Nonzero-sum Stochastic Games

This paper treats of stochastic games. We focus on nonzero-sum games and provide a detailed survey of selected recent results. In Section 1, we consider stochastic Markov games. A correlation of strategies of the players, involving ``public signals'', is described, and a correlated equilibrium theorem proved recently by Nowak and Raghavan for discounted stochastic games with general state space is presented. We also report an extension of this result to a class of undiscounted stochastic games, satisfying some uniform ergodicity condition. Stopping games are related to stochastic Markov games. In Section 2, we describe a version of Dynkin's game related to observation of a Markov process with random assignment mechanism of states to the players. Some recent contributions of the second author in this area are reported. The paper also contains a brief overview of the theory of nonzero-sum stochastic games and stopping games which is very far from being complete.