The Complexity of Solving Stochastic Games on Graphs

Authors:
Daniel Andersson;Peter Bro Miltersen
Affiliations:
Department of Computer Science, Aarhus University, Denmark;Department of Computer Science, Aarhus University, Denmark
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

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Abstract

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.