Price Competition in Two-Sided Markets with Heterogeneous Consumers and Network Effects

We model a two-sided market with heterogeneous customers and two heterogeneous network effects. In our model, customers on each market side care differently about both the number and the type of customers on the other side. Examples of two-sided markets are online platforms or daily newspapers. In the latter case, for instance, readership demand depends on the amount and the type of advertisements. Also, advertising demand depends on the number of readers and the distribution of readers across demographic groups. There are feedback loops because advertising demand depends on the numbers of readers, which again depends on the amount of advertising, and so on. Due to the difficulty in dealing with such feedback loops when publishers set prices on both sides of the market, most of the literature has avoided models with Bertrand competition on both sides or has resorted to simplifying assumptions such as linear demands or the presence of only one network effect. We address this issue by first presenting intuitive sufficient conditions for demand on each side to be unique given prices on both sides. We then derive sufficient conditions for the existence and uniqueness of an equilibrium in prices. For merger analysis, or any other policy simulation in the context of competition policy, it is important that equilibria exist and are unique. Otherwise, one cannot predict prices or welfare effects after a merger or a policy change. The conditions are related to the own- and cross-price effects, as well as the strength of the own and cross network effects. We show that most functional forms used in empirical work, such as logit type demand functions, tend to satisfy these conditions for realistic values of the respective parameters. Finally, using data on the Dutch daily newspaper industry, we estimate a flexible model of demand which satisfies the above conditions and evaluate the effects of a hypothetical merger and study the effects of a shrinking market for offline newspapers.