Optimal Strategies in Turn-Based Stochastic Tail Games
Résumé
Infinite stochastic games are a natural model for open reactive processes: one player represents the controller, and the other represents an hostile environment. The evolution of the system depends on the decisions of the players, supplemented by a random function. The problems on such games can be sorted in two categories: the qualitative analysis ponders whether a player can win with probability one (or arbitrarily close to one), while the quantitative analysis is concerned about the maximal (or supremal) value a player can achieve. In this paper, we establish the existence of optimal strategies in finite simple stochastic games. We also present a general effective procedure to derive quantitative results from qualitative algorithms. It also follows from the correctness of this procedure that optimal strategies are no more complex than almost-sure strategies.
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