Stationary Almost Markov ε-Equilibria for Discounted Stochastic Games with Borel Spaces and Unbounded Payoffs

This paper is concerned with nonzero-sum discrete-time stochastic games in Borel state and action spaces under the expected discounted payoff criterion. The payoff function can be unbounded. The transition probability is a convex combination of finite probability measures that are dominated by a probability measure on the state space and depend on the state variable. Under suitable conditions, the authors establish the existence of stationary almost Markov ε-equilibria and give an approximation method via some stochastic games with bounded payoffs. Finally, a production game is introduced to illustrate the applications of the main result, which generalizes the bounded payoff case.