In this paper, we consider a zero-sum undiscounted stochastic game which has finite state space and finitely many pure actions. Also, assume the transition probability of is controlled by one player all optimal strategies are strictly positive. Under above assumptions, show that $\beta$-discounted games with same payoff matrices $\beta$ sufficiently close to 1 also completely mixed. We give cou...

We introduce stochastic priority games — a new class of perfect information stochastic games. These games can take two different, but equivalent, forms. In stopping priority games a play can be stopped by the environment after a finite number of stages, however, infinite plays are also possible. In discounted priority games only infinite plays are possible and the payoff is a linear combination...

We study the complexity of a class of Markov decision processes and, more generally, stochastic games, called 1-exit Recursive Markov Decision Processes (1-RMDPs) and Simple Stochastic Games (1-RSSGs) with strictly positive rewards. These are a class of finitely presented countable-state zero-sum stochastic games, with total expected reward objective. They subsume standard finite-state MDPs and...