On the computational complexity of solving stochastic mean-payoff games

We consider some well known families of two-player, zero-sum, turn-based, perfect information games that can be viewed as specical cases of Shapley’s stochastic games. We show that the following tasks are polynomial time equivalent: • Solving simple stochastic games, • solving stochastic mean-payoff games with rewards and probabilities given in unary, and • solving stochastic mean-payoff games with rewards and probabilities given in binary.