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Permissive Equilibria in Multiplayer Reachability Games

Authors Aline Goeminne, Benjamin Monmege

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ACM Subject Classification
  • Software and its engineering → Formal methods
  • Theory of computation → Logic and verification
  • Theory of computation → Solution concepts in game theory
Keywords
  • multiplayer reachability games
  • penalties
  • permissive equilibria

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Abstract

We study multi-strategies in multiplayer reachability games played on finite graphs. A multi-strategy prescribes a set of possible actions, instead of a single action as usual strategies: it represents a set of all strategies that are consistent with it. We aim for profiles of multi-strategies (a multi-strategy per player), where each profile of consistent strategies is a Nash equilibrium, or a subgame perfect equilibrium. The permissiveness of two multi-strategies can be compared with penalties, as already used in the two-player zero-sum setting by Bouyer, Duflot, Markey and Renault [Patricia Bouyer et al., 2009]. We show that we can decide the existence of a multi-strategy profile that is a Nash equilibrium or a subgame perfect equilibrium, while satisfying some upper-bound constraints on the penalties in PSPACE, if the upper-bound penalties are given in unary. The same holds when we search for multi-strategies where certain players are asked to win in at least one play or in all plays.

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Aline Goeminne and Benjamin Monmege. Permissive Equilibria in Multiplayer Reachability Games. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CSL.2025.23

Author Details

Aline Goeminne
  • F.R.S.-FNRS & UMONS - Université de Mons, Belgium
Benjamin Monmege
  • Aix-Marseille Univ, CNRS, LIS, Marseille, France

Funding

  • Goeminne, Aline: Postdoctoral Researcher of the Fonds de la Recherche Scientifique - FNRS.
  • Monmege, Benjamin: This author was partially funded by ANR JCJC Quasy ANR-23-CE48-0008.

References

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