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SODA'10 (Symposium on Discrete Algorithms), United States (2010)

Solving Simple Stochastic Tail Games

Hugo Gimbert 1, Florian Horn 2

(2010-01-20)

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.

1:	Laboratoire Bordelais de Recherche en Informatique (LaBRI)
	CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – Ecole Nationale Supérieure d'Electronique, Informatique et Radiocommunications de Bordeaux – Université Victor Segalen - Bordeaux II
2:	Laboratoire Spécification et Vérification [Cachan] (LSV)
	CNRS : UMR8643 – INRIA – École normale supérieure de Cachan - ENS Cachan

Subject

:

Computer Science/Computer Science and Game Theory

Keyword(s): stochastic games – algorithmic game theory

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From: Hugo Gimbert <>

Submitted on: Friday, 4 September 2009 10:13:00

Updated on: Friday, 4 September 2009 10:17:44