Job Market Paper

Stochastic Games in Continuous Time: Persistent Actions in Long-Run Relationships

In many instances, a long-run player is influenced not only by considerations of its future but also by actions it has taken in the past. For example, the quality of a firm's product may depend on past as well as current investments. This paper studies a new class of stochastic games in which the actions of a long-run player have a persistent effect on payoffs. The setting is a continuous time game of imperfect monitoring between a long-run and a representative myopic player. The main result of this paper is to establish general conditions for the existence of Markovian equilibria and conditions for the uniqueness of a Markovian equilibrium in the class of all Perfect Public Equilibria. The existence proof is constructive and characterizes, for any discount rate, the explicit form of equilibrium payoffs, continuation values, and actions in Markovian equilibria as a solution to a second order ODE. Action persistence creates a channel to provide intertemporal incentives, and offers a new and different framework for thinking about the reputations of firms, governments, and other long-run agents.