Optimal Strategies in Infinite-state Stochastic Reachability Games

Václav Brožek

We consider perfect-information reachability stochastic games for 2 players on infinite graphs. We identify a subclass of such games, and prove two interesting properties of it: first, Player Max always has optimal strategies in games from this subclass, and second, these games are strongly determined. The subclass is defined by the property that the set of all values can only have one accumulation point – 0. Our results nicely mirror recent results for finitely-branching games, where, on the contrary, Player Min always has optimal strategies. However, our proof methods are substantially different, because the roles of the players are not symmetric. We also do not restrict the branching of the games. Finally, we apply our results in the context of recently studied One-Counter stochastic games.

In Giovanna D'Agostino and Salvatore La Torre: Proceedings Second International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2011), Minori, Italy, 15-17th June 2011, Electronic Proceedings in Theoretical Computer Science 54, pp. 60–73.
Published: 4th June 2011.

ArXived at: http://dx.doi.org/10.4204/EPTCS.54.5 bibtex PDF
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