Solving Simple Stochastic Tail Games

Stochastic games are a natural model for open reactive processes: one player represents the controller and his opponent represents a hostile environment. The 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 B?chi conditions. hal-00413430,version1-4Sep2009 Author manuscript, published in "SODA'10 (Symposium on ...

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Hugo Gimbert, Florian Horn
• Keywords: Discrete Algorithms, Qualitative Analysis, Quantitative Analysis, SODA 2010, Stochastic Tail Games