Nash equilibria conditions for stochastic positional games

We formulate and study a class of stochastic positional games using a game-theoretical concept to finite state space Markov decision processes with an average and expected total discounted costs optimization criteria. Nash equilibria conditions for the considered class of games are proven and some approaches for determining the optimal strategies of the players are analyzed. The obtained results extend Nash equilibria conditions for deterministic positional games and can be used for studying Shapley stochastic games with average payoffs.