Solving Simple Stochastic Tail Games

Hugo Gimbert (1) , Florian Horn (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LSV - Laboratoire Spécification et Vérification [Cachan]

Stochastic games are a natural model for open reactive processes: one player represents the controller and his opponent represents a hostile environnment. Teh evolution of the system depends on the decisions of the players, supplemented by random transitions. There are two main algorithmic problems on such games: computing the values (quantitative analysis) and deciding whether a player can win with probability 1 (qualitative analysis). In this paper we reduce the quantitative analysis to the qualitative analysis: we provide an algorithm for computing values which uses qualitative analysis as a sub-procedure. The correctness proof of this algorithm reveals several nice properties of perfect-information stochastic tail games, in particular the existence of optimal strategies. We apply these results to games whose winning conditions are boolean combinations of mean-payoff and Buchi conditions.

Mots clés: stochastic games; algorithmic game theory

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

Hugo Gimbert, Florian Horn. Solving Simple Stochastic Tail Games. SODA'10 (Symposium on Discrete Algorithms), Jan 2010, Austin, United States. pp.1000. ⟨hal-00413430⟩