Using Persistence to Generate Incentives in a Dynamic Moral Hazard Problem

Abstract

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 i¬ rm, 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 payoi¬€relevant state variable, e.g. the quality of a product depends on both current and past investment choices. I obtain a characterization of actions and payoi¬€s in Markov Perfect Equilibria (MPE), for a i¬ xed discount rate. I show that the perfect public equilibrium (PPE) payoi¬€ set is the convex hull of the MPE payoi¬€ set. Finally, I derive sui¬ƒcient conditions for a MPE to be the unique PPE. Persistence creates ei¬€ective 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.