On Nash Equilibria in Stochastic Positional Games with Average Payoffs

We consider a class of stochastic positional games that extends deterministic positional games with average payoffs. The considered class of games we formulate and study applies the game-theoretical concept to finite state space Markov decision processes with an average cost optimization criterion. Necessary and sufficient conditions for the existence of Nash equilibria in stochastic positional games with average payoffs are proven and some approaches for determining the optimal stationary strategies of the players are analyzed. For antagonistic positional games are proposed. Iterative algorithms for determining the saddle points. Additionally we show that the obtained results can be used for studying the problem of the existence of Nash equilibria in Shapley stochastic games with average payoffs.