Stationary Nash Equilibria for Average Stochastic Positional Games

Abstract

An average stochastic positional game is a stochastic game with average payoffs in which the set of states is divided into several disjoint subsets such that each subset represents the position set for one of the player and each player controls the Markov process only in his position set. In such a game each player chooses actions in his position set in order to maximize his average reward per transition. We show that an arbitrary average stochastic positional game possesses a stationary Nash equilibrium. Based on this result we propose an approach for determining the optimal stationary strategies of the players.