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We extend the Aumann-Shapley value and the Aumann-Dr\\`eze value to coalition structures in which each coalition is treated as a restricted nonatomic game, yielding a marginal-contribution-based payoff density that governs incentives for agents to remain in, exit, or join coalitions. We derive deterministic mean-field dynamics from decentralized switching rules and show that payoff-difference switching recovers replicator dynamics as a special case. We characterize exit-and-join equilibrium by the absence of profitable positive-mass deviations and prove its equivalence with stationarity of the induced mass dynamics under incentive-compatible and strictly payoff-responsive switching rates. For mass-based cooperative games, we construct a Lyapunov function and establish global convergence under strict concavity. We further show that ","title":"Exit-and-Join Dynamics and Equilibrium in Continuum Cooperative Games","url":"https://arxiv.org/abs/2606.28824","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.28824v1 Announce Type: cross \nAbstract: This paper develops a continuum theory of exit-and-join coalition dynamics in nonatomic cooperative games. We extend the Aumann-Shapley value and the Aumann-Dr\\`eze value to coalition structures in which each coalition is treated as a restricted nonatomic game, yielding a marginal-contribution-based payoff density that governs incentives for agents to remain in, exit, or join coalitions. We derive deterministic mean-field dynamics from decentralized switching rules and show that payoff-difference switching recovers replicator dynamics as a special case. We characterize exit-and-join equilibrium by the absence of profitable positive-mass deviations and prove its equivalence with stationarity of the induced mass dynamics under incentive-compatible and strictly payoff-responsive switching rates. For mass-based cooperative games, we construct a Lyapunov function and establish global convergence under strict concavity. 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