Mixed Nash Equilibria in Concurrent Terminal-Reward Games

Bouyer, Patricia; Markey, Nicolas; Stan, Daniel

doi:10.4230/lipics.fsttcs.2014.351

Cited by 5 publications

(4 citation statements)

References 11 publications

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“…For two-player games, it was erroneously claimed (cf. [3]) first by Chatterjee et al [5] and later again by Ummels and Wojtczak [20] that a simple adaptation of an example of a zero-sum game of Everett resulted in a deterministic reach-a-set game without a Nash equilibrium. Thus it remains an open question whether every deterministic two-player reach-a-set game has a Nash equilibrium.…”

Section: Conclusion and Further Problemsmentioning

confidence: 99%

“…On the other hand an ε-optimal stationary equilibrium always exists. Do every two-player game where one player has a reachability objective and one player a safety objetive 1 These payoff vectors are (1, 1) and (3,1). It is easy to construct two 4 × 4 bimatrix games with only payoffs from the set {0, 1} in which the unique equlibrium payofff vectors are ( 1 4 , 1 4 ) and ( 3 4 , 1 4 ), respectively, which may replace (1, 1) and (3,1) always have a stationary ε-Nash equilibrium?…”

Section: Conclusion and Further Problemsmentioning

confidence: 99%

“…Do every two-player game where one player has a reachability objective and one player a safety objetive 1 These payoff vectors are (1, 1) and (3,1). It is easy to construct two 4 × 4 bimatrix games with only payoffs from the set {0, 1} in which the unique equlibrium payofff vectors are ( 1 4 , 1 4 ) and ( 3 4 , 1 4 ), respectively, which may replace (1, 1) and (3,1) always have a stationary ε-Nash equilibrium? In the case of turn-based games, it is an open problem whether every three-player deterministic game has a stationary Nash equilibrium.…”

Section: Conclusion and Further Problemsmentioning

confidence: 99%

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A Stay-in-a-Set Game without a Stationary Equilibrium

Hansen

Raskin

2019

Electron. Proc. Theor. Comput. Sci.

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Section: Conclusion and Further Problemsmentioning

confidence: 99%

Section: Conclusion and Further Problemsmentioning

confidence: 99%

Section: Conclusion and Further Problemsmentioning

confidence: 99%

See 1 more Smart Citation

A Stay-in-a-Set Game without a Stationary Equilibrium

Hansen

Raskin

2019

Electron. Proc. Theor. Comput. Sci.

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“…Since then, Das et al [12] improved this, by showing undecidability of recursive games with non-negative terminal rewards with just 5 players. In the more general setting of concurrent games, Bouyer et al [7] even showed undecidability of the problem of existence of a NE where a given player is surely winning for deterministic concurrent 3-players games with reachability objectives.…”

Section: Introductionmentioning

confidence: 99%

Existential Theory of the Reals Completeness of Stationary Nash Equilibria in Perfect Information Stochastic Games

Hansen,

Sølvsten

2020

Preprint

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We show that the problem of deciding whether in a multi-player perfect information recursive game (i.e. a stochastic game with terminal rewards) there exists a stationary Nash equilibrium ensuring each player a certain payoff is ∃R-complete. Our result holds for acyclic games, where a Nash equilibrium may be computed efficiently by backward induction, and even for deterministic acyclic games with non-negative terminal rewards. We further extend our results to the existence of Nash equilibria where a single player is surely winning. Combining our result with known gadget games without any stationary Nash equilibrium, we obtain that for cyclic games, just deciding existence of any stationary Nash equilibrium is ∃R-complete. This holds for reach-a-set games, stay-in-a-set games, and for deterministic recursive games.

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Synthesis of equilibria in infinite-duration games on graphs

Bruyère

2021

ACM SIGLOG News

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In this survey, we propose a comprehensive introduction to game theory applied to computer-aided synthesis. We study multi-player turn-based infinite-duration games played on a finite directed graph such that each player aims at maximizing a payoff function. We present the well-known notions of Nash equilibrium and subgame perfect equilibrium, as well as interesting strategy profiles of players as response to the strategy announced by a specific player. We provide classical and recent results about the related threshold synthesis problem.

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Mixed Nash Equilibria in Concurrent Terminal-Reward Games

Cited by 5 publications

References 11 publications

A Stay-in-a-Set Game without a Stationary Equilibrium

A Stay-in-a-Set Game without a Stationary Equilibrium

Existential Theory of the Reals Completeness of Stationary Nash Equilibria in Perfect Information Stochastic Games

Synthesis of equilibria in infinite-duration games on graphs

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