Algorithms and Computation

Volume 5878 of the series Lecture Notes in Computer Science pp 112-121

The Complexity of Solving Stochastic Games on Graphs

  • Daniel AnderssonAffiliated withDepartment of Computer Science, Aarhus University
  • , Peter Bro MiltersenAffiliated withDepartment of Computer Science, Aarhus University

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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.