The Complexity of Solving Stochastic Games on Graphs

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We consider some well-known families of two-player zero-sum perfect-information stochastic games played on finite directed graphs. The families include stochastic parity games, stochastic mean payoff games, and simple stochastic games. We show that the tasks of solving games in each of these classes (quantitiatively or strategically) are all polynomial time equivalent. In addition, we exhibit a linear time algorithm that given a simple stochastic game and the values of all positions of that game, computes a pair of optimal strategies.

Work supported by Center for Algorithmic Game Theory, funded by the Carlsberg Foundation. A large fraction of the results of this paper appeared in a preprint [10], co-authored by Vladimir Gurvich and the second author of this paper. Vladimir Gurvich’s contributions to that preprint will appear elsewhere.