The Complexity of SPEs in Mean-Payoff Games

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

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Author Details

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


We wish to thank the anonymous reviewers for their useful comments, in particular for the question that led us to add Lemma 1 to this paper.

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Léonard Brice, Jean-François Raskin, and Marie van den Bogaard. The Complexity of SPEs in Mean-Payoff Games. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 116:1-116:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We establish that the subgame perfect equilibrium (SPE) threshold problem for mean-payoff games is NP-complete. While the SPE threshold problem was recently shown to be decidable (in doubly exponential time) and NP-hard, its exact worst case complexity was left open.

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
  • Games on graphs
  • subgame-perfect equilibria
  • mean-payoff objectives


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