Two-Sided Markets and Price Competition with Multi-homing

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 multihome. Network effects are captured within a vertical differentiation framework. Under single-homing there exists an interior equilibrium where networks exhibit asymmetric sizes and both firms enjoy positive profits. 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 profits for both platforms replicates the collusive outcome