I study how the persistence of past choices can be used to create incentives in a continuous time stochastic game in which a large player, such as a firm, interacts with a sequence of short-run players, such as customers. The long-run player faces moral hazard and her past actions are imperfectly observed – they are distorted by a Brownian motion. Persistence refers to the fact that actions impact a payoffrelevant state variable, e.g. the quality of a product depends on both current and past investment choices. I obtain a characterization of actions and payoffs in Markov Perfect Equilibria (MPE), for a fixed discount rate. I show that the perfect public equilibrium (PPE) payoff set is the convex hull of the MPE payoff set. Finally, I derive sufficient conditions for a MPE to be the unique PPE. Persistence creates effective intertemporal incentives to overcome moral hazard in settings where traditional channels fail. Several applications illustrate how the structure of persistence impacts the strength of these incentives.