Spatial competition among multiple platforms

We study spatial competition in two-sided markets, in which platforms engage in price competition in a circular city. After analyzing the pricing and profits of the unique symmetric equilibrium for a given number of platforms, we derive the number of platforms under free entry and compare it with the social optimum. We consider the case with or without a price restriction. In contrast to the excess entry result in Salop's (1979) model, the number of platforms is smaller than the social optimum if a minimum price binds, and if cross-group network effects are sufficiently large for a group of agents.