Borel Stochastic Games with Lim Sup Payoff

Maitra, A.; Sudderth, William D.

doi:10.1214/aop/1176989271

Cited by 62 publications

(34 citation statements)

References 18 publications

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“…This result is related to a result due to Maitra and Sudderth (1993), for general stochastic games. In such games, the players receive a payoff in each stage.…”

Section: Introductionsupporting

confidence: 68%

Stopping games with randomized strategies

Rosenberg¹,

Solan²,

Vieille³

2001

Probab Theory Relat Fields

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“…This result is related to a result due to Maitra and Sudderth (1993), for general stochastic games. In such games, the players receive a payoff in each stage.…”

Section: Introductionsupporting

confidence: 68%

Stopping games with randomized strategies

Rosenberg¹,

Solan²,

Vieille³

2001

Probab Theory Relat Fields

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“…For a proof in the context of the general theory of stochastic games see the book Maitra-Sudderth [4] in discrete state spaces, and the paper [3] for general state spaces.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Programming Principle for tug-of-war games with noise

Manfredi

Parviainen

Rossi³

2010

ESAIM: COCV

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Abstract. Consider a two-player zero-sum-game in a bounded open domain Ω described as follows: at a point x ∈ Ω, Players I and II play an ε-step tug-of-war game with probability α, and with probability β (α + β = 1), a random point in the ball of radius ε centered at x is chosen. Once the game position reaches the boundary, Player II pays Player I the amount given by a fixed payoff function F .We give a detailed proof of the fact that the value functions of this game satisfy the dynamic programming principleu(y) dy, for x ∈ Ω with u(y) = F (y) when y ∈ Ω. This principle implies the existence of quasioptimal Markovian strategies.

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“…These games are more general than they appear at first sight. Stochastic liminf-payoff games have been studied by Maitra and Sudderth in the more general concurrent setting with infinitely many positions [15,16]. In particular, they show that concurrent stochastic liminf-payoff games have a value and that this value can be expressed through a transfinite iteration.…”

Section: Introductionmentioning

confidence: 99%

“…In the deterministic setting, we consider total-payoff games which have been introduced as a refinement of mean-payoff games [18,10]. In the stochastic setting, our class is a turn-based variant of liminf-payoff games [15,16,4]. In both settings, we provide a non-trivial characterization of the values through nested fixpoint equations.…”

mentioning

confidence: 99%

Games through Nested Fixpoints

Gawlitza¹,

Seidl²

2009

Computer Aided Verification

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Abstract. In this paper we consider two-player zero-sum payoff games on finite graphs, both in the deterministic as well as in the stochastic setting. In the deterministic setting, we consider total-payoff games which have been introduced as a refinement of mean-payoff games [18,10]. In the stochastic setting, our class is a turn-based variant of liminf-payoff games [15,16,4]. In both settings, we provide a non-trivial characterization of the values through nested fixpoint equations. The characterization of the values of liminf-payoff games moreover shows that solving liminf-payoff games is polynomial-time reducible to solving stochastic parity games. We construct practical algorithms for solving the occurring nested fixpoint equations based on strategy iteration. As a corollary we obtain that solving deterministic total-payoff games and solving stochastic liminf-payoff games is in UP ∩ co−UP.

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Borel Stochastic Games with Lim Sup Payoff

Cited by 62 publications

References 18 publications

Stopping games with randomized strategies

Stopping games with randomized strategies

Dynamic Programming Principle for tug-of-war games with noise

Games through Nested Fixpoints

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