Neuronic Nash Equilibrium: An EEG Data-Driven Game-Theoretic Framework for BCI-Enabled Multi-Agent Behaviors

A central goal of neuroeconomics is to understand how humans make decisions and how their neural processes interact during strategic situations. Game theory provides mathematical tools for modeling such interactions, with equilibrium concepts, most notably the Nash equilibrium, predicting stable patterns of behavior. Classical equilibrium analysis, however, treats cognition as a black box and assumes fully rational agents, whereas human decision making is shaped by bounded rationality, heuristics, and neural constraints. To bridge this gap, we investigate equilibrium behavior directly in the space of neurocognitive activity. Electroencephalogram (EEG) signals provide a high-resolution measurement of neural dynamics underlying attention, conflict monitoring, and evidence accumulation. In this work, we introduce a neuronic Nash equilibrium, an equilibrium concept defined not in the action space but in the EEG-derived neural representation space. We develop a framework for analyzing two-player turn-based games in EEG space by constructing DMD-based neural embeddings and associated directed network representations. Dynamic Mode Decomposition (DMD) reveals statistically significant differences between the neural dynamics associated with distinct strategic actions, demonstrating that EEG-derived features preserve behaviorally meaningful cognitive structure. The resulting neuronic network representation enables equilibrium analysis directly at the neural level and provides a principled method for linking strategic behavior with stable patterns of neural activity. Our findings suggest that neural-state equilibrium concepts can capture the cognitive foundations of strategic interaction and offer a pathway toward characterizing cognitive equilibrium outcomes in multi-agent settings.