Price Competition in Multi-Sided Markets

Abstract

This paper studies a general model of price competition among platforms offering differentiated services in multi-sided markets. We incorporate a general form of both within-side and cross-side externalities into a discrete choice model of random utility maximization by consumers on each side of the markets. We consider a two-stage game in which the platforms choose prices (or user fees) simultaneously in the first stage, followed by consumers on all sides simultaneously deciding which platform to join (single-homing) in the second stage. We show that in a symmetric setting with full market coverage, there exists a symmetric equilibrium in prices and the equilibrium price on each side follows a simple rule: The price equals the cost, plus a mark-up due to product differentiation, minus a subsidy due to cross-side externalities. The subsidy to each side accounts for the degree of the aggregate marginal externalities of that side imposed on all the other sides. As competition among platforms increases, both the product differentiation effect and the cross-subsidy are shown to decrease. As such, the price on one side can decrease while the price on another side may increase with the number of platforms. We also discuss the incentives for platforms to merge and the extent of excessive free entry of platforms into the markets as compared to the social optimum. We further compare uniform pricing rule with discriminatory pricing across different sides of the markets and find that the average price across sides under the discriminatory pricing is higher than the uniform price when the externalities are small or when the number of platforms is large. The impacts of consumers’ outside options on the equilibrium prices are also studied.

Keywords: Multi-Sided Markets, Platform Price Competition, Cross Subsidization, Discrete Choice Models, Free Entry, Merger Incentives, Discriminatory Pricing, Uniform Pricing, Outside Option

JEL Classification: L13, L4