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Two-Sided Markets and Price Competition with Multi-homing
Jean J. Gabszewicz and Xavier Y. Wauthy†‡ April 19, 2004

Abstract We model duopoly competition between two platforms.They operate in a two-sided market where agents are heterogeneous on both sides of the market and are allowed to mulithome. Network effects are captured within a vertical differentiation framework.Under single-homing thereexists an interior equilibrium where networks exhibit asymmetric sizes and both rms enjoy positive pro ts.When all agents are allowed to patronize the two platforms, we show that in equilibrium multi-homing takes place on one side of the market only. Moreover, the only equilibrium exhibiting positive pro ts for both platforms replicates the collusive outcome. Keywords : two-sided markets,networks, vertical differentiation JEL Classi cation :L13



This paper proposes a very simple framework to capture network externalities in two-sided markets, and their implications on price competition. In particular, it captures a key-feature of two-sided markets : the prices determine the equilibrium network sizes and, thus, the quality of the services offered by the platforms.Moreover, it allows for a simple treatment of multihoming behaviour. We model duopoly competition between two platforms which operate in a two-sided market with heterogeneous agents on both sides. Buyers and sellers interact through the platforms, with network effects operating from one market to the other, and vice-versa. Buyers are attracted by platforms housing many sellers and, conversely, sellersare drawn to platforms housing many buyers. A signi cant number of real-life markets operates under these features. Consider, as speci c examples, shopping malls, media markets, credit cards. The larger the number of shoppers attracted in a shopping mall, the higher the willingness of a retailer to locate in that shopping mall. Conversely, the larger the number of shops located in the shoppingmall, the higher the willingness of shoppers to pay a visit to it. Similarly, in exhibition centers, the larger the number of visitors, the larger the number of exhibitors who want to participate. In the same manner,the larger the number of exhibitors in an exhibition center, the larger the number of visitors. Another example is provided by the outgrowth of newspapers distributed for free to
CORECEREC et CORE ‡ We are grateful to Paul Belle amme and Jean Tirole for very stimulating comments on the paper. We remain solely responsible for remaining errors.

rst draft of this


readers, like Metro and 20 Minutes in France. These newspapers can be viewed as platforms on which readers and advertisers interact. The larger the readership of such a newspaper, the higher the willingnessto pay of an advertiser for inserting a commercial in it. Conversely, when readers bene t from a positive externality nding commercials in these newspapers, the larger the number of ads in a newspaper, the higher their willingness to read it. Consider now the platforms consisting of two companies issuing credit cards, and selling them to buyers and sellers as means of payment. Clearly the largerthe number of merchants accepting a particular credit card,the larger the willingness of a buyer for holding that credit card. Conversely, the larger the number of potential buyers holding that credit card, the larger the willingness of a merchant to subscribe to its issuer. All the above examples share two speci c features. First, they all display multihoming competition. Indeed, there is apriori no reason why a buyer or a seller should choose to interact through a single platform only, at the exclusion of the other. In the rst example above, in which two shopping malls compete for attracting buyers or visitors, there is no reason why one should a priori exclude a particular shopper to visit both shopping malls, and a particular retailer to settle a shop in both malls. Similarly, in...