Exit-and-Join Dynamics for Decentralized Coalition Formation

2026-06-17

AI Summary

This study addresses the dynamic stability of coalition formation in decentralized environments, where individuals autonomously reach stable coalition structures through local decisions. The authors propose a dynamic mechanism driven by unilateral deviations—individuals evaluate the payoff of local moves using the Aumann-Dreze value, thereby integrating cooperative game-theoretic allocations with non-cooperative best-response behavior. By innovatively embedding the Aumann-Dreze value into the dynamic process, they establish an equivalence between terminal partitions and the absence of profitable deviations, and elucidate how switching and acceptance costs influence local stability. Employing Lyapunov function analysis, exact potential function arguments, and numerical simulations, the paper proves the existence of equilibria, finite-time convergence, and demonstrates the model’s efficacy in convex games as well as its sensitivity to cost parameters.

Abstract

This paper studies coalition formation as a decentralized dynamical process driven by unilateral exit-and-join decisions. Agents evaluate local moves using the Aumann-Dreze value, so payoffs are computed within the agent's current coalition rather than through a globally negotiated coalition structure. The resulting model links cooperative payoff allocation with noncooperative best-response behavior: a terminal partition is precisely a coalition structure with no admissible, individually profitable exit-and-join deviation. We establish equilibrium characterizations, identify conditions under which the dynamics admit scalar Lyapunov or exact-potential representations, and analyze how switching and acceptance costs shape local stability. Numerical experiments test finite-time stabilization, cost sensitivity, and a special convex-game benchmark.

Problem

• decentralized coalition formation
• exit-and-join dynamics
• Aumann-Dreze value
• individual deviations
• local stability

Innovation

• decentralized coalition formation
• exit-and-join dynamics
• Aumann-Dreze value
• exact-potential game
• Lyapunov stability