2025/02/10 by Bruyère, Véronique, Grandmont, Christophe, Raskin, Jean-François
#Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.2503.04759
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.