Persistence in a dynamic moral hazard game

Abstract

This paper explores how the persistence of past choices creates incentives in a continuous time stochastic game involving a large player (e.g., a firm) and a sequence of small players (e.g., customers). The large player faces moral hazard and her actions are distorted by a Brownian motion. Persistence refers to how actions impact a payoff‐relevant state variable (e.g., product quality depends on past investment). 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. Persistence can serve as an effective channel for intertemporal incentives in a setting where traditional channels fail. Applications to persistent product quality and policy targeting demonstrate the impact of persistence on equilibrium behavior.