1 research outputs found
Determinacy in Stochastic Games with Unbounded Payoff Functions
We consider infinite-state turn-based stochastic games of two players, Box
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 (epsilon-)optimal strategies for both
players