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Rational Behaviour and Strategy Construction in Infinite Multiplayer Games

  • Michael Ummels
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4337)

Abstract

We study infinite games played by arbitrarily many players on a directed graph. Equilibrium states capture rational behaviour in these games. Instead of the well-known notion of a Nash equilibrium, we focus on the notion of a subgame perfect equilibrium. We argue that the latter one is more appropriate for the kind of games we study, and we show the existence of a subgame perfect equilibrium in any infinite game with ω-regular winning conditions.

As, in general, equilibria are not unique, it is appealing to compute one with a maximal payoff. This problem corresponds naturally to the problem of deciding given a game and two payoff vectors whether the game has an equilibrium with a payoff in between the given thresholds. We show that this problem is decidable for games with ω-regular winning conditions played on a finite graph and analyse its complexity. Moreover, we establish that any subgame perfect equilibrium of a game with ω-regular winning conditions played on a finite graph can be implemented by finite-state strategies.

Finally, we consider logical definability. We state that if we fix the number of players together with an ω-regular winning condition for each of them and two payoff vectors the property that a game has a subgame perfect equilibrium with a payoff in between the given thresholds is definable in the modal μ-calculus.

Keywords

Nash Equilibrium Rational Behaviour Subgame Perfect Equilibrium Winning Strategy Kripke Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Michael Ummels
    • 1
  1. 1.Mathematische Grundlagen der InformatikRWTH AachenGermany

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