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

We study the problem of the existence of stationary Nash equilibria in infinite $n$-person stochastic games with limiting average payoff criteria for the players. The state and action spaces in the games are assumed to be finite. We present some results for the existence of stationary Nash equilibria in a multichain average stochastic game with $n$ players. Based on constructive proof of these results we propose an approach for determining the optimal stationary strategies of the players in the case when stationary Nash equilibria in the game exist.