Games with $Ï$-Automatic Preference Relations
Games with $Ï$-Automatic Preference Relations
This paper investigates Nash equilibria (NEs) in multi-player turn-based games on graphs, where player preferences are modeled as $Ï$-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 $Ï$-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 $Ï$-automatic relations and their implications in the existence of equilibria.
Véronique Bruyère、Christophe Grandmont、Jean-François Raskin
计算技术、计算机技术
Véronique Bruyère,Christophe Grandmont,Jean-François Raskin.Games with $Ï$-Automatic Preference Relations[EB/OL].(2025-06-30)[2025-07-24].https://arxiv.org/abs/2503.04759.点此复制
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