Persistence in a dynamic moral hazard game

This paper studies how the persistence of past choices can be used to create incentives in a continuous time stochastic game. A large player, such as a firm, interacts with a sequence of small players, such as customers. The large player faces moral hazard and her actions are imperfectly observed---they are distorted by a Brownian motion. Persistence refers to the impact that actions have on a payoff-relevant state variable, e.g. the quality of a product depends on both current and past investment choices. I characterize actions and payoffs in Markov Perfect Equilibria (MPE) for a fixed discount rate, show that the perfect public equilibrium (PPE) payoff set is the convex hull of the MPE payoff set, and derive sufficient conditions for a MPE to be the unique PPE. These results illustrate how persistence provides a channel for effective intertemporal incentives in a setting where traditional channels fail. Applications to persistent product quality, policy targeting, and complementary investment demonstrate how the structure of persistence impacts the strength of incentives and the dynamics of equilibrium behavior.