Title: Endogenous Communication in Repeated Games with Learning Agents
Primary area: learning theory
Keywords: multi-agent learning, repeated games, cheap talk, communication, information bottleneck, equilibrium, representation learning

Abstract: Communication among learning agents often emerges without explicit supervision. We study endogenous protocol formation in infinitely repeated stage games with a costless pre-play channel. Each agent has a representation map that compresses private signals into messages subject to an information budget. Agents update strategies by no-regret learning with stochastic approximation and choose representation maps by a myopic objective that trades off predictive value and encoding cost. We provide three main results. First, if the stage game admits a folk-theorem set and the information budget exceeds a task-specific threshold, there exists a stable communication equilibrium in which messages are sufficient statistics for continuation payoffs. Second, when the budget is below the threshold, any stable equilibrium must be pooling on a finite partition that we characterize with a minimax information bound. Third, we give polynomial sample-complexity guarantees for convergence to an approximately efficient communicating equilibrium under mild regularity. Our analysis connects cheap talk, representation learning with information constraints, and multi-agent no-regret dynamics. The framework yields testable predictions for when emergent messages are interpretable, when they collapse, and how much data is needed for stable coordination.

TL;DR: We show when cheap-talk communication learned by agents in repeated games is predictive, incentive-compatible, and sample-efficient, giving tight conditions for stable emergent protocols.