Stationary Equilibria for Nonzero-Sum Average Payoff Ergodic Stochastic Games with General State Space

Abstract

This paper treats of nonzero-sum average payoff stochastic games with arbitrary state spaces. Such models of games very well fit in some studies in economic theory. A natural uniform geometric ergodicity condition, often used in control theory of Markov chains, is imposed on the transition probabilities of the games. A correlation of strategies of the players, involving “public signals”, is allowed in this paper. The main result is an extension of the correlated equilibrium theorem proved recently by the author and Raghavan for dynamic games with discounting to the average payoff stochastic games. Also some special classes of games that possess Nash equilibria without public signals are discussed. This paper also provides a brief overview of the theory of nonzero-sum stochastic games which is very far from being complete.