Extending Finite Memory Determinacy to Multiplayer Games

Roux, Stéphane; Pauly, Arno

doi:10.4204/eptcs.218.3

Cited by 4 publications

(4 citation statements)

References 17 publications

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“…This article extends and supersedes the earlier [19] which appeared in the proceedings of Strategic Reasoning 2016.…”

Section: Introductionsupporting

confidence: 65%

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Extending finite-memory determinacy to multi-player games

Roux¹,

Pauly²

2018

Information and Computation

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We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding class of multi-player multi-outcome games. This generalizes a previous result by Brihaye, De Pril and Schewe. We provide a number of example that separate the various criteria we explore. Our proofs are generally constructive, that is, provide upper bounds for the memory required, as well as algorithms to compute the relevant Nash equilibria.

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“…This article extends and supersedes the earlier [19] which appeared in the proceedings of Strategic Reasoning 2016.…”

Section: Introductionsupporting

confidence: 65%

“…Theorem 12 below captures this idea. It is a generalization of our main result in [19]. (The new Assumption 2 is indeed weaker.…”

Section: By Lemma 15supporting

confidence: 55%

Extending finite-memory determinacy to multi-player games

Roux¹,

Pauly²

2018

Information and Computation

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“…Similarly, Gurevich and Harrington's game-based proof of Rabin's decidability theorem for monadic second-order logic over infinite binary trees [16] relies on the existence of finite-state strategies. 4 These facts explain the need for studying the existence and properties of finite-state strategies in infinite games [17,18,19,20]. In particular, the seminal work by Dziembowski, Jurdziński, and Walukiewicz [21] addressed the problem of determining upper and lower bounds on the size of finite-state winning strategies in games with Muller winning conditions.…”

Section: Related Workmentioning

confidence: 99%

Finite-state strategies in delay games

Winter

Zimmermann

2020

Information and Computation

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What is a finite-state strategy in a delay game? We answer this surprisingly non-trivial question by presenting a very general framework that allows to remove delay: finite-state strategies exist for all winning conditions where the resulting delay-free game admits a finite-state strategy. The framework is applicable to games whose winning condition is recognized by an automaton with an acceptance condition that satisfies a certain aggregation property. Our framework also yields upper bounds on the complexity of determining the winner of such delay games and upper bounds on the necessary lookahead to win the game. In particular, we cover all previous results of that kind as special cases of our uniform approach. ⋆ Supported by the projects "TriCS" (ZI 1516/1-1) and (LO 1174/3-1) of the German Research Foundation (DFG). The work presented here was carried out while the second author was a member of the Reactive Systems Group at Saarland University. 3 The models of Gale-Stewart games and arena-based games are interreducible, but delay games are naturally presented as a generalization of Gale-Stewart games. This is the reason we prefer this model here.

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“…Similarly, Gurevich and Harrington's game-based proof of Rabin's decidability theorem for monadic second-order logic over infinite binary trees [25] relies on the existence of finite-state strategies. 2 These facts explain the need for studying the existence and properties of finite-state strategies in infinite games [17,26,27,29]. In particular, the seminal work by Dziembowski, Jurdziński, and Walukiewicz [6] addressed the problem of determining upper and lower bounds on the size of finite-state winning strategies in games with Muller winning conditions.…”

Section: Introductionmentioning

confidence: 99%

Finite-state Strategies in Delay Games

Zimmermann

2017

Electron. Proc. Theor. Comput. Sci.

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What is a finite-state strategy in a delay game? We answer this surprisingly non-trivial question and present a very general framework for computing such strategies: they exist for all winning conditions that are recognized by automata with acceptance conditions that satisfy a certain aggregation property. Our framework also yields upper bounds on the complexity of determining the winner of such delay games and upper bounds on the necessary lookahead to win the game. In particular, we cover all previous results of that kind as special cases of our uniform approach.Comment: In Proceedings GandALF 2017, arXiv:1709.01761. Full version at arXiv:1704.0888

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Extending Finite Memory Determinacy to Multiplayer Games

Cited by 4 publications

References 17 publications

Extending finite-memory determinacy to multi-player games

Extending finite-memory determinacy to multi-player games

Finite-state strategies in delay games

Finite-state Strategies in Delay Games

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