Zhu's new model unifies coalition dynamics for multi-agent AI systems

Quanyan Zhu's new paper on arXiv develops a continuum theory of exit-and-join coalition dynamics for nonatomic cooperative games. It extends the Aumann-Shapley and Aumann-Drèze values to coalition structures, providing a marginal-contribution-based payoff density that governs incentives for agents to stay, leave, or join coalitions. The work derives deterministic mean-field dynamics from simple decentralized switching rules and shows that payoff-difference switching recovers the well-known replicator dynamics as a special case.

The paper characterizes equilibrium by the absence of profitable positive-mass deviations and proves its equivalence to stationarity under incentive-compatible switching rates. For mass-based cooperative games, a Lyapunov function is constructed, establishing global convergence under strict concavity. The equilibrium is shown equivalent to a Wardrop equilibrium of an induced nonatomic population game, admitting a variational inequality formulation. The framework extends to switching costs and endogenous acceptance rules, leading to constrained equilibria described by quasi-variational inequalities. This work unifies cooperative value allocation, noncooperative coalition mobility, mean-field dynamics, evolutionary game theory, and population games into a single mathematical framework.