 1.1 .474 .371
.103
0 1.1 1.1 .480 .238
.242
0.5 1.1 1.1 .442 .432
.010

Π
Dc Dm Dc Dm
.177 .311 .823 .256
.071 .244 .629 .153
.186 .327 .784 .256
.080 .266 .607 .162

g
c
0.0 0
0 0.5
0
0
0 0.5

µ
1.0
1
1
1

B. Cartel
Network 1
g
0.1
0.1
0.1
0.1

Network 2
g
c
0.0 0
0 0.5
0
0
0 0.5

µ
1.0
1
1
1

τ
fc
fm fc − fm
1.0 .349 .265
.084
1 .307 .464
-.157
1 .356 .261
.095
1 .311 .461
-.150
23

Π
Dc Dm Dc Dm
.225 .413 .735 .304
.104 .363 .536 .195
.221 .403 .739 .298
.102 .350 .539 .189

4 Alternative Fee Structures and Assumptions
In this section, we consider alternative fee structures and assumptions and discuss
how our results might be affected.
Reversed Multihoming
Consider the case where merchants pay fixed fees and consumers pay per-transaction fees. In the United States, some banks have started to charge per-transaction
fees for online debit cards. Some observers of payment markets have suggested
that the fixed fees associated with installing personal identification number pads
may keep certain merchants from accepting them.
Given that consumers pay fixed fees and can only choose to be a member of
one network, we found that consumers consider the number of merchants that
accept a certain payment product in their decision to purchase payment services
from that network. However, merchants only consider the net benefits of accepting cards for a single transaction because they multihome. Reversing who pays
fixed fees and singlehomes and who pays per-transaction fees and multihomes,
we would expect to see merchants choosing to accept payment cards based on
the number of consumers that carry them and consumers choosing to hold both
payment products because there is no cost in doing so.
In the United States, it is not uncommon to see consumers multihome among
and across payment products. For credit cards, merchant acceptance of American Express and Discover credit cards is less than that of MasterCard and Visa
cards.19 While consumers may prefer the former cards, they may carry the latter
cards as insurance against merchants not accepting the former cards. Interestingly,
most consumers multihome when it comes to signature-based and PIN-based debit
cards, but merchants have started to reject certain types of debit cards and steer
their customers to using a certain type of debit card.
Nonetheless, the results obtained from our model still hold, if the two market
sides are switched. This can be easily done by re-interpreting all variables and
parameters with a m superscript as referred to the consumers, and all variables
and parameters with a c superscript as referred to the merchants.
19

For comparison, we are considering charge cards in this example. A substantial part of American Express cards are charge cards where consumers are not able to revolve. It is also noteworthy
that American Express dominates the corporate card market suggesting that there are indeed strong
consumer preferences.

24

Endogenous Single/Multihoming
In the model presented in this paper, one side adopts a single platform (singlehome) whereas the other one can use more than one platform (multihome). This
configuration can emerge whenever the fixed cost of joining a network is sufficiently high, so that the cost of having a secondary payment instrument outweighs
the potential benefits. This is, for example, the typical case of credit cards in most
European countries, where consumers pay a fixed membership fee and typically
carry only one card.
Ideally, as membership fee is endogenously determined within the model, so
should be the single/multihoming decision. Endogeneizing this choice, however,
can easily make the model analytically intractable. To our knowledge, only one
paper (Hermalin and Katz (2004)) has addressed the issue of bilateral multihoming, through extensive use of numerical simulations.
Furthermore, new issues arise. For example, if both sides have both instruments available, who decides which platform will be used? Can one side refuse
to accept or to adopt one instrument, only to steer the other side to the most preferred alternative? Clearly, these are all interesting issues, whose investigation
falls, however, outside the scope of this paper.
Bertrand-like Competition
Instead of assuming that benefits are independently drawn for each payment network, consider the opposite polar case of perfect correlation. For example, a consumer may value the possibility of making credit card transactions, irrespective of
the type of card. Yet, cards may be qualitatively differentiated. Basic benefits are
the same for the two payment instruments, although they are consumer-specific.
This case can be accommodated by assuming that a uniform random variable
x in the interval [0, 1] is drawn for each consumer, and basic benefits are obtained
by multiplying this variable by (network-specific) maximum basic benefits τ i . In
this case:
(16)
U c = max{0, xτ1 D1m − f1c , xτ2D2m − f2c }
Again, to be chosen, a card must provide net benefits:



fic
m
c
xτi Di ≥ fi ⇒ x ≥ min 1,
τi Dim

(17)

and it must be better than the alternative one. Using the indifference condition:
xτi Dim − fic = xτj Djm − fjc
25

(18)

we can define two sets, [0, x] and [x, 1], identifying the range of values of x, for
which one network is preferred to the other. 20
The market share of a network is given by the intersection of this “preference set” and the set defined by equation 17. Of course, this intersection may be
empty. There is one exception: when total maximum benefits and consumer fees
are equal, the two market areas overlap and the consumer is indifferent between
the two cards. In this case, we can assume that the market is equally split.
To understand how prices are set in a symmetric duopolistic equilibrium, start
from arbitrary initial fee levels. On the consumer side, total demand would then
be determined by the viability condition 17. From this point on, a slight reduction in the consumer fee or, equivalently, in the merchant fee, could allow each
competitor to conquer the whole market (although total demand would change
only marginally). That is, each competitor has an incentive to undercut either by
lowering the consumer fee or by lowering the merchant fee.
The outcome is a special type of Bertrand price war with two instruments
and the equilibrium is found when profits are dissipated. Each network tries to
offer higher net benefits to the subscribing consumers. In equilibrium, consumer
net benefits are maximized, under the constraint of non-negative profit for the
networks.21
This result is a direct consequence of the perfect correlation in the distribution
of consumers’ benefits. In real markets, consumers are likely to have both ‘brand
preferences’ and ‘payment tool preferences,’ irrespective of brand. In terms of
Figure 1, consumers would then be located inside a positively sloped ‘cloud’ of
points, and the market equilibrium would fall somewhere in between the two polar
cases analyzed in this paper (perfect correlation vs. independent distributions of
consumer benefits).

5 Policy Implications
Recently, pricing policies of credit card networks and debit card networks have
been investigated by authorities in various jurisdictions. The apparent barriers to
competition in the payment card industry and its harm to consumers and merThe implicit assumption here is 0 ≤ x ≤ 1. Alternative cases are trivial.
A similar result is found by Guthrie and Wright (2003). In their model, however, consumers
get their draw of transactional benefits after having subscribed a card. This implies that consumers
are ex-ante equal, when making a subscription decision. However, Guthrie and Wright do not
consider positive subscription fees.
20
21

26

chants has been the basis for investigations by the Reserve Bank of Australia, the
U.S. courts along with authorities in other jurisdictions. 22 However, few academic
models address the issue of platform competition in the provision of payment services. As far as we aware, we are the first to consider competition among differentiated payment products being supplied by a single network or different networks. Our modelling strategy is justified by the coexistence of multiple payment
networks that may serve various niche markets for a given payment instrument
and/or supply multiple payment instruments.
In this paper, we address the effect of competing payment networks on consumer and merchant welfare. We find that competition unambiguously increases
consumer and merchant welfare suggesting that policymakers should promote
competition among networks providing similar products and those offering different products. Within a payment type such as credit cards, debit cards, or checks,
providers offer various differentiated products. Our results suggest that not only
are there benefits to competition within a payment type but also across payment
types. Thus, when determining policies regarding payment networks, competitive
pressures from similar and different payment products should be considered.
For an example of the effects of competition on price level, we look to the
entry of credit cards in the U.S. grocery store market. In certain market segments,
such as grocery stores in the United States, the acceptance of lower cost alternatives such as PIN-based debit cards resulted in lower merchant discounts for
MasterCard and Visa branded credit cards.23 During the same time, there were no
noticeable differences on the consumer side. In fact, certain card issuers are offering additional benefits to those cardholders that make purchases at grocery stores.
To isolate the effect of competition on price structure is a bit more difficult. However, with the recent interchange fee regulation in Australia, some industry reports
suggest that consumer benefits such as frequent-use enhancements will decrease
because of lower interchange fees. Given that regulatory changes only recently
took place, it is too early to tell the effect on the total volume of transactions.
We ignore some benefits of a single platform providing payment services or
cooperation between payment networks. Payment services most likely exhibit
22

For a discussion of competition among payment instruments, see Reserve Bank of Australia
2002. For a discussion of the recently settled merchant lawsuit against MasterCard and Visa, see
Chakravorti (2003).
23
Note that the benefits to grocers from credit cards may be less than other types of merchants.
Some analysts have argued that some consumers may be reluctant to make food and other “necessary” good purchases on credit. For more details, see McAndrews and Stefanadis (1999).

27

economies of scale and scope.24 However, as noted above, consumers and merchants may have strong preferences for product differentiation resulting in potentially restricting scale economies. Some economists have argued that certain types
governance structures may limit monopoly rents. Hausman, Leonard, and Tirole
(2003) suggest that if the payment platforms are not-for-profit entities and are not
allowed to share profits with members, cooperation among the networks may limit
the rents that could be earned. We leave these issues for future research.

6 Conclusion
To date most theoretical models consider a single platform with varying levels of
competition among network participants. Few theoretical models have considered
competing payment platforms. Unlike previous models, we consider networkspecific benefits for consumers and merchants. We investigate the impact of competing payment networks on consumer and merchant welfare, network profits, and
the ratio of consumer and merchant prices. We find that competition always improves consumer and merchant welfare. As expected, network profits decrease
with competition. The ratio of consumer and merchant prices depend on the differences in the benefits.
However, we ignore some aspects of the payment industry captured by others.
Most notably, we ignore strategic reasons for merchants to accept other payment
products. Guthrie and Wright (2003) consider intratemporal business stealing as a
motivation for merchants to accept payment cards. Business stealing would affect
the level of merchant fees. However, the aggregate welfare of merchants does not
improve with business stealing because net sales presumably remain constant. In
fact, Chakravorti and To (2003) suggest that intertemporal business stealing may
decrease merchant welfare under certain conditions.
In reality, consumers and merchants both multihome to some extent. Unfortunately, there are difficulties in modeling an environment where consumers and
merchants both multihome in the presence of fixed fees. In markets such as the
U.S. where consumers carry several payment products, consumers may still prefer to use one payment instrument for most transactions. Alternatively, consumers
may have preferences for one payment instrument based on the value and type of
the transaction. Therefore, consumers may carry more than one card as insurance
24

For discussion of scale and scope economies in payment services, see Chakravorti and Kobor
(2003).

28

when one card is not accepted by the merchant or for some technical reason does
not function. The underlying reasons why consumers multihome has not been
modelled and remains a future direction of research.
In this paper, we extend the literature on payment networks that sheds light
on the effects of competition on consumer and merchant welfare by considering
a specific level of benefits for each consumer and merchant for each network’s
payment services. We find threshhold values when competition affects consumer
prices or merchant prices more. While there are theoretical models that investigate
network competition, these models have not been empirically tested. This type of
empirical research is vital for policymakers to adopt the optimal polices regarding
payment networks.

29

References
Ahlborn, Christian, Howard H. Chang, and David S. Evans (2001), “The Problem
of Interchange Fee Analysis: Case Without a Cause,” European Competition Law
Review, 22, 304-312.
Armstrong, Mark (2004), “Competition in Two-Sided Markets,” Mimeo, presented at “The Economics of Two-Sided Markets” conference held at the University of Toulouse.
Balto, David A. (2000) “The Problem of Interchange Fees: Costs without Benefits,” European Competition Law Review, 21, 215-224.
Baxter, William F. (1983), “Bank Interchange of Transactional Paper: Legal and
Economic Perspectives,” Journal of Law & Economics, 26, 541-588.
Caillaud, Bernard and Bruno Jullien (2001), “Chicken & Egg: Competing Matchmakers,” Mimeo.
Caillaud, Bernard and Bruno Jullien (2003), “Chicken & Egg: Competition
among Intermediation Service Providers,” RAND Journal of Economics, 24, 309328.
Chakravorti, Sujit (2003), “Theory of Credit Card Networks: A Survey of the
Literature,” Review of Network Economics, 2, 50-68.
Chakravorti, Sujit and William R. Emmons (2003), “Who Pays for Credit Cards?”
Journal of Consumer Affairs, 37, 208-230.
Chakravorti, Sujit and Emery Kobor (2003), “Why Invest in Payment Innovations,” Federal Reserve Bank of Chicago Emerging Payments Occasional Paper
Series, No1B.
Chakravorti, Sujit and Timothy McHugh (2002), “Why Do We Write so Many
Checks?” Federal Reserve Bank of Chicago Economic Perspectives, Third Quarter, 44-59.
Chakravorti, Sujit and Alpa Shah (2003), “The Study of the Interrelated Bilateral
Transactions in Credit Card Networks,” The Antitrust Bulletin, Spring, 53-75.

30

Chakravorti, Sujit and Ted To (2003), “A Theory of Credit Cards,” Mimeo, Federal Reserve Bank of Chicago.
Cruickshank, Don (2000), Competition in UK Banking: Report to the Chancellor
of the Exchequer.
European Commission (2002), “Case No. Comp/29.373 - Visa International Multilateral Interchange Fee,” Official Journal of the European Communities,
2002/L318/17, November 22.
Evans, David S. (2003), “Some Empirical Aspects of Multi-Sided Platform Industries,” Review of Network Economics, 2 (3), 191-209.
Farrell, Joseph and Garth Saloner (1985), “Standardization, Compatibility and
Innovation,” Rand Journal of Economics, 16, 70-83.
Frankel, Alan S. (1998), “Monopoly and Competition in the Supply and Exchange
of Money,” Antitrust Law Journal, 66, 311-361.
Gans, Joshua S. and Stephen P. King (2003), “The Neutrality of the Interchange
Fees in the Payment System,” Topics in Economic Analysis & Politics, 3, article 1
located at http://www.bepress.com/bejeap/topics/vol3/iss1/art1.
Guthrie, Graeme and Julian Wright (2003), “Competing Payment Schemes,”
Working Paper No. 0311, Department of Economics, National University of Singapore.
Hausman, Jerry A., Gregory K. Leonard, Jean Tirole (2003), “On Nonexclusive
Membership in Competing Joint Ventures,” Rand Journal of Economics, 34, 4362.
Hermalin, B.E., and Katz, M.L., (2004), “Your Network or Mine? The Economics
of Routing Rules,” presented at “The Economics of Two-Sided Markets” conference held at the University of Toulouse, January.
IMA Market Development AB (2000), Study Regarding the Effects of the Abolition of the Non-Discrimination Rule in Sweden, IMA Market Development AB:
Lerum, Sweden.
Little, Ian and Julian Wright, (2000), “Peering and Settlement in the Internet: an
Economic Analysis,” Journal of Regulatory Economics, 18, 151-173.
31

Jullien, Bruno (2001), “Competing in Network Industries: Divide and Conquer,”
Mimeo, IDEI and GREMAQ, University of Toulouse.
Katz, Michael L. (2001), Reform of Credit Card Schemes in Australia II, Sydney,
Australia: Reserve Bank of Australia.
Katz, Michael L. and Carl Shapiro (1985), “Network Externalities, Competition,
and Compatibility,” American Economic Review, 75, 424-440.
McAndrews, James J. and Chris Stefanadis (1999), “The Issues of Exclusivity and
Overlapping Governance in the Visa and MasterCard Antitrust Case,” Mimeo,
Federal Reserve Bank of New York.
Reserve Bank of Australia (2002), Reform of Credit Card Schemes in Australia
IV: Final Reforms and Regulation Impact Statement, Sydney, Australia: Reserve
Bank of Australia.
Rochet, Jean-Charles, and Jean Tirole (2002), “Cooperation among Competitors:
The Economics of Payment Card Associations,” Rand Journal of Economics, 33,
549-570.
Rochet, Jean-Charles, and Jean Tirole (2003), “Platform Competition in TwoSided Markets,” Journal of European Economic Association, 1, 990-1029.
Rochet, Jean-Charles, and Jean Tirole (2004), “Two-Sided Markets: An
Overview,” mimeo, IDEI University of Toulouse. A preliminary version was presented at “The Economics of Two-Sided Markets” conference, held at the University of Toulouse, January.
Roson, Roberto (2003), “Incentives for the Expansion of Network Capacity in a
Peering Free Access Settlement” Netnomics, 5, 149-159.
Schiff, Aaron (2003), “Open and Closed Systems of Two-Sided Networks,” Information Economics and Policy, 15, 425-442.
Schmalensee, Richard (2002), “Payment Systems and Interchange Fees,” Journal
of Industrial Economics, 50, 103-122.
Schwartz, Marius and Daniel R. Vincent (2002), “Same Price, Cash or Card:
Vertical Control by Payments Networks,” Mimeo, University of Maryland.
United States v. Visa U.S.A., Inc. (2001) 163 F. Supp. 2d 322 (S.D. N.Y.).
32

Vis, E. and J. Toth (2000), The Abolition of the No-Discrimination Rule, ITM
Research for Competition DG: Amsterdam.
Wright, Julian (2003), “Optimal Card Payment Systems,” European Economic
Review, 47, 587-612.
Wright, Julian (2004), “The Determinants of Optimal Interchange Fees in Payment Systems,” Journal of Industrial Economics, 52, 1-26.

33

7 Appendix:
Sub-optimal Price Structures in Duopoly
In the paper, we showed that network competition unambiguously reduces equilibrium prices, and increases the number of subscribing merchants and consumers,
as well as their welfare. However, neither monopoly nor competitive price structures are welfare-efficient. Furthermore, the introduction of market competition
may not bring about better price structures, in terms of aggregate welfare of consumers and merchants. We show this for the symmetric case, using parameter
values and prices of Table 1. Platform profits have been defined as:
Π = (f c − g)Dc + (f m − c)Dc Dm
Keeping the profit level fixed, a marginal change in the consumer fee would
be compensated by a marginal change in the merchant fee if:
δf c
= −δf m
Dm
Thus, we ask the following question: starting from any of the equilibria reported in Table 1, would it be possible to get a higher aggregate welfare for consumers and merchants, for the same level of platform profits?
To answer, we need first to identify the consumer and merchant welfare in
the symmetric equilibria. For each single platform, aggregate consumer welfare
(CW ) and aggregate merchant welfare (MW ) are given, in the symmetric case,
by:25
 µ
MW =
(h − f m )Dc dh
fc



fc



m

CW =
0


(h − f )dh dk +

m

c

fc

fc



m

(h − f c )dh dk

k

where m = τ Dm . This gives, under the assumption of uniform distribution:
CW =

1  (τ Dm − f c )2 f c (τ Dm − f c )3
+
(τ Dm )2
2
6

25
Since we are considering a symmetric duopoly, total welfare can be easily computed by doubling the results.

34

MW = Dc

(µ − fm )2
2µ

To assess the welfare impact of a profit-neutral price rebalancing between the
two market sides, we construct the following index: 26
η=

 ∂CW
∂fc

 ∂CW
∂MW
∂MW
m
D −
+
+
∂fc
∂fm
∂fm

Therefore, a positive η means that it would be possible to get a higher aggregate welfare (consumer welfare + merchant welfare), by slightly augmenting f c ,
while reducing fm so as to keep profits unchanged. The computation of η for
parameter values and prices of Table 1 gives the following results for duopolistic
competition (C) and monopolistic cartel (M):
g
0
0
0.2
0
0

c
0
0.5
0
0
0

µ τ η-C
η-M
1 1 0.361 0.255
1 1 0.278 0.256
1 1 0.265 0.221
2 1 0.417 0.130
1 2 0.564 0.522

Notice that: (1) the η index is always positive, meaning that consumer fees are
“too low”, and (2) introducing competition actually worsens the price structure.
This is, of course, a direct consequence of the consumer fees falling relatively
more in the competitive regime.
Summing up, market competition implies a downward pressure on prices, associated with a change in the price structure. The first effect is welfare-improving,
whereas the second one may have negative welfare consequences. In our setting,
the first effect dominates the second one, so that welfare of both consumers and
merchants improves in any case.27

Remember that, to keep profits unchanged, an increase (decrease) in f m must be associated
with a proportional decrease (increase) in f c , by a factor Dm .
27
However, if we choose a different starting point, like a price-constrained monopoly, the second
effect may be determinant, and competition may actually reduce welfare.
26

35

Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
Does Bank Concentration Lead to Concentration in Industrial Sectors?
Nicola Cetorelli

WP-01-01

On the Fiscal Implications of Twin Crises
Craig Burnside, Martin Eichenbaum and Sergio Rebelo

WP-01-02

Sub-Debt Yield Spreads as Bank Risk Measures
Douglas D. Evanoff and Larry D. Wall

WP-01-03

Productivity Growth in the 1990s: Technology, Utilization, or Adjustment?
Susanto Basu, John G. Fernald and Matthew D. Shapiro

WP-01-04

Do Regulators Search for the Quiet Life? The Relationship Between Regulators and
The Regulated in Banking
Richard J. Rosen
Learning-by-Doing, Scale Efficiencies, and Financial Performance at Internet-Only Banks
Robert DeYoung
The Role of Real Wages, Productivity, and Fiscal Policy in Germany’s
Great Depression 1928-37
Jonas D. M. Fisher and Andreas Hornstein

WP-01-05

WP-01-06

WP-01-07

Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy
Lawrence J. Christiano, Martin Eichenbaum and Charles L. Evans

WP-01-08

Outsourcing Business Service and the Scope of Local Markets
Yukako Ono

WP-01-09

The Effect of Market Size Structure on Competition: The Case of Small Business Lending
Allen N. Berger, Richard J. Rosen and Gregory F. Udell

WP-01-10

Deregulation, the Internet, and the Competitive Viability of Large Banks
and Community Banks
Robert DeYoung and William C. Hunter

WP-01-11

Price Ceilings as Focal Points for Tacit Collusion: Evidence from Credit Cards
Christopher R. Knittel and Victor Stango

WP-01-12

Gaps and Triangles
Bernardino Adão, Isabel Correia and Pedro Teles

WP-01-13

A Real Explanation for Heterogeneous Investment Dynamics
Jonas D.M. Fisher

WP-01-14

Recovering Risk Aversion from Options
Robert R. Bliss and Nikolaos Panigirtzoglou

WP-01-15

Economic Determinants of the Nominal Treasury Yield Curve
Charles L. Evans and David Marshall

WP-01-16

1

Working Paper Series (continued)
Price Level Uniformity in a Random Matching Model with Perfectly Patient Traders
Edward J. Green and Ruilin Zhou

WP-01-17

Earnings Mobility in the US: A New Look at Intergenerational Inequality
Bhashkar Mazumder
The Effects of Health Insurance and Self-Insurance on Retirement Behavior
Eric French and John Bailey Jones

WP-01-18

The Effect of Part-Time Work on Wages: Evidence from the Social Security Rules
Daniel Aaronson and Eric French

WP-01-20

Antidumping Policy Under Imperfect Competition
Meredith A. Crowley

WP-01-21

WP-01-19

Is the United States an Optimum Currency Area?
An Empirical Analysis of Regional Business Cycles
Michael A. Kouparitsas

WP-01-22

A Note on the Estimation of Linear Regression Models with Heteroskedastic
Measurement Errors
Daniel G. Sullivan

WP-01-23

The Mis-Measurement of Permanent Earnings: New Evidence from Social
Security Earnings Data
Bhashkar Mazumder

WP-01-24

Pricing IPOs of Mutual Thrift Conversions: The Joint Effect of Regulation
and Market Discipline
Elijah Brewer III, Douglas D. Evanoff and Jacky So

WP-01-25

Opportunity Cost and Prudentiality: An Analysis of Collateral Decisions in
Bilateral and Multilateral Settings
Herbert L. Baer, Virginia G. France and James T. Moser

WP-01-26

Outsourcing Business Services and the Role of Central Administrative Offices
Yukako Ono

WP-02-01

Strategic Responses to Regulatory Threat in the Credit Card Market*
Victor Stango

WP-02-02

The Optimal Mix of Taxes on Money, Consumption and Income
Fiorella De Fiore and Pedro Teles

WP-02-03

Expectation Traps and Monetary Policy
Stefania Albanesi, V. V. Chari and Lawrence J. Christiano

WP-02-04

Monetary Policy in a Financial Crisis
Lawrence J. Christiano, Christopher Gust and Jorge Roldos

WP-02-05

Regulatory Incentives and Consolidation: The Case of Commercial Bank Mergers
and the Community Reinvestment Act
Raphael Bostic, Hamid Mehran, Anna Paulson and Marc Saidenberg

WP-02-06

2

Working Paper Series (continued)
Technological Progress and the Geographic Expansion of the Banking Industry
Allen N. Berger and Robert DeYoung

WP-02-07

Choosing the Right Parents: Changes in the Intergenerational Transmission
of Inequality  Between 1980 and the Early 1990s
David I. Levine and Bhashkar Mazumder

WP-02-08

The Immediacy Implications of Exchange Organization
James T. Moser

WP-02-09

Maternal Employment and Overweight Children
Patricia M. Anderson, Kristin F. Butcher and Phillip B. Levine

WP-02-10

The Costs and Benefits of Moral Suasion: Evidence from the Rescue of
Long-Term Capital Management
Craig Furfine

WP-02-11

On the Cyclical Behavior of Employment, Unemployment and Labor Force Participation
Marcelo Veracierto

WP-02-12

Do Safeguard Tariffs and Antidumping Duties Open or Close Technology Gaps?
Meredith A. Crowley

WP-02-13

Technology Shocks Matter
Jonas D. M. Fisher

WP-02-14

Money as a Mechanism in a Bewley Economy
Edward J. Green and Ruilin Zhou

WP-02-15

Optimal Fiscal and Monetary Policy: Equivalence Results
Isabel Correia, Juan Pablo Nicolini and Pedro Teles

WP-02-16

Real Exchange Rate Fluctuations and the Dynamics of Retail Trade Industries
on the U.S.-Canada Border
Jeffrey R. Campbell and Beverly Lapham

WP-02-17

Bank Procyclicality, Credit Crunches, and Asymmetric Monetary Policy Effects:
A Unifying Model
Robert R. Bliss and George G. Kaufman

WP-02-18

Location of Headquarter Growth During the 90s
Thomas H. Klier

WP-02-19

The Value of Banking Relationships During a Financial Crisis:
Evidence from Failures of Japanese Banks
Elijah Brewer III, Hesna Genay, William Curt Hunter and George G. Kaufman

WP-02-20

On the Distribution and Dynamics of Health Costs
Eric French and John Bailey Jones

WP-02-21

The Effects of Progressive Taxation on Labor Supply when Hours and Wages are
Jointly Determined
Daniel Aaronson and Eric French

WP-02-22

3

Working Paper Series (continued)
Inter-industry Contagion and the Competitive Effects of Financial Distress Announcements:
Evidence from Commercial Banks and Life Insurance Companies
Elijah Brewer III and William E. Jackson III

WP-02-23

State-Contingent Bank Regulation With Unobserved Action and
Unobserved Characteristics
David A. Marshall and Edward Simpson Prescott

WP-02-24

Local Market Consolidation and Bank Productive Efficiency
Douglas D. Evanoff and Evren Örs

WP-02-25

Life-Cycle Dynamics in Industrial Sectors. The Role of Banking Market Structure
Nicola Cetorelli

WP-02-26

Private School Location and Neighborhood Characteristics
Lisa Barrow

WP-02-27

Teachers and Student Achievement in the Chicago Public High Schools
Daniel Aaronson, Lisa Barrow and William Sander

WP-02-28

The Crime of 1873: Back to the Scene
François R. Velde

WP-02-29

Trade Structure, Industrial Structure, and International Business Cycles
Marianne Baxter and Michael A. Kouparitsas

WP-02-30

Estimating the Returns to Community College Schooling for Displaced Workers
Louis Jacobson, Robert LaLonde and Daniel G. Sullivan

WP-02-31

A Proposal for Efficiently Resolving Out-of-the-Money Swap Positions
at Large Insolvent Banks
George G. Kaufman

WP-03-01

Depositor Liquidity and Loss-Sharing in Bank Failure Resolutions
George G. Kaufman

WP-03-02

Subordinated Debt and Prompt Corrective Regulatory Action
Douglas D. Evanoff and Larry D. Wall

WP-03-03

When is Inter-Transaction Time Informative?
Craig Furfine

WP-03-04

Tenure Choice with Location Selection: The Case of Hispanic Neighborhoods
in Chicago
Maude Toussaint-Comeau and Sherrie L.W. Rhine

WP-03-05

Distinguishing Limited Commitment from Moral Hazard in Models of
Growth with Inequality*
Anna L. Paulson and Robert Townsend

WP-03-06

Resolving Large Complex Financial Organizations
Robert R. Bliss

WP-03-07

4

Working Paper Series (continued)
The Case of the Missing Productivity Growth:
Or, Does information technology explain why productivity accelerated in the United States
but not the United Kingdom?
Susanto Basu, John G. Fernald, Nicholas Oulton and Sylaja Srinivasan

WP-03-08

Inside-Outside Money Competition
Ramon Marimon, Juan Pablo Nicolini and Pedro Teles

WP-03-09

The Importance of Check-Cashing Businesses to the Unbanked: Racial/Ethnic Differences
William H. Greene, Sherrie L.W. Rhine and Maude Toussaint-Comeau

WP-03-10

A Structural Empirical Model of Firm Growth, Learning, and Survival
Jaap H. Abbring and Jeffrey R. Campbell

WP-03-11

Market Size Matters
Jeffrey R. Campbell and Hugo A. Hopenhayn

WP-03-12

The Cost of Business Cycles under Endogenous Growth
Gadi Barlevy

WP-03-13

The Past, Present, and Probable Future for Community Banks
Robert DeYoung, William C. Hunter and Gregory F. Udell

WP-03-14

Measuring Productivity Growth in Asia: Do Market Imperfections Matter?
John Fernald and Brent Neiman

WP-03-15

Revised Estimates of Intergenerational Income Mobility in the United States
Bhashkar Mazumder

WP-03-16

Product Market Evidence on the Employment Effects of the Minimum Wage
Daniel Aaronson and Eric French

WP-03-17

Estimating Models of On-the-Job Search using Record Statistics
Gadi Barlevy

WP-03-18

Banking Market Conditions and Deposit Interest Rates
Richard J. Rosen

WP-03-19

Creating a National State Rainy Day Fund: A Modest Proposal to Improve Future
State Fiscal Performance
Richard Mattoon

WP-03-20

Managerial Incentive and Financial Contagion
Sujit Chakravorti, Anna Llyina and Subir Lall

WP-03-21

Women and the Phillips Curve: Do Women’s and Men’s Labor Market Outcomes
Differentially Affect Real Wage Growth and Inflation?
Katharine Anderson, Lisa Barrow and Kristin F. Butcher

WP-03-22

Evaluating the Calvo Model of Sticky Prices
Martin Eichenbaum and Jonas D.M. Fisher

WP-03-23

5

Working Paper Series (continued)
The Growing Importance of Family and Community: An Analysis of Changes in the
Sibling Correlation in Earnings
Bhashkar Mazumder and David I. Levine

WP-03-24

Should We Teach Old Dogs New Tricks? The Impact of Community College Retraining
on Older Displaced Workers
Louis Jacobson, Robert J. LaLonde and Daniel Sullivan

WP-03-25

Trade Deflection and Trade Depression
Chad P. Brown and Meredith A. Crowley

WP-03-26

China and Emerging Asia: Comrades or Competitors?
Alan G. Ahearne, John G. Fernald, Prakash Loungani and John W. Schindler

WP-03-27

International Business Cycles Under Fixed and Flexible Exchange Rate Regimes
Michael A. Kouparitsas

WP-03-28

Firing Costs and Business Cycle Fluctuations
Marcelo Veracierto

WP-03-29

Spatial Organization of Firms
Yukako Ono

WP-03-30

Government Equity and Money: John Law’s System in 1720 France
François R. Velde

WP-03-31

Deregulation and the Relationship Between Bank CEO
Compensation and Risk-Taking
Elijah Brewer III, William Curt Hunter and William E. Jackson III

WP-03-32

Compatibility and Pricing with Indirect Network Effects: Evidence from ATMs
Christopher R. Knittel and Victor Stango

WP-03-33

Self-Employment as an Alternative to Unemployment
Ellen R. Rissman

WP-03-34

Where the Headquarters are – Evidence from Large Public Companies 1990-2000
Tyler Diacon and Thomas H. Klier

WP-03-35

Standing Facilities and Interbank Borrowing: Evidence from the Federal Reserve’s
New Discount Window
Craig Furfine

WP-04-01

Netting, Financial Contracts, and Banks: The Economic Implications
William J. Bergman, Robert R. Bliss, Christian A. Johnson and George G. Kaufman

WP-04-02

Real Effects of Bank Competition
Nicola Cetorelli

WP-04-03

Finance as a Barrier To Entry: Bank Competition and Industry Structure in
Local U.S. Markets?
Nicola Cetorelli and Philip E. Strahan

WP-04-04

6

Working Paper Series (continued)
The Dynamics of Work and Debt
Jeffrey R. Campbell and Zvi Hercowitz

WP-04-05

Fiscal Policy in the Aftermath of 9/11
Jonas Fisher and Martin Eichenbaum

WP-04-06

Merger Momentum and Investor Sentiment: The Stock Market Reaction
To Merger Announcements
Richard J. Rosen

WP-04-07

Earnings Inequality and the Business Cycle
Gadi Barlevy and Daniel Tsiddon

WP-04-08

Platform Competition in Two-Sided Markets: The Case of Payment Networks

WP-04-09

Sujit Chakravorti and Roberto Roson

7