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Doomsday Equilibria for Omega-Regular Games

  • Krishnendu Chatterjee
  • Laurent Doyen
  • Emmanuel Filiot
  • Jean-François Raskin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8318)

Abstract

Two-player games on graphs provide the theoretical framework for many important problems such as reactive synthesis. While the traditional study of two-player zero-sum games has been extended to multi-player games with several notions of equilibria, they are decidable only for perfect-information games, whereas several applications require imperfect-information games.

In this paper we propose a new notion of equilibria, called doomsday equilibria, which is a strategy profile such that all players satisfy their own objective, and if any coalition of players deviates and violates even one of the players objective, then the objective of every player is violated.

We present algorithms and complexity results for deciding the existence of doomsday equilibria for various classes of ω-regular objectives, both for imperfect-information games, and for perfect-information games.We provide optimal complexity bounds for imperfect-information games, and in most cases for perfect-information games.

Keywords

Perfect Information Imperfect Information Winning Strategy Acceptance Condition Parity Objective 
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 2014

Authors and Affiliations

  • Krishnendu Chatterjee
    • 1
  • Laurent Doyen
    • 2
  • Emmanuel Filiot
    • 3
  • Jean-François Raskin
    • 3
  1. 1.IST AustriaAustria
  2. 2.LSV, ENS Cachan & CNRSFrance
  3. 3.CSUniversité Libre de Bruxelles – U.L.BBelgium

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