Solving Simple Stochastic Games with Few Random Vertices

Hugo Gimbert (1) , Florian Horn (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

We present a new algorithm for solving Simple Stochastic Games (SSGs). This algorithm is based on an exhaustive search of a special kind of positional optimal strategies, the \emph{f-strategies}. The running time is O( |Vr| (|V||E|+|p|) ), where |V|, |Vr|, |E| and |p| 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.

Mots clés: simple stochastic games; algorithms; games

Domaines: Informatique et théorie des jeux [cs.GT]

Hugo Gimbert, Florian Horn. Solving Simple Stochastic Games with Few Random Vertices. 2007. ⟨hal-00195914v1⟩