Stationary Nash equilibria for two-player average stochastic games with finite state and action spaces

The problem of the existence and determining stationary Nash equilibria in two-player average stochastic games with finite state and action spaces is considered. We show that an arbitrary two-player average stochastic game can be formulated in the terms of stationary strategies where each payoff is graph-continuous and quasimonotonic with respect to player’s strategies. Based on this result we ground an approach for determining the optimal stationary strategies of the players in the considered games. Moreover, based on the proposed approach a new proof of the existence of stationary Nash equilibria in two-player average stochastic games is derived and the known methods for determining the optimal strategies for the games with quasimonotonic payoffs can be applied.