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arXiv · 2503.04759

Games with $\omega$-Automatic Preference Relations

Véronique Bruyère·Christophe Grandmont·Jean-François Raskin
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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 $\omega$-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 $\omega$-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 $\omega$-automatic relations and their implications for the existence of equilibria.

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Véronique Bruyère, Christophe Grandmont, Jean-François Raskin. 2025-02-10. Games with $\omega$-Automatic Preference Relations. https://doi.org/10.4230/lipics.mfcs.2025.31

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