BROŽEK, Václav. Determinacy and Optimal Strategies in Infinite-state Stochastic Reachability Games. Theoretical Computer Science. Amsterdam: Elsevier, 2013, vol. 493, No 1, p. 80-97. ISSN 0304-3975. doi:10.1016/j.tcs.2012.10.038.
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Basic information
Original name Determinacy and Optimal Strategies in Infinite-state Stochastic Reachability Games
Authors BROŽEK, Václav (203 Czech Republic, guarantor, belonging to the institution).
Edition Theoretical Computer Science, Amsterdam, Elsevier, 2013, 0304-3975.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10201 Computer sciences, information science, bioinformatics
Country of publisher Netherlands
Confidentiality degree is not subject to a state or trade secret
WWW URL
Impact factor Impact factor: 0.516
RIV identification code RIV/00216224:14330/13:00080195
Organization unit Faculty of Informatics
Doi http://dx.doi.org/10.1016/j.tcs.2012.10.038
UT WoS 000321410000007
Keywords in English Stochastic games; Reachability; Determinacy; Optimal strategies
Tags International impact, Reviewed
Changed by Changed by: RNDr. Pavel Šmerk, Ph.D., učo 3880. Changed: 22. 5. 2015 06:16.
Abstract
We consider perfect-information reachability stochastic games for 2 players on countable graphs. Such a game is strongly determined if, whenever we fix an inequality ~E{>,>=} and a threshold p, either Player Max has a strategy which forces the value of the game to satisfy ~p against any strategy of Player Min, or Min has a strategy which forces the opposite against any strategy of Max. One of our results shows that whenever one of the players has an optimal strategy in every state of a game, then this game is strongly determined. This significantly generalises, e.g., recent results on finitely-branching reachability games. For strong determinacy, our methods are substantially different, based on which player has the optimal strategy, because the roles of the players are not symmetric. We also do not restrict the branching of the games, and where we provide an extension of results for finitely-branching games, we had to overcome significant complications and employ new methods as well. The other result is finding a subclass of stochastic games where Player Max has an optimal strategy in each state. The subclass is defined by the property that if v is an accumulation point of the set of all values of a game then v=0. These results complement recent results classifying the existence of an optimal strategy for Player Min, and our general strong-determinacy theorem applies here as well. We also apply our results for Max in the context of recently studied One-Counter stochastic games. This work extends a workshop version of this paper which appeared in GandALF 2011, in particular, we prove a conjecture raised in that paper for the class of all reachability games.
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