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LICS'09, IEEE Symposium on logic in computer science, Los Angeles : États-Unis d'Amérique (2009)

Qualitative Determinacy and Decidability of Stochastic Games with Signals

Nathalie Bertrand 1, Blaise Genest 2, Hugo Gimbert 3

(15/08/2009)

We consider the standard model of finite two-person zero-sum stochastic games with signals. We are interested in the existence of almost-surely winning or positively winning strategies, under reachability, safety, Büchi or co-Büchi winning objectives. We prove two \emph{qualitative determinacy} results. First, in a reachability game either player 1 can achieve almost-surely the reachability objective, or player 2 can ensure surely the complementary safety objective, or both players have positively winning strategies. Second, in a Büchi game if player 1 cannot achieve almost-surely the Büchi objective, then player 2 can ensure positively the complementary co-Büchi objective. We prove that players only need strategies with finite-memory, whose sizes range from no memory at all to doubly-exponential number of states, with matching lower bounds. Together with the qualitative determinacy results, we also provide fix-point algorithms for deciding which player has an almost-surely winning or a positively winning strategy and for computing the finite memory strategy. Complexity ranges from EXPTIME to 2-EXPTIME with matching lower bounds, and better complexity can be achieved for some special cases where one of the players is better informed than her opponent.

1 :	VERTECS (INRIA)
	INRIA
2 :	DISTRIBCOM (INRIA - IRISA)
	CNRS : UMR6074 – INRIA – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université de Rennes 1
3 :	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

Équipe de recherche : LaBRI; IRISA

Domaine

:

Informatique/Informatique et théorie des jeux

Mots Clés : stochastic games – partial observation – imperfect information – parity games – determinacy

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Contributeur : Hugo Gimbert <>

Soumis le : Mardi 27 Janvier 2009, 17:52:14

Dernière modification le : Jeudi 23 Juillet 2009, 10:44:02