The Complexity of Nash Equilibria in Limit-Average Games

Ummels, Michael; Wojtczak, Dominik

doi:10.1007/978-3-642-23217-6_32

Cited by 39 publications

(65 citation statements)

References 34 publications

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“…Relaxing any of these two design choices may lead to computational problems. Recent work on games has shown that allowing randomization, either in the strategies [31] or in the arenas [29] where the games are played may result in scenarios where computing the Nash equilibria of a game is undecidable, even for reachability objectives which can easily be expressed in LTL. However with respect to binary payoff sets, decidability can be recovered [30].…”

Section: Future Workmentioning

confidence: 99%

Iterated Boolean games

Gutiérrez

Harrenstein

Wooldridge

2015

Information and Computation

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Iterated games are well-known in the game theory literature. We study iterated Boolean games. These are games in which players repeatedly choose truth values for Boolean variables they have control over. Our model of iterated Boolean games assumes that players have goals given by formulae of Linear Temporal Logic (LTL), a formalism for expressing properties of state sequences. In order to represent the strategies of players in such games, we use a finite state machine model. After introducing and formally defining iterated Boolean games, we investigate the computational complexity of their associated game-theoretic decision problems, as well as semantic conditions characterising classes of LTL properties that are preserved by equilibrium points (pure-strategy Nash equilibria) whenever they exist.

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Section: Future Workmentioning

confidence: 99%

Iterated Boolean games

Gutiérrez

Harrenstein

Wooldridge

2015

Information and Computation

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“…It is known that randomization, either in the strategies [37] or the arenas [36] can lead to undecidability; however, w.r.t. binary payoff sets, decidability can be recovered [35].…”

Section: Analysis and Related Workmentioning

confidence: 99%

Equilibria of concurrent games on event structures

Gutiérrez

Wooldridge

2014

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Nin

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Event structures form a canonical model of concurrent behaviour which has a natural game-theoretic interpretation. This game-based interpretation was initially given for zero-sum concurrent games. This paper studies an extension of such games on event structures to include a much wider class of game types and solution concepts. The extension permits modelling scenarios where, for instance, cooperation or independent goal-driven behaviour of computer agents is desired. Specifically, we will define non-zero-sum games on event structures, and give full characterisations-existence and completeness results-of the kinds of games, payoff sets, and strategies for which Nash equilibria and subgame perfect Nash equilibria always exist. The game semantics of various logics and systems are outlined to illustrate the power of this framework.

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“…Note that a pure Nash equilibrium is resistant to randomized strategies. On the other hand the existence of a randomized Nash equilibrium with a particular payoff is undecidable [12]. If the game contains a (pure) Nash equilibrium with some payoff payoff i for each player p i , then PRALINE returns at least one Nash equilibrium with payoff payoff i such that for every player p i , payoff i ≥ payoff i .…”

Section: Computing Nash Equilibriamentioning

confidence: 99%

“…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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The Complexity of Nash Equilibria in Limit-Average Games

Cited by 39 publications

References 34 publications

Iterated Boolean games

Iterated Boolean games

Equilibria of concurrent games on event structures

PRALINE: A Tool for Computing Nash Equilibria in Concurrent Games

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