Two-Player Nonzero-Sum ω-Regular Games

Chatterjee, Krishnendu

doi:10.1007/11539452_32

Cited by 12 publications

(10 citation statements)

References 14 publications

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“…Also here, the existence of ε-equilibrium has only been established in special cases, for example for twoplayer stochastic games with parity payoffs, cf. Chatterjee [5].…”

Section: Introductionmentioning

confidence: 99%

Equilibrium in Two-Player Stochastic Games with Shift-Invariant Payoffs

Flesch¹,

Solan²

2022

Preprint

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“…Also here, the existence of ε-equilibrium has only been established in special cases, for example for twoplayer stochastic games with parity payoffs, cf. Chatterjee [5].…”

Section: Introductionmentioning

confidence: 99%

Equilibrium in Two-Player Stochastic Games with Shift-Invariant Payoffs

Flesch¹,

Solan²

2022

Preprint

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“…For applications in logic and computer science, games played on graphs have received more focus; also, computer scientists have been mostly looking for algorithmic solutions for deciding the existence and effectively computing equilibria and ǫ-equilibria [15,10,40].…”

Section: Introductionmentioning

confidence: 99%

“…For two-player concurrent games with Büchi objectives, the existence of ǫ-equilibria (in randomised strategies) was proved by Chatterjee [10]. However, exact Nash equilibria need not exist; turn-based games with Büchi objectives are an important subclass where Nash equilibria (even in pure strategies) always exist [15].…”

Section: Introductionmentioning

confidence: 99%

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Pure Nash Equilibria in Concurrent Deterministic Games

Bouyer¹,

Brenguier²,

Markey³

et al. 2015

Logical Methods in Computer Science

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Abstract. We study pure-strategy Nash equilibria in multi-player concurrent deterministic games, for a variety of preference relations. We provide a novel construction, called the suspect game, which transforms a multi-player concurrent game into a two-player turnbased game which turns Nash equilibria into winning strategies (for some objective that depends on the preference relations of the players in the original game). We use that transformation to design algorithms for computing Nash equilibria in finite games, which in most cases have optimal worst-case complexity, for large classes of preference relations. This includes the purely qualitative framework, where each player has a single ω-regular objective that she wants to satisfy, but also the larger class of semi-quantitative objectives, where each player has several ω-regular objectives equipped with a preorder (for instance, a player may want to satisfy all her objectives, or to maximise the number of objectives that she achieves.)

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“…There has recently been a lot of focus on the algorithmic aspect of Nash equilibria for games played on graphs [4,11,12]. Thanks to these efforts, the theoretical bases are understood well enough, so that we have developed effective algorithms [1,2].…”

Section: Introductionmentioning

confidence: 99%

PRALINE: A Tool for Computing Nash Equilibria in Concurrent Games

Brenguier

2013

Lecture Notes in Computer Science

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Abstract. We present PRALINE, which is the first tool to compute Nash equilibria in games played over graphs. We consider concurrent games: at each step, players choose their actions independently. There can be an arbitrary number of players. The preferences of the players are given by payoff functions that map states to integers, the goal for a player is then to maximize the limit superior of her payoff; this can be seen as a generalization of Büchi objectives. PRALINE looks for pure Nash equilibria in these games. It can construct the strategies of the equilibrium and users can play against it to test the equilibrium. We give the idea behind its implementation and present examples of its practical use.

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Two-Player Nonzero-Sum ω-Regular Games

Cited by 12 publications

References 14 publications

Equilibrium in Two-Player Stochastic Games with Shift-Invariant Payoffs

Equilibrium in Two-Player Stochastic Games with Shift-Invariant Payoffs

Pure Nash Equilibria in Concurrent Deterministic Games

PRALINE: A Tool for Computing Nash Equilibria in Concurrent Games

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