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N. Bertrand, B. Genest, Gimbert. H.. Qualitative Determinacy and Decidability of Stochastic Games with Signals. In 24th Annual IEEE Symposium on Logic in Computer Science (LICS'09), Pages 319-328, Los Angeles, CA, USA, August 2009.

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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 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


Nathalie Bertrand http://www.irisa.fr/prive/nbertran/

BibTex Reference

   Author = {Bertrand, N. and Genest, B. and H, Gimbert.},
   Title = {Qualitative Determinacy and Decidability of Stochastic Games with Signals},
   BookTitle = {24th Annual IEEE Symposium on Logic in Computer Science (LICS'09)},
   Pages = {319--328},
   Publisher = {IEEE Computer Society Press},
   Address = {Los Angeles, CA, USA},
   Month = {August},
   Year = {2009}

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