A Theory of Multilevel Interactive Equilibrium in NeuroAI
Authors: Zhe Sage Chen, Quanyan Zhu
Organizations: Department of Psychiatry, New York University Grossman School of Medicine, New York, NY 10016, USA · Department of Neuroscience, New York University Grossman School of Medicine, New York, NY 10016, USA · Institute for Translational Neuroscience, New York University Grossman School of Medicine, New York, NY 10016, USA · Department of Biomedical Engineering, Tandon School of Engineering, New York University, Brooklyn, NY 11201, USA · Department of Electrical and Computer Engineering, Tandon School of Engineering, New York University, Brooklyn, NY 11201, USA
Abstract
We propose a game-theoretic framework for adaptive multi-agent intelligent systems. Unlike classical game theory, which often treats strategies as primitive objects chosen by perfectly rational agents, the proposed framework provides a mathematical foundation for studying equilibrium in NeuroAI and can be viewed as an extension of game theory under relaxed assumptions, including partial observability, bounded computation, and uncertainty. At its core, Multilevel Interactive Equilibrium (MIE) generalizes the classical Nash equilibrium to intelligent systems with internal computation. Rather than being defined solely at the level of observable behavior, equilibrium emerges when neural learning dynamics, cognitive representations, and behavioral strategies mutually stabilize between interacting agents. This framework applies uniformly to interactions between two biological brains, two artificial agents, or hybrid human-AI systems. We discuss applications of multilevel game theory to human-autonomous vehicle driving, human-machine interaction, human-large language model (LLM) interaction, and computational psychiatry. We also outline experimental strategies and computational methods for estimating MIE and discuss challenges and prospects for future research.
Collective intelligence emerges across biological, physical, and artificial systems without central coordination, yet a unifying principle governing such behaviour remains elusive. The Free Energy Principle explains how individual agents adapt through variational inference, while game theory formalises strategic interactions. Here we introduce the Game-Theoretic Free Energy Principle, a unified framework showing that multi-agent systems performing local free-energy minimisation implicitly implement a stochastic game. We prove that, under bounded rationality and local information constraints, stationary points of collective free energy correspond to approximate Nash equilibria of an induced game. Conversely, a broad class of cooperative games admits a variational representation in which equilibria arise as Gibbs distributions over coalitions, establishing a bridge between Bayesian inference and strategic interaction. To characterise higher-order effects, we introduce a free-energy formulation of the Harsanyi dividend, isolating irreducible multi-agent synergy. This yields a predictive theory of cooperation, including a falsifiable non-monotonic relationship between sensory precision and agent influence. We validate this prediction across neural, biological, and artificial multi-agent systems. These results identify a common variational principle underlying inference, thermodynamics, and game-theoretic equilibrium.
This paper studies feedback Nash equilibrium (FBNE) seeking for multi-agent trajectory planning in nonlinear dynamical systems with unknown agents' objectives and state-dependent inter-agent coupling. While dynamic game theory provides a principled framework for such problems, existing approaches typically assume fully rational agents with known objectives or rely on fixed regularization, limiting their ability to capture bounded rationality and spatially varying interaction intensity in safety-critical settings. To this end, we propose a KL-regularized dynamic game with a state-dependent weight that adaptively balances optimality and behavioral priors. To infer unknown cost parameters from demonstrated behaviors, we develop a context-aware inverse game module based on maximum-entropy inverse reinforcement learning with physics-informed regularization, ensuring structural consistency with the forward game. We establish per-iteration well-posedness of the regularized local game and show that the adaptive weighting function remains Lipschitz continuous under bounded nominal-trajectory updates. Numerical simulations and multi-robot experiments on cooperative navigation and merging scenarios validate the effectiveness of the proposed framework.
The serious games between humans and AI have only just begun. Evolutionary Game Theory (EGT) models the competitive and cooperative strategies of biological entities. EGT could help predict the potential evolutionary equilibrium of humans and AI. The objective of this work was to examine EGT models relevant to human-AI interaction, evolution, and co-evolution. Of thirteen EGT models considered, three were examined: the Hawk-Dove Game, Iterated Prisoner's Dilemma, and the War of Attrition. This selection was based on the widespread acceptance and clear relevance of these models to potential human-AI evolutionary dynamics and co-evolutionary trajectories. The Hawk-Dove Game predicts balanced mixed-strategy equilibria based on the costs of conflict. Iterated Prisoner's Dilemma suggests that repeated interaction may lead to cognitive co-evolution. The War of Attrition suggests that competition for resources may result in strategic co-evolution, asymmetric equilibria, and conventions on sharing resources. Each model was examined from the perspective of human and AI decision-making, from psychological and biological perspectives, and from an AI viewpoint. AI is being shaped by human input and is evolving in response to it. So too, neuroplasticity allows the human brain to evolve in response to stimuli. If humans and AI converge in future, what might be the result of human neuroplasticity combined with an ever-evolving AI? There are profound ethical and cognitive implications. EGT may provide a suitable framework to understand and predict human-AI interaction, evolution, and co-evolution. However, future research should extend beyond EGT and explore additional frameworks, empirical validation methods, and interdisciplinary perspectives. In the spirit of further exploration, an illustrative computational simulation is provided.