We examine the following paradox: in a dynamic setting, equilibria can be radically different in a model with a finite number of agents than in a model with a continuum of agents. We present a simple strategic setting in which this paradox is a general phenomenon. However, the paradox disappears when there is noisy observation of the players' actions, and the aggregate level of noise does not disappear too rapidly as the number of players increases. We give several economic examples in which this paradox has recently received attention: durable-goods monopoly, corporate takeovers, and time consistency of optimal government policy.