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Rational Verification for Nash and Subgame-Perfect Equilibria in Graph Games

Authors Léonard Brice, Jean-François Raskin, Marie van den Bogaard

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Léonard Brice
  • Université Libre de Bruxelles, Belgium
Jean-François Raskin
  • Université Libre de Bruxelles, Belgium
Marie van den Bogaard
  • Univ Gustave Eiffel, CNRS, LIGM, F-77454 Marne-la-Vallée, France

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Léonard Brice, Jean-François Raskin, and Marie van den Bogaard. Rational Verification for Nash and Subgame-Perfect Equilibria in Graph Games. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.MFCS.2023.26

Abstract

We study a natural problem about rational behaviors in multiplayer non-zero-sum sequential infinite duration games played on graphs: rational verification, that consists in deciding whether all the rational answers to a given strategy satisfy some specification. We give the complexities of that problem for two major concepts of rationality: Nash equilibria and subgame-perfect equilibria, and for three major classes of payoff functions: energy, discounted-sum, and mean-payoff.

Subject Classification

ACM Subject Classification
  • Software and its engineering → Formal methods
  • Theory of computation → Logic and verification
  • Theory of computation → Solution concepts in game theory
Keywords
  • Games on graphs
  • Nash equilibria
  • subgame-perfect equilibria

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