This paper develops a framework to analyze platform competition in two‐sided markets in which agents endogenously decide on which side of a platform to join. We characterize the equilibrium pricing structure and perform a comparative statics analysis on how the distribution of agents’ preferences affects the platforms’ profits. We also show that the market equilibrium under profit‐maximizing platforms leads to the first best social surplus, which illustrates the importance of the price mechanism to induce more balanced participation across the two sides. This framework can be applied to analyze market competition for “rental” or “sharing” platforms. In addition, we extend our analysis to consider an initial investment stage, which makes participants the owner of some durable goods to rent out.