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					                                Multihoming and Compatibility
                              in Asymmetric Two-sided Markets

                                           XU Li         CHEN Hong-min1
                Aetna School of Management Shanghai Jiao tong University, Shanghai China
                                                       Abstract
       In network industry, especially in two-sided markets, an increasing number of consumers
purchase products from competing incompatible firms so as to get greater network benefits.
Although interconnection is mandated in telecommunications, policymakers do not concern
compatibility of many other industries with the same characteristics. We find that the possibility of
consumers to multihome has much impact on firms’ pricing strategy and their choice to be
compatible in asymmetric two-sided markets. In the presence of multihoming, firms prefer to
incompatibility when self- and cross-network externality take place simultaneously. In such
situation, from the social optimal point, social welfare is improved if network compatibility is
available. The universal-usage reforms in China payment card industry ensure our opinion.
       Keywords:          Two-sided       markets            Network       externality               Multihoming
                          Compatibility




          1. Introduction
       Since 1990s, the development of new economy has obtained a huge success. The information
technology has not only profoundly changed the way of people’s work and life, but also the world
economy and the international competency of the various countries, among which, as the
representative of high-tech industry communication, computer, internet, etc, have already obtained
the rapid development. And along with the development of new economy, more and more
traditional industry has been reconstructed based on the information technology and network
technology, which is represented as entering information age from industrialization age in
developed countries; while in developing countries, represented as that information technology
impetus industrialization.
       However, while the new economy changes the consumers’ lifestyle, at the same time, it also


1
    We would like to thank Professor Guofu Tan, for his very helpful comments. We are grateful to National Natural
Science Foundation of China for the generous financial support, which made this research possible.
Contact Author. Aetna School of Management Shanghai Jiao tong University. shirleyxu@sjtu.edu.cn(XU Li)
moblephone:13918499226



                                                         1
enables concentration of the industry with network externality2 unceasingly to rise. Therefore,
from the end of last century until now, antitrust institutions in Europe have carried antitrust survey
on the industry with network externality. In such cases, firms with network externality operating in
two-sided markets are attracted much attention. For instance, Microsoft antitrust case, Microsoft
provides the products to the consumers and application software developers at the same time. The
interactions between two-sided markets strengthen Microsoft’s monopoly predominance, resulting
in antitrust lawsuit by EU. As the typical firms in two-sided markets, With their increasing
enhanced market power in acquirer markets and issuer markets, International payment card
associations, for example, MasterCard and Visa have been under lawsuit from antitrust institutions
in Australia and EU, and finally ended by the international card association losted. Moreover, after
AOL merged Time Warner, because the integration of ISP, information service and traditional
media service strengthened the market power of AOL and Time Warner, which induces the antitrust
survey by antitrust institution of EU and US.
     The antitrust survey on Microsoft, Visa and MasterCard are carried deeply by the countries
around the world, industry with two-sided markets characteristics has attracted more and more
economists’ attention. According to Rochet and Tirole’s research, two-sided (or more generally
multi-sided) markets are roughly defined as markets in which one or more several platforms enable
interaction between end-users, and try to get the two (or multiple) sides “on board” by
appropriately charging each side, then make profits or at least not lose money overall. Unlike
traditional market, the demands of two-sided market depend not only on the pricing level but also
on pricing structure of two-sided markets. Unlike the traditional enterprises, firms in two-sided
markets need to operate two highly interdependent and correlated markets to make the profits or at
least maintain the balance. Examples of two-sided markets readily come to mind. For instance,
Videogame providers such as Atari, Nintendo, Sega Sony Play Station, and Microsoft X-Box, need
to attract consumers continuously to persuade game developers to do the design based on their
platforms, and at the same time also need to persuade software developers of game to develop the
products based on their platforms. Payment card associations, such as Visa and MasterCard, need to
attract consumers to use its payment card through promoting its payment brand in order to induce
merchant to accept their payment card. At the same time they advertise their brand and increase the
number of merchants accepting its card in acquirer market, which makes easier for consumers to
                                                                                                         3
use the payment card. Different from the general network externality conception , network
     2
      Markets with network externalities have been widely analyzed, especially since the contributions by Katz and
Shapiro (1985), Farrell and Saloner (1985). Network externalities exist when consumer utility in a certain market
depends (most positively) on the total number of consumers who purchase compatible products, which can be
distinguished by direct and indirect network externality. The first refers that consumption benefits depend on the
number of consumers who purchase the same goods or services .The later is that consumption benefits do not
depend directly on the size of the same network, instead, on the number of provision of complementary products
      3
        General network externalities are said to exist when consumer utility in a certain market depends positively on
consumption of the same good or service by other consumers, such as consumption benefits in telecommunications.

                                                          2
externality in two-sided markets represents the network benefits obtained by every consumer will
not only rise with the increasing demands of platform in the same sided market, but also rise with
demands in other sided market.
     Industries with two-sided markets characteristics represent three unique characteristics. First,
different from the traditional single-sided market, their demand comes from the joint demands of
two -sided markets. Without any side’s demands, the other side’s demands cannot happen. For
instance, if there are no merchants to accept the payment card, consumers will not choose the
payment card to do shopping; the more merchants accepts the payment card, the more consumer
will use the payment card. Vice versa. Therefore, obviously, two-sided markets face the celebrated
“chicken-and-egg” problem. Secondly, different from what we usually mentioned single- sided
market network externality, network externality in two-sided markets can be further represented as
self- and cross network externality. Specifically, although each transaction will bring the benefits to
the consumers in two-sided markets, price of each transaction is different, and the price of each
transaction cannot reflect the consumers’ returns or loss. Market has strong indirect network
externality. So for the firms operating in such markets, not only demands is related to pricing level
but also pricing structure will has a big impact on the combination of joint demands of two-sided
markets in great degree. In pricing strategy, because price in one side market will influence the
other side’s demand, besides price level in two-sided markets, firms need to consider the
distribution problem of total price in two-sided markets, namely pricing structure. What should be
paid attention is that in the industry with two-sided markets characteristics, firms will usually
choose the skewed pricing structure and asymmetric profit business model, which treats one side
market as profit center while the other side as a investment market in order to attract consumers
from profit center. For example, American Express charge its merchant very high, 82% of its
profits come from the merchant but the charge for cardholder is relatively low. Dutch and Europe’s
debit card system usually don’t charge the fee to the consumers when they’re shopping but charge
high fees for merchants. In order to obtain profit, game producers charge high fee to the
manufacturer and application software developer through patent authorization, but does not charge
fee to the terminal consumers or the charge is very low. Internet branch operators provide accessing
service to the consumers freely, only charge the fee to the website. Shopping mall not only don’t
charge consumers, but also provide free parks service and so on. But merchants actually must pay a
higher rate to the shopping mall to get approval from authorization to sell products. Portal, media
and TV cable usually are free to provide the information service, but charges the high fee for
advertisement business. (see Table 1).
     Thirdly, in traditional industry, consumers usually choose one product from the various
products of competing firms. But in two-sided markets, although the competing firms provide the
alternative products, as the result of universal existence of complementary between different
products based on the network, therefore, in order to obtain the maximized network utility, more

                                                  3
and more consumers tend to simultaneously have several products from alternative competitive
merchants. We call such consumer behavior as Multihoming4.
         Table 1: Sources of revenue in selected two-sided markets
         Products                                      Investment market               revenue sources
Software                   Video Game Console                Game Players                    Game developers
                           Streaming media                   Consumers                       Servers
                           Browsers                          Users                           Web Servers
                           Text Processing                   Readers/Viewers                 Writers
                           Operating systems           Application developers                Clients
IC                   IP provider (e.g. ARM)                  IC designer               IC designer /Foundry
                           EDA provider                      IC designer               IC designer /Foundry
Media                Journals and newspaper                  Readers                         Advertisers
                           Portals                           “Eyeballs”/viewers              Advertisers
                           TV networks                       TV Audience                     Advertisers
                           Search engines                    Consumers                       Advertisers
Payment              Credit    card     association          Cardholders                     Merchants
system               ( e.g.Amex , Visa 、
                     MasterCard)
                     Online debitcard network5               Merchants                       Cardholders

Others                     Shopping mall               Buyers(free parking)                  Shops
                     Internet backbone services              Consumers                       Websites
                           B2B                               Buyers/sellers                  Sellers/ Buyers
                           Internet                          Web sites                 Dial-up consumers
      In the network industry, some characteristics represented by demand are very similar to that of
supplier characteristics. For example, scale economy reflects the relationship between manufacture
cost and output. While network externality represents the relationship between the number of
consumption of same products and benefits obtained by consumers. So network externality is
always regarded as the scale economy in demands. Similarly, multihoming can regard as
compatibility chioce in the demand side. Multihoming in the industry with two-sided markets


     4
       Multihoming was originally an Internet term referred to when a host has more than one connection to the
Internet. For instance, multihoming captures the technique of connecting a host to the Internet via two or more
Internet Service Providers (ISPs) to maintain network connectivity even if one connection fails. Multihoming has
been analyzed in this context by Cre´mer et al. (2000). Caillaud and Jullien(2003) , Rochet and Tirole(2003)and
Doganoglu and Wright (2003) use this terminology to refer to consumers purchase two competing products
simultaneously

     5
       At present, credit card and debit card in China accomplish their transactions by the same payment network,
and the business model is similar to credit card payment network in United States and countries in Eouropean.

                                                        4
characteristics is very popular. (See table 2).


      Table 2: The presence of multihoming in selected two-sided markets
    Firms             Market    A    Presence              of    Market B             Presence         of
                                     multihoming                              multihoming
Credit         card   Cardholders    Common:             Most    Merchants    Common:           American
association                          American        Express                  Express       cardholders
                                     cardholders         also                 can use Visa and
                                     carry at least one                       MasterCard at almost
                                     Visa or MasterCard.                      all places that take
                                                                              American Express.


Operating             Consumers      Uncommon:                   Developers   Common: As noted
systems                              Individuals typically                    earlier, the number of
                                     use      only        one                 developers that
                                     operating       system.                  develop for various
                                     Common:                                  operating          systems
                                     Individuals use at                       indicates that
                                     least two operating                              developers
                                     system                                   engage           significant
                                                                              multihoming


Video         Game    Game           Varies: The average         Game         Common:                 For
Console               players        household           (that   Developers   example,         Electronic
                                     owns at least one                        Arts,        a        game
                                     console) owns 1.4                        developer,        develops
                                     consoles in United                       for              Nintendo’s
                                     States                                   GameCube,
                                                                              Microsoft’s Xbox, and
                                                                              Sony’s      Playstation2,
                                                                              among other consoles.
B2B                   Buyers         Varies: For example,        Sellers      Varies:     Multihoming
                                     multihoming may be                       may be unnecessary
                                     unnecessary          for                 since the B2B can
                                     some online B2B                          inexpensively reach a
                                     sites, since buyers                      large audience.
                                     can go directly to

                                                     5
                                   the B2B platform
                                   Instead of contacting
                                   multiple     individual
                                   suppliers.
Instant             Consumers      Consumers       always    Advertisers   Coca      Cola       places
massenger                          people may sign up                      television
                                   to AIM and MSN                          advertisements on
                                   instant      messaging                  MSN and AIM
                                   services,    and   use
                                   AIM and MSN in
                                   the same time.
Newspapers and      Reader         Common: In 1996,          Advertiser    Common:                For
Magazines                          the average number                      example,             Sprint
                                   of magazines issues                     advertised in the New
                                   read per person per                     York     Times,       Wall
                                   month was 12.3.                         Street    Journal,     and
                                                                           Chicago          Tribune,
                                                                           among       many      other
                                                                           newspapers, on Aug.
                                                                           20, 2002.


     Some Source: Evans, David (2002). “The Antitrust Economics of Two-Sided Markets,”
AEI-Brookings Joint Center working paper.
     Table 2 implies that in two-sided markets, the demands of platform operators, regardless of
consumer or merchants, are to multihome universally. For example, in the PC market, the
application software developer usually can have the Windows operating system, Linux system
Unix system and so on simultaneously. Consumers may purchase both Microsoft Windows and
Linux simultaneously. Merchants may accept several types of credit cards simultaneously. People
may sign up to AOL and MSN Instant Messaging services simultaneously. Enterprise can seek the
employee through different job hunter company; merchants may accept several types of credit
cards; the consumer can also simultaneously have Visa and American Express and so on.
Multihoming not only influences the Firms’ pricing level but also pricing structure in the industry
with two-sided markets characteristics.
     Surprisingly, few existing literatures on compatibility take into account the self-and cross
network externality in asymmetric two-sided markets. Starting with Katz and Shapiro (1985) and
Farrell and Saloner (1985), the current literatures about network externality, compatibility and
standardization mainly concentrates on the single-sided market and seldom considers self-and cross

                                                  6
network externality simultaneously, such as Carte and Wright (1999), Laffont(1998). For examples,
researches on telecommunications carried by Carte and Wright (1999) show: In single-sided market,
network externalities allow the incumbent to use the terms of interconnection to maintain its
dominant position. The researches on the two-sided markets network externality have recently
developed. Baxter(1983), Frankel(1998)and Evans(2002) did some researches on two-sided
markets by investigating on payment card system. Rochet and Tirole (2002) firstly established
normative framework to study on two-sided markets in the context of the credit card market. Later,
Rochet and Tirole.(2003) provide theoretical frameworks of two-sided markets to explain what is
two-sided markets and how the structure of prices is determined under monopoly and
oligopoly .Armstrong (2005) considers three basic settings: (I) a monopoly platform; (II) two-sided
single-homing where two platforms that are differentiated based on the Hotelling model compete
for each group, but all users join a single platform exclusively; and (III) competitive bottlenecks
where two platforms compete for one group of users, who join a single platform exclusively, but
not for the other group of users, who join both platforms (multihome).Armstrong, M and J. Wright
(2004) discussed the factors that impact on the pricing structure in two-sided markets and the
influence of exclusive dealing on market equilibrium.
     Although multihoming are commonplace, current literatures on compatibility and
standardization seldom allow for the issue. Most of the literatures assume consumers can purchase
only one of the competing products (foe example, Sony versus Nintendo). In fact, Multihoming
was commonplace in the early introduction of the telephone in the United States. At the start of the
1900s, there were competing but not interconnected telephone networks in many cities. In the
absence of interconnection, users would require separate phone lines connecting to each network so
as to reach a wider number of people. According to the research done by Mueller (1998), almost all
the high types (large-scale enterprises) are to multihome in order to build relations with more
customers. Despite telecommunications network have been mandated to interconnect in order that
only one phone connection can get all network benefits. In other network industries, such as
payment systems and game platforms, there does not seem to be any serious consideration of
network compatibility, arguably because of the presence of widespread multihoming in these
markets. This raises the question: In the presence of self-and cross network externality, does
multihoming mean policymakers need not be concerned about compatibility problem, in which
firms do not make their networks compatible even though doing so is socially desirable in
asymmetric two-sided markets? An early paper to consider multihoming is Church and King (1993),
who consider the equilibrium versus socially optimal level of learning of a second language. De
Palma et al. (1999) assumed compatibility choices take place first, and then firms compete for
quantity, where consumers are heterogeneous with respect to network benefits but not with respect
to how they value the firms’ products. The model implies, in the absence of multihoming, that firms
will always differentiate their product vertically by offering networks of different sizes. The

                                                 7
possibility of multihoming eliminates this vertical differentiation and results in a continuum of
symmetric equilibria. Despite equilibriums is complex, they show that double purchases
“drastically affect the nature of the product market equilibrium as well as compatibility choices
made by the firms” (p. 209). De Palma et al. concluded that in the presence of multihoming, firms
are too likely to become compatible though it is inefficient and that welfare is maximized by
imposing complete incompatibility, relying instead on multihoming. Cre´mer et al. (2000) analysis
the interconnection of “Backbone market” in the internet in the presence of mulithoming.Bernard
Caillaud and Bruno Jullien (2003) analyze a model of imperfect price competition between
intermediation service providers (ISPs) with indirect network externalities, whose Intermediation
services usually are not exclusive. In their model, intermediation service providers act as
matchmakers and can use sophisticated pricing (registration fees, and possibly transaction fees
provided the intermediaries observe transactions). Indeed, one of their contributions is to show that
dominant Firms are better off charging transactions rather than registrations when deterring entry.
They also show that competition is more intense when platforms cannot deter multihoming.
Doganoglu and Wright (2003) use Hotelling model to analyze the consequences of multihoming on
private and social incentives to compatibility, and substitution between multihoming and
compatibility from private and social point. Different from De Palma et al., theirs indicates in the
presence of multihoming, even the compatibility between firms can enhance the social welfare, but
consumers will give up multihoming after firms making compatible available, which leads to the
high competition pressure on firms, then firms will choose incompatibility. However, Doganoglu
and Wright analysis mainly on single-sided and then replicate the model to symmetric two-sided
markets, in which they only care cross network externality and overlook self-network externality.
They did not allow for the impact of self- and cross network externality on competition and
compatibility in asymmetric two-sided markets, which are very important. Moreover, they ignored
the fact that many two-sided markets are asymmetric (see table 1). Taking into account self- and
cross network externality simultaneously which is popular in asymmetric two-sided markets, this
paper analyzes the impact of multihoming on the compatibility of the firm and social welfare under
oligopoly.
     The rest of the paper proceeds as follows. Section 2-4 develops a model in which consumers
can purchase from one or both of two firms in asymmetric two-sided markets, and compares with
case with and without multihoming, and with and without compatibility. Section 5, we compares
with private and social optimal with and without multihoming, and with and without compatibility.
Section 6 offers some brief concluding thoughts and discusses the case of payment card industry in
China.
     2. The model
     A standard hotelling model of competition with network externality established by Kazt and
Shapiro (1985), Then Fallall and Saloner(1992), Shy(2001), and Armstrong(2005) use the model to

                                                 8
analyzed compatibility problem. Doganoglu and Wright (2003) extend this standard approach by
allowing consumers to be heterogeneous in terms of their marginal valuations of network size so
that multihoming arises as an equilibrium outcome. We extend Doganoglu and Wright’ approach to
study competition in asymmetric two-sided markets in which self-and cross network externality
play an important role simultaneously.
      Based on Doganoglu and Wright, this paper analyzes the consequences of self- network
externality and cross network externality in asymmetric two-sided markets and the presence of
multihoming on the firms and social desirability of compatibility, Unlike single-sided markets, such
as telecommunications, the network utility of consumers is generally correlative to the number of
consumers who get services from same telecommunication network. In asymmetric two-sided

markets, two symmetric firms (platforms) i , i = 1, 2 operates on two markets A, B . There are two

distinguished consumers belong to different markets A, B , denoted N and m. The market share of

                                N i , mi separately. Market share of Firm i , i = 1, 2 in market B
firm i in markets A, B equal to

cannot be affected by consumer’s behavior. Network benefits of consumers in market A do not
depend on the numbers of consumers in the same market (market A ), but on the numbers of
consumers in opposite market (market B ).
     To describe the multihoming, we assume consumers to be heterogeneous in terms of their
marginal valuations of network size of market A . In market A, assuming there are two types of
consumers who have different preference for marginal network benefits. The one who has the high
evaluation is called high types, while who has the low evaluation is called low types. Take payment
card as examples, if the banks are incompatible, consumers holding the card issued by bank A can
not fulfill the payment card transactions with merchant whose payment card transactions is
disposed by bank B. Therefore, high types with high time added-value wouldn’t spend much time
on finding a POS, which can fulfill the payment card transactions when banks are incompatible.
Then the high types will have to hold two or more payment cards issued by different bank to avoid
transactions unavailable. That is to realize “compatibility” by themselves and enjoy greater network
benefits. On the contrary, low types have low time added value. They would like to spend time on
finding a POS that can fulfill the payment card transactions. If holding payment card will be
charged positive fee the low types will usually hold only one payment card6.

     Suppose in asymmetric two-sided markets, there are two firms i , i = 1, 2 , located at either end

of unit interval [0,1] , providing goods or services with horizontal diversity to market A and B .

     6
      According to a survey, after China four state-own banks announced payment card will be charged annual
fee(¥10 per year),59.8% consumers among the interviewees will quit their cards used infrequently,22.0% of them
are reluctant to quit their cards,18.2% of them are indeterminable.

                                                          9
                         x1 = 0 .Firm 2 is located at x2 = 1 . Consumers belong to market A are
Firm 1 is located at

uniformly distributed on the unit interval [0,1] . Consumers belong to market A get network

benefits from two ways .One is from the expected number of consumers belong to market B , who
interact with consumers belong to market A through the same firm (platform), the other is from
the expected number of consumers belong to market A , who get the same goods or service as
consumers in market A .
      As Consumers have different network benefit evaluation, Consumers get service or goods
from either firm 1,or firm 2, or both firms if possible, that is to say some consumer may multihome.

Market A ’s consumer get network benefits from Market B is equal to
                                                                            α mi , α is the average

value of marginal network benefit getting from market B , which exhibits the strength of cross

network externality.
                       mi is the market share of firm i in market B 。 Market A , there are two types
                                                                     In

of consumers according to their marginal valuation of the network benefits. Each consumer get

                                           bN i , i = 1, 2 , where b = bH or bL , denotes
network benefits from Market A is equal to

marginal network benefits getting from market A . A fraction λ , λ ∈ [0,1] of consumers’ value the

                                                                 b = bH . By contraries, a fraction of
network benefits highly from market A (high types) and have

1 − λ value the network benefits lowly, and have b = bL ≥ 0 .Generally, we assume that

bH > bL > 0 。 N i represents the total number of consumers that get service or goods from firm i in

market A . The average value of the network benefits parameter b is denoted by

β , β = λbH + (1 − λ )bL , which exhibits the strength of self-network externality

     Consumers obtain intrinsic benefits
                                            v0 from a transaction through a single firm. Throughout


  the paper we assume that
                                v0 is sufficiently high so that all consumers will have at least one

  transaction。It should be emphasized that: although consumers can obtain extra intrinsic benefits
  by choosing two firms for transactions, the main purpose of multihoming is to finish the
  transaction easily and quickly. Therefore, we assume the intrinsic benefits they get from

                         v0 even if consumers with multihoming. Assume unit transportation cost is
  transaction is still
  t , which depict the consumer’s preference to goods or services provided by firms. If consumers
  purchase from firm 1,she will bear transportation costs tx . If consumers purchase from firm

  2,she will bear transportation costs t (1 − x) . To avoid the possibility of corner solution, we will


                                                  10
 adopt the standard assumption that the transportation cost parameter is greater than the relevant

 network benefits parameter, that is t >        β 。We assume the game is: In stage 1, two firms

 determine whether to be compatible. Stage 2, two firms decide the investment and the size of
 market B. Stage 3, firms set prices in market A and consumers choose one or both firms in stage
 4.we look for subgame perfect equilibrium, which imply that consumers have rational
 expectations to determine the size of each network given the prices set in stage 3. To get
 subgame perfect equilibrium, we deduce backward.

        3. Full Incompatibility without Multihoming
        3.1 Pricing competition and the choice of market B

    Let
           si and ni denote the share of high and low types that get goods or services from firm i


 respectively. Assume that there are λ high types, a share
                                                                        s1 of which get goods or services


 from firm 1, and there are (1 − λ ) low types, a share 1 of which get goods or services from
                                                        n

 firm 1, the total number of consumers that get goods or services from firm 1 is

  N1 = λ s1 + (1 − λ )n1 . Likewise N 2 = λ s2 + (1 − λ )n2 from firm 2。Then a consumer located at
  x gets unity through transaction:

    ⎧U1(x, b, N1) = v0 − p1 − tx +αm1 + b(λs1 + (1− λ)n1)                            f romf i rm1
    ⎨
    ⎩U2 (x, b, N2 ) = v0 − p2 − t(1− x) +αm2 + b(λ(1− s1) + (1− λ)(1− n1))           f romf i rm2

              p1 , p2 is the price of firm 1 and firm2 in market A separately. Assuming consumers
    Where
 are not able to multihome, the number of consumers joining each firm can be found by equating

  U1 to U 2 . We can find the high-values and the low-values who are indifferent between

 purchasing from each form.

                                ⎧U1 ( s1 , bH , N1 ) = U 2 ( s2 , bH , N 2 )
                                ⎨
                                ⎩U1 ( s1 , bL , N1 ) = U 2 ( s2 , bL , N 2 )                        (1)
    Solving      these   equations     simultaneously         and      simplifying   them   implies   :

        1 p2 − p1 + α (m1 − m2 ) p2 − p1 + α (m1 − m2 )bH
s1N =     +                     +
        2           2                   2t (t − β )                                                   ,

        1 p2 − p1 + α (m1 − m2 ) p2 − p1 + α (m1 − m2 )bL
n1N =     +                     +
        2           2                   2t (t − β )

    With
            N1 = λ s1 + (1 − λ )n1 , s2 = 1 − s1 , n2 = 1 − n1 and β = λbH + (1 − λ )bL , using the


                                                     11
market share function above, we find that: In market A, market share of firm 1:

           1 p2 − p1 + α (m1 − m2 )                                 1 p − p2 − α (m1 − m2 )
N1N =        +                                                N 2N = + 1
           2       2(t − β )        ; Market share of firm 2:       2      2(t − β )        .

     In order to obtain the platform competition advantage, most firms (platforms) develop market
B by direct investment, such as providing free product or service to market B. Their purpose is to
attract the consumers in market B to choose their products or services, then attract consumers
belong to market A. (See table 1). For instance, in payment card industry, to attract consumers use
their payment card, some banks provide free acquirer service to the merchants in acquirer market.
To do all above, bank will take some cost, such as instruments investment, training program, etc.

                                      dϕ (mi )      d 2ϕ (mi )
                                               >0              >0
Assume cost function is
                        ϕ (mi ) ,where dmi        ,
                                                       dmi2       ,We assume that the cost

                                                                         1
                                                              ϕ (mi ) = mi2
function of firm i to promote the size of market B is:                   2     。Therefore, the payment

                                                 1
                          π iN = ( pi − f ) N i − mi2
function of firm i is :                          2      ,where f represents constant marginal cost of

providing a service to consumers .
  . Taking the first order condition, we can get the equilibrium prices of two firms, then
equilibrium market share, equilibrium profits.

                             α (m1 − m2 )                           α (m1 − m2 )
      p1N = (t − β ) + f +                  , p2 = (t − β ) + f −
                                               N

                                  3                                      3         ;

               1 α (m1 − m2 )        1 α (m2 − m1 )
      N1N =      +             N 2N = +
               2   6(t − β ) ,       2   6(t − β )

         [3(t − β ) + α (m1 − m2 )]2
     π = N
                                     − ϕ (m1 )
                 18(t − β )
        1


         [3(t − β ) − α (m1 − m2 )]2
     π =N
                                     − ϕ (m2 )
                 18(t − β )
        2



          ∂N1     ∂N       ∂p1     ∂p
              > 0, 2 > 0       > 0, 2 > 0
     with
          ∂m1     ∂m2    ;
                           ∂m1     ∂m2    ,we get:

     Proposition 1 When firms (platform operators) are incompatible, each firm’s demand will
increase with its size of market B. The bigger the size in market B, the higher the price in market A
will be.
  Comparing with the traditional market, demands of one side in two-sided market depend not
only on the price which set by firm in one side market (market A), but also on the size of other side


                                                     12
(market B) that promoted by firm. The more consumers of the firm in market B, the more
consumers in market A would like to transact by this firm (platform), then firm (platform operator)
will charge high price for the customers.
  Substituting the equilibrium market prices, equilibrium market share into the payment function.

                                  ∂π i                                                     α
                                       =0                                        m1 = m2 =
Taking the first order condition:
                                  ∂mi     . The size of two firms in market B is           3。

                                                       α
                                       m1N = m2 =
                       1                      N

Where,α < 3(t − β ) .Substituting
                       2
                                                         3   into
                                                                    p1N , p2 , N1N , N 2N ,π 1N , π 2N , we
                                                                           N



can get the equilibrium prices of two firms, then equilibrium market share, equilibrium profits:

                  1                                          (t − β ) α 2
   N1N = N 2N =                                π 1N = π 2N =         −
                  2 ; p1 = p2 = (t − β ) + f ;
                       N    N
                                                                2      18 。

  Firstly, pricing difference between platform operators and traditional firms is mainly represented

as the self-network externality β in the market A and the cross network externality α in the

market B. Secondly, the competition between incompatible firms is very severely due to the
presence of cross network externality. Market equilibrium prices are lower than that of traditional
Hotelling. Thirdly, profits will decrease because of the severe market competition. Comparing with

                                                                            α 2 + 9β
the traditional Hotelling model, the equilibrium profit is decreased by          18    。When α → 0 ,

the cross network externality becomes weaker, and self-network externality plays a leading role. In
single market competition, though network externality affects the profits of firms, the strength of
network externality is weaker than that of two-sided markets, which shows cross network
externality enhance the competition of the firms. To capture more install-base in two-sided markets,
firms lower their price to aggrandize their market share, so profits decrease.
     3.3 Equilibrium social welfare under incompatibility without multihoming
     Equilibrium social welfare under incompatibility without multihoming is the sum of firms and
consumers. The consumer surplus is the sum surplus of the high types and low types consumers in
market A, and consumers in market B getting from the transaction through platform transaction
(see table 3). The total social welfare is:

                                                 β       2α 2     t
                                   CSTN = v0 +       +        −f−                                   (1)
                                                 2        9       4
     The first three terms are the intrinsic and network benefits when there is no compatibility and
no multihoming. Unlike the network industry of single market, network benefits of two-sided
markets is not related to the size of one side market, but also related to the other side market.



                                                  13
    t
(f + )
    4           represents the costs of providing the service and consumers’ average transportation

costs. Firms earn high margins if their products are more differentiated (transport costs are high)
and low margins if network effects are strong (in which case firms compete severely in an attempt
to capture whole market).

         4. Full Incompatibility with Multihoming
        4.1 Pricing competition and the choice of market B
    In order to investigate the multihoming impact on equilibrium in the incompatible firms
competition, we rule out two extreme cases in market A. First, there are no equilibria in which all
consumers multihome, since charged for positive prices each consumer has no reason to multihome.
Second, we are interested in the multihoming effects on competition in asymmetric two-sided
markets so we rule out that no consumer chooses to multihome in equilibrium, as in this case
allowing consumers to multihome will not change the results. Based on the above assumption, we
assume all low types singlehome (subscribe to one firm only) and all high types multihome. Then

the total network benefits of high types obtained from two-sided markets are,
                                                                                             α (m1 + m2 ) + bH .

Because high types choose two platforms to do the transaction, the unit transportation cost they

            s = 1 , N i = λ + (1 − λ )ni , i = 1, 2 。Other assumption is same as above.。
take is t , i
                  M             M



        Then the consumer located at x gets unity through transaction:

                      ⎧ U1 ( x, b, N1 ) = v0 + α m1 − p1 − tx + b[λ + (1 − λ )n1 ]               from f i r m1
                      ⎪
                      ⎨U 2 ( x, b, N 2 ) = v0 + α m2 − p2 − t (1 − x) + b[λ + (1 − λ )n2 ]       from f i r m2
                      ⎪ U ( x, b, N ) = v − p − p − t + b+α (m +m )
                      ⎩                   0     1    2                1   2                       from Bot h

    And have
                    U1 (n1 , bL , N1 ) = U 2 (n2 , bL , N 2 ) ,yield to the market share of firm 1 in low types:

                1 α (m1 − m2 ) + ( p2 − p1 ) M 1 α (m2 − m1 ) + ( p1 − p2 )
        n1M =     +                         , n2 = +
                2     2[t − bL (1 − λ )]          2  2[t − bL (1 − λ )]     7
    As high types, instead of selecting firm according to its size, to obtain two network benefits,
the high types will choose multihoming to make up the inconvenience caused by the
incompatibility between firms. As low types, comparing with the incompatibility without
multihoming, though the low types’ price sensitivity of demands is less than that of under
incompatibility without multihoming, the consumers’ choice to firms are still influenced by the
network size of market B. The demands of low types are more sensitive to price than that of the
traditional Hotelling model。


    7
        由于
             t > β ,因此, n1 , n2 仍然在 [0,1] 上。

                                                         14
                                                                       1 2
      The payment function of firm i is the same:π i = ( pi − f ) N i − mi , i = 1, 2 ,
                                                    M                M
                                                                                       where f
                                                                                    2
is the cost of service for firms, N i = λ + (1 − λ )ni 。From payment function, because high types
                                            M



will select the two firms simultaneously, their main competition objects for firms are low types。
                  M     M
Substituting n1 , n2            into firm’s payment function. Taking the first order, yield to equilibrium

market price:
                  1+ λ                     α (m1 − m2 ) M         1+ λ                     α (m2 − m1 )
      p1M = f +        [t − bL (1 − λ )] +             , p2 = f +      [t − bL (1 − λ )] +
                  1− λ                          3                 1− λ                          3
The market share of firms are:

              (1 + λ )    α (m1 − m2 )               (1 + λ )    α (m2 − m1 )
      N1M =            +                    , N 2M =          +
                 2       6[t − bL (1 − λ )]             2       6[t − bL (1 − λ )]

      Proposition 2 The presence of multihoming weaken the scale advantage of firms in market B
compared to that of full incompatibility without multihoming,

                                                                                            ∂N iN ∂N iM
      Proof: since t > β ,            β = λbH + (1 − λ )bL , so t > bL (1 − λ ) , 从 而            >      ,
                                                                                            ∂mi    ∂mi

∂piN ∂piM
    =     > 0 。The impact of Market B’s size on firm’s demands is decreased, but no impact
∂mi ∂mi

on firm’s market pricing. The presences of multihoming weaken the scale advantage of firms in
market B.
      Substituting the equilibrium market price, market share into payment function, according to

                                         ∂π i
the   first   order     condition             = 0 , the market share of two firms in market
                                         ∂mi

                      α (1 + λ )                           1
                                                                                               α (1 + λ )
B: m1 = m2 =
      M       M
                                    where       α < 3(t − β ) 2 。 Substituting m1M = m2 =
                                                                                      M
                                                                                                            into
                            3                                                                      3

p1 , p2 ,N1 , N 2 ,π 1 , π 2 ,then we can get equilibrium market share, equilibrium market price and

equilibrium profits(See table 3)。
                                                                 1+ λ
      Since t > β ,then t > bL (1 − λ ) , ∆p                   =(      − 1)[t − bL (1 − λ )] + λ bH > 0 。
                                                          MN
                                         so                                                              Since
                                                                  1− λ
dpiM 2t − (1 − λ ) 2 bL                       ∂piM
    =                   , t > bL (1 − λ ) ,so      > 0。
 dλ      (1 − λ ) 2                            ∂λ
      Proposition 3 under full incompatibility with multihoming, equilibrium price will increased
with the proportion of consumer to multihome, while the network externality caused by the
presence of the single-homing consumers constrain the price to rise.

                                                          15
     Obviously, even in the presence of full incompatibility, if multihoming exists, the equilibrium
price will go up when market reaches equilibrium. The increasing proportion of multihoming will
push the price in market A go up. But the increasing price will still be limited by the network
externality.
     Firms will take the opportunity that the high types will choose the two firms at the same time
to charge high price for them in order to get more profits. But the presence of low types will
restrain the price go up. Because firms find that if they cut price and charge lower than their rivals,
which will not only make the high types give up choosing the rival’s platform but also can attract
more low types when the more high types are captured. So two firms will cut price. The lower
portion of high types, the more incentives to cut price .The existence of multihoming make the two
firms to trade off the benefits brought by charging high price for high types and market share of
low types. Obviously, the presence of multihoming cause the firms to set high price and earn more
profits, but the low types makes the firms have to face the competition pressure and have incentive
to cut price. The result is that market price will be affected by the network externality absolutely,
and the price is not equal to the equilibrium price when network externality is not existed.
     When                    the                       proportion                  of                multihoming

                       α2                        1 (1 + λ ) 2                        λ b α 2 λ (2 + λ )
satisfies: λ ≥                      , ∆π        = (           − 1)(t − (1 − λ )bL ) + H −               >0
                                           MN

                 α 2 + 3(t − bL )                2 (1 − λ )                            2       18

                         1
                                                  α2            α2                              ∂π iM
。Since α < 3(t − β ) 2 , equaling to t >                +β >         + (1 − λ )bL , yield to:         > 0。
                                                   9            9                                ∂λ
     Proposition 4 under full incompatibility with multihoming, when the proportion of consumer

                                            α2
                              λ≥
to multihome satisfies
                                    α 2 + 3(t − bL ) , the equilibrium profit will increase with the
proportion of consumers to multihome.
     Though the market competition become severely due to full incompatibility and their profits
go down, the proposition 3 and proposition 4 shows that multihoming reduce competitive
pressures ,and bargain power of firms increase, then equilibrium prices and profits of firms go up.
      4.2 Equilibrium social welfare under incompatibility with multihoming
     Equilibrium social welfare under incompatibility with multihoming is still the sum of the
firm’s profits and consumers’ surpluses. The consumer surplus is the sum surplus of the high types
and low types consumers in market A, and consumers in market B getting from the transaction
through platform transaction (see table 3). The total social welfare is:

                                          1− λ2       2α 2 (1 + λ ) 2                (1 + 3λ )t
                       CSTM = v0 + λbH + (      )bL +                 − (1 + λ ) f −            (2)
                                            2               9                            4
     The first three terms represent the intrinsic and network benefits. From the point of network

                                                           16
benefits, high types that multihome not only increase the network benefits they get, but also make
the network benefits of low types in market A to increase correspondingly. Where
               (1 + 3λ )t
(1 + λ ) f +              represents the costs of providing the service and consumers’ average
                   4
transportation costs.

      5. Full Compatibility
      5.1 Pricing competition and the choice of market B
     Under full compatibility, firstly, firms need to spend fixed cost F to realize compatibility.
Secondly, under full compatibility, except extra cost, to multihome will not bring extra benefits to
the customers. So under full compatibility, consumers will not multihome. Thirdly, because of the
product differentiation between firms (platform operators), consumers in asymmetric two-sided
markets will obtain more utility when finish the transaction through the same platform than
differential platforms. For instance, if interconnection (universal-usage) is realized among banks,
cardholders can not only realize account transfer、deposit and withdrawal funds in any banks, but
also can consume by payment cards even if their issue bank and the merchant’s acquirer bank are
not the same, which means consumers can not get extra network benefits through multihoming. So
consumers will not pay for extra cost caused by multihoming. In this case, all consumers will only
hold one payment card. Additionally, promotions of issue banks will be done in the merchants
whose acquirer bank is the same as the issue bank. For examples, attractive frequent-user programs,
payment facilities, co-branding and corporate cards, and so on. Even if interconnection
(universal-usage) between different banks is realized, consumers can get more benefits from
transacting with merchants whose acquirer bank also issue the payment card, which consumers
hold than that of others.
     We assume: if the consumers in market A and market B belong to the customers who use the
same platform, the value of marginal network benefit of consumers in Market A getting from
market B is α ; if the consumers in market A and market B belong to the customers who use
different platform to fulfill transaction, value of marginal network benefit of the consumers in
Market A getting from market B is       γ . Based on the above, obviously α > γ .
     Then a consumer located at x gets unity through transaction:

                            ⎧U1 ( x, b, N1 ) = v0 + α m1 + γ m2 − p1 − tx + b            from Fi r m 1
                            ⎨
                            ⎩U 2 ( x, b, N 2 ) = v0 + γ m1 + α m2 − p2 − t (1 − x) + b   from Fi r m 2

     According to U1 ( x, b, N1 ) = U 2 ( x, b, N 2 ) , the market share of high types and low types

                                       1 p2 − p1 (α − γ )(m1 − m2 )
captured by Firm 1 is: s1 = n1 =         +      +
                             c     c
                                                                    . the market share of high
                                       2   2t            2t
types and low types owned by Firm 2 is: s2 = 1 − s1 , n2 = 1 − n1 。
                                             c        c   c         c




                                                    17
     In order to be compatible, firm i need to pay for compatible cost, its payment function
                     1
π ic = ( pi − f ) Ni − mi2 − F , i = 1, 2 . Substituting n1c , n2 ,s1c , s2 into payment function, taking
                                                                c         c

                     2
                                                                               (α − γ )(m1 − m2 )
the first order, the market price and market share is : p1 = f + t +
                                                                    c
                                                                                                  ,
                                                                                        3
           (α − γ )(m2 − m1 )                                        1 (α − γ )(m1 − m2 )
p2 = f + t +
 c
                                            ;             s1c = n1c = +                           ,
                    3                                                2         6t
         1 (α − γ )(m2 − m1 )
s2 = n2 = +
 c    c
                              。
         2           6t
     Substituting the equilibrium market price, equilibrium market share in the price competition

                                                          ∂π i
stage into above payment function, taking first order          = 0 , we can get the market size of two
                                                          ∂mi
                                 (α − γ )
firms in market B, m1 = m2 =
                      c     c
                                          , then market equilibrium price, equilibrium market share
                                    3
                                                   1             t (α − γ ) 2
and equilibrium profits is: p = p = f + t ; N = N = ; π 1 = π 2 = −           −F 。
                             c        c            c    c  c  c
                             1        2            1       2
                                                   2             2    18
     5.2 Equilibrium social welfare under full compatibility
     Equilibrium social welfare in full compatibility is still the sum of the firm’s profits and
consumers’ surpluses. The consumer surplus is the sum surplus of the high types and low types
consumers in market A, and consumers in market B getting from the transaction through platform
transaction (see table 3). The total social welfare is:

                                               2α 2 − 4γ 2 + 6αγ      t
                                 CS = v0 + β +
                                      c
                                      T                          − f − − 2F                       (3)
                                                       9              4
     The first three terms represent the consumers’ intrinsic and network benefits under full
compatibility. From the point of network benefit, comparing to fully incompatibility without
multihoming, because of self- and cross network externality network benefits that consumers get

                                                               (6αγ − 4γ 2 )
from market A increase β / 2 , getting from market B increases      9        , network externality

cause social welfare to increase. At the same time, the cost spending on realizing compatibility
decreases the total social welfare.

      6. Compatibility choice of Firms and policymakers
     6.1 Without multihoming
     We have discussed the conduction of oligopolies in three cases: full incompatibility without
multihoming; full incompatibility with multihoming and full compatibility. The research shows that
compatibility and multihoming have important effects on social welfare and on the firms’ choose of
the size of market B and the pricing in market A. (see table 3).

                                                   18
       Before considering the case with multihoming, we first think about the conventional case in
which multihoming is not considered, and analyses the choice of firms and policymakers to be
compatible. In the condition of full compatibility, firms don’t need to cut price for capturing more
install-base and sustain price at higher level. Because network compatibility is costly, to make full
compatible, firms need to upgrade their technology, even replacing their network system, which
needs high investment. So firms would like to choose full compatible only when full compatibility
could make the firms more profitably.
       Table3: Market equilibrium in different market structures
                            Full incompatibility    Full incompatibility with                       Full compatibility
                            without multihoming                multihoming
Equilibrium                            1/2                   (1 + λ )                                      1/2
market                                                          2

share:
           Ni

                                                         1+ λ
Equilibrium
                        (t − β ) + f               f+         [t − bL (1 − λ )]              f +t
market                                                   1− λ

price:
         pi

Equilibrium             α                          α (1 + λ )                                (α − γ )
size               in   3                                3                                      3
market:            B

mi

Equilibrium
                        (t − β ) α 2               (1 + λ ) 2 t          α2                  t (α − γ ) 2
                                −                            [     − bL − ]                    −          −F
profits:
              πi           2      18                   2      1− λ       9                   2    18

Consumer
                             3β α 2                                     λ 2 + 4λ + 3                     5 (α 2 − γ 2 )
                        v0 +    +   −f−
                                        5t         v0 + λbH + (                        )bL   v0 + β − f − t +
surplus;                                                                     2
                              2   3     4                                                                4      3
                                                       α (1 + λ )
                                                         2              2
CS B                                               +              − (1 + λ ) f
                                                          3
                                                     (λ 2 + 10λ + 5)t
                                                   −
                                                         4(1 − λ )
Social
                              β2α 2       t                      1− λ2                                  2α 2 − 4γ 2 + 6αγ
                        v0 + +      − f −          v0 + λbH + (          )bL                 v0 + β +
              CST           2   9         4                          2                                          9
welfare:
                                                     2α 2 (1 + λ ) 2                              t
                                                   +                                         − f − − 2F
                                                           9                                      4
                                                                  (1 + 3λ )t
                                                   −(1 + λ ) f −
                                                                       4


                                                    19
       Proposition 5 When the consumers’ average value of marginal network benefits getting from

                          9β 3γ
                     α>      +
  market B meets          8γ   4 , compatibility decreases the firm’s profits, firms will not choose

  to be compatible, social welfare will decrease.
       From the points of industries regulators, compatibility will be beneficial only if compatibility

                                                                                    β       6αγ − 4γ 2
can cause social welfare to increase. When CS c > CS N , then                 F<        +              .
                                                                                    4          18

             9β 3γ
When α >        + , for firms, to be compatible will decrease the profits. But from the points of
             8γ  4

industries regulators, compatibility will increase the social welfare. Further investigation shows

            3 6β
that   α>        , which implies when the impact of cross network externality is stronger than that
              4
of self-network externality, namely when consumers’ average value of marginal network benefits
getting from market B is high, compatibility between firms will be hard to achieve, social welfare
will be decreased.
       6.2 With multihoming
       When multihoming is possible, firms’ incentives to be compatible become more complex.
Under fully incompatibility, multihoming reduces effective competition and rise the price. At the
same time, demands go up due to multihoming, both of which increase the firms’ profits. If firms
are compatible, consumers can obtain all the network benefits, then consumers will not like to
multihome. Provided that profits are increased by allowing multihoming, so firms are less inclined
to be compatible.
       Proposition 6 When the consumers’ average value of the network benefits getting from

                          64t       19bL 2 f
                  β>              +     +
market A meet          10(1 − λ )     5   5 , although firms are not compatible, the presence of

multihoming cause consumers’ total surplus to increase.

       Proof: When the consumers’ average value of the network benefits getting from market A: β ,

                64t       19bL 2 f
        β>              +     +
meet         10(1 − λ )    5    5 , where CS M > CS N 。
                                            B      B

       When the consumers have the high evaluation on network benefits in market A, the presence
of multihoming relaxes the competition in market A. Firms can charge high price for high types
and get higher profits. So it is obvious that the presence of multihoming increase the firm’s
capability to make profits. On the other hand, comparing to the full incompatibility without


                                                    20
multihoming, although high types need to pay for higher cost       λ f and undertake the transportation
         3λ
costs       t in order to obtain more network benefits, proposition 7 implies: multihoming of high
          4
types is not only make themselves to obtain more network benefits, but also increase the network
benefits of low types. So comparing to fully incompatibility without multihoming, the consumers’
total surplus doesn’t fall.
     When the consumers have the high evaluation on network benefits in market A, even full
incompatibility, the consumers’ surplus will be improved if only part of consumers to multihome
Does it mean that it’s not mandatory for industry regulators to boost compatibility in the presence
of multihoming. Proposition8 and 9 show: when the ratio of consumes with multihoming reach
some degree, the incentive for firms to make compatible will be lower. Even in the presence of
multihoming, consumers’ surplus is still lower than that of in full compatibility. Define
       Π
H M = FM − FM to be the difference between firms’ profits change and social welfare’s change
            W



                                                                                     Π
with and without compatibility in the presence of multihoming. Define H N = FN − FN
                                                                                           W
                                                                                               to be the

difference between firms’ profits change and social welfare’s change with and without
compatibility when multihoming does not exist. If part of consumers to multihome, namely λ ≠ 0 ,

                     f (9 − λ )t (10 + 5λ )α 2
and also      bL <    +          −             , then ∆H = H M − H N < 0 . This implies:
                     2 8(1 − λ )      36
comparing to full compatibility without multihoming, even if high types multihome, when
single-homing consumers’ average value of the network benefits getting from market A are
relatively low, the ability of part consumers to multihome further decreases the firms’ motivation to
make compatible. The reason is that when single-homing consumers have low evaluation on
network benefits in market A, the demands of low types will decrease. Provided there is fully
incompatible between firms, high types can obtain the network benefits from market A and market
B through multihoming. Firms can obtain higher profits from multihoming without spending
compatible cost, which induce firms have insufficient motivation to be compatible.
        Proposition 7 The presence of parts of consumers to multihome further decreases the
incentive of firms to make compatible, which is harm to social welfare.

     Define       FM = π c − π M to be the firms’ profits change between with and without
                   Π



compatibility when multihoming is possible. When parts of consumers to multihome,

                              (1 + λ ) 2 bL λ (3 + λ )t (1 + λ ) 2 α 2 − (α − γ ) 2
if , π > π                                 −           +                            > F , the firms will
        c     M
                  ,namely
                                   2         2(1 − λ )              18

choose to compatibility. FM = CS − CS
                                W       c      M
                                                   represents the social welfare change between with


                                                    21
and without compatibility when multihoming is possible. From the points of policymaker, if
compatibility can increase social welfare, then mandatory compatibility is useful.

                                       (1 − λ ) 2 bL       3λ  6αγ − 2α 2 λ (2 + λ ) − 4γ 2
     From CS > CS
              c       M
                          , we get:                  +λ f + t+                              > 2F .
                                            2               4              9
When single-homing consumers’ average value of the network benefits getting from market

              (λ 2 + 6λ + 1)bL (15λ + λ 2 )t λ f 4αγ − 6λα 2 − 3λ 2α 2 − 3γ 2
A: bL meets                   <             +   +                             , choosing
                      4          8(1 − λ )    2             18
compatibility will decrease the firms’ profits, so the firms would not like to be compatible. Further
investigation shows that although the presence of multihoming can increase consumers’ surplus, if

                                                                     85
the ration of consumers to multihome:            λ meets 1 > λ >        − 1 ≈ 0.024 , under full
                                                                     9
incompatibility, even the presence of multihoming can increase consumer surplus, the consumer
surplus is still lower than that of under full compatibility. That means only if the industry realizes
full compatibility can let consumers obtain more benefits and social welfare be further improved.
     Proposition 8. Although the presence of parts of consumers to multihome can increase
consumer surplus, under full compatibility consumers can get more benefits, and social welfare will

                                                                       85
                                                            1> λ >        −1
increases when the ration of consumers to multihome meets              9     .
     We suggest that industry regulator shouldn’t ignore the compatibility among firms though
multihoming increases network benefits in some degree. The industry regulator should pay much
attention to compatibility especially even if the ratio of consumer to multihome is not high, which
cause significant cost to consumers.

      6. Conclusions
     Underlying the recent surge of academic interest in the network economy, compatibility and
standardization are always concerned by economists, public and private decision makers. The point
of this paper is to illustrate that firm’s incentive to compatibility is weaker when consumers are to
multihome in asymmetric two-sided markets, while the social desirability increases. Policymakers
should generally be more concerned about the lack of compatibility when multihoming is present.
This paper shows that the presence of multihoming in consumers cause price and profits of firms to
go up; though multihoming makes consumers achieve more network benefits and the consumer
surplus increases, the total social welfare decreases when self-network externality and
cross-network externality take place simultaneously, which weaken policymakers to concern the
issue of compatibility of networks. Generally speaking, multihoming may add inconvenience for
consumers, while weaken competition between the firms and make them less likely to prefer
compatibility. From the view of industry performance, only are fully compatible among the firms

                                                  22
can increase consumer surplus, and is social welfare improved greatly.
     Our findings have implications for the universal-usage reforms in China payment card
industry. Payment card industry in China has only developed for several years. At the beginning,
each bank established its payment card network. That is, every bank not only issued its card, but
also exploited its own acquirer market. For a long time, In Chinese payment card industry,
universal-usage8 can not be achieve among the banks, but payment card can not be used in
branches of same bank when the issue bank and acquire bank were not the same one. To
cardholders, payment card did not mean efficient and quick payment method; instead, bring in
certain inconveniency to cardholders. In addition, from the point of original intention to payment
card services, our commercial banks were very different from that of overseas commercial banks.
Since the commercial banks by no means has taken the payment card service as retail bank
operation continuously, and specially regarded the debitcard as the main tool to get deposits.
Therefore, Chinese consumer took the payment card usually as “salary card” (just as
electro-deposit book).A few cardholders applied for payment card initiatively. Thus, when the
consumer changed his work, he also would have a new payment card. As a result, the presence of
multihoming several card is universal. The ways of developing payment card operation on their
own ability cause bank have little incentive to be compatible. Moreover, the presences of
multihoming in cardholder make policymakers to pay litter attention to universal-usage in Chinese
payment card industry9, so that the problem of universal-usage continuously become the bottleneck
and blocks the Chinese payment card industry to expand, which lead to Chinese payment card
industry maintain inefficiently.
        To improve efficiency, Chinese payment card industry must be realized universal-usage,
which can make consumer benefits to increase. Therefore, when universal-usage can not facilitated
by market mechanism, policymakers should implement it, improve the payment card-accepting
environment, and impel the national payment card industry to develop.
        On March 26, 2002, agreed by the State Council, and authorized by the People's Bank of
China, based on the national payment card information exchange center and bank card information
c exchange center in 17 cities, Industry and Commerce bank of China, Agriculture Bank of China,
Bank of China, China construction bank, and bank of communication, more than 80 financial
organs as initiators set up China unionpay. As first bank card organization in China, CUP is devoted
to establish and operate nation payment card information exchange network, lets payment card to


    8
       Universal-usage is the term of compatibility in payment card industry. Universal-usage means: Authorized
by the People's Bank of China, commercial banks, the countryside credit associations, postal offices etc., who
operate the payment card within the boundaries of China, should let their computer network system, the terminal
machines (ATM/POS), and the merchant as well as the technical service method etc., is connected with the payment
card exchange information system, realizes payment card service to be universally used.
9 Although “the golden card project" has been carry out since 1993,before China union pay established, not only
commercial banks would not want to bring universal-usage into effect ,but also local authorities are deficient
enthusiasm to impel universal-usage process, so that universal-usage can not be achieved.

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be universal-usage in nation scope, reduces the payment card redundant terminal building waste;
Realizes all POS/ATM universal-usage in 3 - 5 years, connects with the international credit card
associations, provides uniform ,safe and efficient payment card settlement services and other
                                                      10
professional card payment guarantees the"314"              project complete smoothly in 2002. Having
established three years, China payment card industry realized compatibility in 2002; the payment
card transaction volume has been double. Having realized universal-usage in 2003, the China
payment card transaction volume has been double again. Obviously, as a payment card association,
the CUP plays an important role in impelling China payment card industry. Universal-usage boosts
the industrial scale to rapid growth. The facts of China payment card industry development have
proven the point of this paper. Meanwhile, the related conclusion in this paper can provide the
essential theory support for the "golden card project” as well as the establishment of CUP.

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10 “314”see www.chinaunionpay.com.

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Without loss of generality,




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