The Complexity of Solving Stochastic Games on Graphs

  • Daniel Andersson
  • Peter Bro Miltersen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)


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.


Optimal Strategy Directed Graph Discount Factor Probability Weight Stochastic Game 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Daniel Andersson
    • 1
  • Peter Bro Miltersen
    • 1
  1. 1.Department of Computer ScienceAarhus UniversityDenmark

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