Two.sided.market

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 there exists 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

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Introduction

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, sellers are 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 shopping