Prices and mergers in a general model of multi-sided markets

We present a general and tractable oligopoly model of multi-sided platforms with endogenous side and platform choices of heterogeneous end-users, considering any mix of single-homing and multi-homing platforms and in which participating on one side could preclude doing so on others. We show the existence of a unique equilibrium number of end-users and characterize optimal platform pricing. Using the equilibrium conditions, we formally derive (across sides and platforms) switching effects that distort optimal pricing, which can lead to markups exceeding the Lerner index and rule out the classical "cross-subsidization" result. We then provide a unifying framework to analyze multi-sided platform mergers, which rationalizes mixed results from the previous literature by providing, based on the switching effects, a set of conditions that predict the upward pricing pressure post-merger. We show that while optimal pricing is determined by the nature of end-users' side choices, their platform choices are crucial for merger analysis.