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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Determinacy in Stochastic Games with Unbounded Payoff Functions
verfasst von : Tomáš Brázdil, Antonín Kučera, Petr Novotný
Erschienen in: Mathematical and Engineering Methods in Computer Science
Verlag: Springer Berlin Heidelberg
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We consider infinite-state turn-based stochastic games of two players, □ and
$\Diamond$
, who aim at maximizing and minimizing the expected total reward accumulated along a run, respectively. Since the total accumulated reward is unbounded, the determinacy of such games cannot be deduced directly from Martin’s determinacy result for Blackwell games. Nevertheless, we show that these games
are
determined both for unrestricted (i.e., history-dependent and randomized) strategies and deterministic strategies, and the equilibrium value is the same. Further, we show that these games are generally
not
determined for memoryless strategies. Then, we consider a subclass of
$\Diamond$
-finitely-branching
games and show that they are determined for all of the considered strategy types, where the equilibrium value is always the same. We also examine the existence and type of (
ε
-)optimal strategies for both players.