EXIT–AND–JOIN DYNAMICS FOR DECENTRALIZED COALITION FORMATION

This paper introduces a decentralized framework for coalition formation, moving away from traditional top-down, centralized optimization models. Instead of assuming a global planner, the author models coalition dynamics as a sequence of unilateral, asynchronous exit-and-join decisions. Agents evaluate their utility using the Aumann-Drèze value, which computes payoffs based solely on the members of their current coalition. This approach allows the model to capture how organizational structures—such as firms, labor markets, or multi-agent task systems—emerge endogenously from local, self-interested behavior.

The system evolves as agents continuously assess whether moving to a different coalition (or forming a singleton) improves their payoff, net of any switching costs. The author defines a formal transition mapping that updates the coalition structure based on these individual moves. A key contribution is the characterization of terminal states: a coalition structure is stable if no agent can find an admissible, profitable deviation. The paper further explores the conditions under which these dynamics can be represented by scalar Lyapunov functions or exact-potential functions, providing a rigorous basis for analyzing convergence and stability in multi-agent systems.

By linking cooperative payoff allocation (Aumann-Drèze) with noncooperative best-response behavior, this framework provides a bridge between cooperative game theory and distributed multi-agent systems. It explains how complex organizational structures can arise without global coordination, offering insights into why certain structures persist even when they are not globally optimal. The inclusion of switching and acceptance costs makes the model highly applicable to real-world scenarios, such as labor mobility or platform-based markets, where institutional frictions significantly influence organizational evolution.