Learning via Compression in Multi Agent Systems

We propose a unified theoretical framework for adaptive behavior in multi-agent environments based on the concept of compression-driven intelligence. In this framework, each agentis modeled as a coupled system consisting of an encoder, which compresses the observed worldstate into a latent representation, and a policy, which maps this representation to actions.Unlike conventional reinforcement learning formulations that assume a fixed reward function,we define reward endogenously as a function of both predictive accuracy and inter-agent representational consistency. This allows us to interpret adaptation as a continuous optimizationprocess over both internal representations and action policies in a non-stationary, interactiveenvironment.We further extend the framework to multi-agent systems, where each agent’s behavior influences and is influenced by the evolving representations of others. This interaction induces acoupled dynamical system over compression structures, leading to emergent equilibrium statescharacterized by mutually consistent representations rather than identical world models.From an economic perspective, the proposed model can be interpreted as a decentralizedsystem of interacting agents performing lossy compression of shared information under strategicconstraints. This provides a bridge between reinforcement learning, information theory, andgame-theoretic equilibrium concepts.We derive the corresponding learning dynamics as a gradient flow over a reward functioncomposed of prediction error and inter-agent divergence, and analyze conditions for convergenceto stable equilibria. The resulting framework provides a unified view of intelligence, learning, andeconomic interaction as a single process of adaptive compression under interaction constraints.