Nonzero-Sum stochastic games

Abstract

This chapter describes a number of results obtained in the last 60 years on the theory of nonzero-sum discrete-time stochastic games. We provide an overview of almost all basic streams of research in this area such as the existence of stationary Nash and correlated equilibria in models on countable and general state spaces, the existence of subgame-perfect equilibria, algorithms, stopping games, and the existence of uniform equilibria. Our survey incorporates several examples of games studied in operations research and economics. In particular, separate sections are devoted to intergenerational games, dynamic Cournot competition and game models of resource extraction. The provided reference list includes not only seminal papers that commenced research in various directions but also exposes recent advances in this field.