Nash Equilibria in Concurrent Games with Büchi Objectives

Authors Patricia Bouyer, Romain Brenguier, Nicolas Markey, Michael Ummels

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Patricia Bouyer
Romain Brenguier
Nicolas Markey
Michael Ummels

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Patricia Bouyer, Romain Brenguier, Nicolas Markey, and Michael Ummels. Nash Equilibria in Concurrent Games with Büchi Objectives. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 375-386, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)


We study the problem of computing pure-strategy Nash equilibria in multiplayer concurrent games with Büchi-definable objectives. First, when the objectives are Büchi conditions on the game, we prove that the existence problem can be solved in polynomial time. In a second part, we extend our technique to objectives defined by deterministic Büchi automata, and prove that the problem then becomes EXPTIME-complete. We prove PSPACE-completeness for the case where the Büchi automata are 1-weak.
  • Concurrent games
  • Nash equilibria
  • Büchi Objectives


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