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Games with ω-Automatic Preference Relations

Authors Véronique Bruyère , Christophe Grandmont , Jean-François Raskin

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ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Software and its engineering → Formal methods
  • Theory of computation → Solution concepts in game theory
  • Theory of computation → Exact and approximate computation of equilibria
Keywords
  • Games played on graphs
  • Nash equilibrium
  • ω-automatic relations
  • ω-recognizable relations
  • constrained Nash equilibria existence problem

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Abstract

This paper investigates Nash equilibria (NEs) in multi-player turn-based games on graphs, where player preferences are modeled as ω-automatic relations via deterministic parity automata. Unlike much of the existing literature, which focuses on specific reward functions, our results apply to any preference relation definable by an ω-automatic relation. We analyze the computational complexity of determining the existence of an NE (possibly under some constraints), verifying whether a given strategy profile forms an NE, and checking whether a specific outcome can be realized by an NE. When a (constrained) NE exists, we show that there always exists one with finite-memory strategies. Finally, we explore fundamental properties of ω-automatic relations and their implications in the existence of equilibria.

Cite As Get BibTex

Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin. Games with ω-Automatic Preference Relations. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.MFCS.2025.31

Author Details

Véronique Bruyère
  • Université de Mons (UMONS), Belgium
Christophe Grandmont
  • Université de Mons (UMONS), Belgium
  • Université libre de Bruxelles (ULB), Belgium
Jean-François Raskin
  • Université libre de Bruxelles (ULB), Belgium

Funding

This work has been supported by the Fonds de la Recherche Scientifique – FNRS under Grant n° T.0023.22 (PDR Rational).
  • Raskin, Jean-François: Supported by Fondation ULB (https://www.fondationulb.be/en/) and the Thelam Fondation.

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