Solving Simple Stochastic Games

Authors:
Hugo Gimbert;Florian Horn
Affiliations:
LaBRI, Université Bordeaux 1, France;LIAFA, Université Paris 7, France
Venue:
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Year:
2008

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Abstract

We present a new algorithm for solving Simple Stochastic Games (SSGs), which is fixed parameter tractable when parametrized with the number of random vertices. This algorithm is based on an exhaustive search of a special kind of positional optimal strategies, the f-strategies. The running time is , where and are respectively the number of vertices, random vertices and edges, and the maximum bit-length of a transition probability. Our algorithm improves existing algorithms for solving SSGs in three aspects. First, our algorithm performs well on SSGs with few random vertices, second it does not rely on linear or quadratic programming, third it applies to all SSGs, not only stopping SSGs.