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Subgame Perfection in Graph Games with $ω$-Recognizable Preference Relations

Year: 2026

Type: preprint

Abstract: This paper investigates the constrained existence problem for subgame perfect equilibria (SPEs) in multiplayer graph games. In the proposed framework, each player has a preference relation over the set of plays, assumed to be $ω$-recognizable. Equivalently, he has a preference relation over a finite set of payoffs, and the set of plays with the same payoff is $ω$-regular, for each payoff. This generic framework avoids the need to focus on specific payoff functions. We show that the constrained SPE existence problem is EXPTIME-complete, as well as for Nash equilibria (NEs).

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.22906

Authors: Bruyère, Véronique, Grandmont, Christophe, Meunier, Noémie, Raskin, Jean-François

Institutions: University of Mons, Université Libre de Bruxelles

Topic: Game Theory and Applications

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: green

Funder: Fonds De La Recherche Scientifique - FNRS

OpenAlex ID: W7214048590

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