I introduce a dynamic framework to analyze platforms. The (single) platform owner sets prices at the beginning of each period. Agents (buyers, sellers, readers, consumers, merchants, etc.) make platform membership decisions occasionally. I show that an optimal platform pricing addresses two externalities: across sides and across time periods. This results in optimal prices which depend on platform size in a nontrivial way. By means of numerical simulations, I examine the determinants of equilibrium platform size, showing that the stationary distribution of platform size may be bimodal, that is, with some probability the platform remains very low or takes very long to increase in size. I also contrast the dynamics of proprietary versus nonproprietary (i.e., zero‐priced) platforms, and consider the specific case of asymmetric platforms (one side cares about the other but not vice versa).