Exit-and-Join Dynamics for Decentralized Coalition Formation

This academic paper introduces a decentralized coalition formation model where agents make unilateral exit-and-join decisions based on local payoff evaluations using the Aumann-Dreze value. The research bridges cooperative game theory with noncooperative dynamics, establishing equilibrium conditions and analyzing how transaction costs affect stability in multi-agent systems.

This theoretical research addresses a fundamental challenge in decentralized systems: how autonomous agents organize into beneficial coalitions without central coordination. The Aumann-Dreze value framework ensures agents evaluate decisions based on their immediate coalition's payoffs rather than global outcomes, reflecting realistic constraints in distributed networks where complete information and centralized negotiation are infeasible.

The work extends classical coalition formation theory by embedding it within a dynamic process where stability emerges through repeated local decisions. Terminal partitions—configurations where no agent benefits from leaving and joining another coalition—serve as equilibrium points analogous to Nash equilibria in traditional game theory. This connection links cooperative payoff allocation with noncooperative behavior, addressing a critical gap in understanding how decentralized systems reach stable states.

The analysis of switching and acceptance costs carries direct relevance to blockchain and distributed systems, where transaction fees and friction genuinely impact agent behavior. By incorporating these realistic constraints, the model provides actionable insights into why certain coalition structures persist despite theoretically superior alternatives. The identification of scalar Lyapunov or exact-potential representations enables practitioners to predict convergence properties without exhaustive simulation.

For decentralized finance and governance applications, this framework offers mathematical foundations for understanding validator coalitions, mining pool dynamics, and DAO membership patterns. The numerical experiments validating finite-time stabilization suggest these dynamics are computationally tractable in practice. Future implementations might apply these insights to design incentive mechanisms that guide agents toward socially beneficial coalition structures through purely local decision-making.

• →Decentralized coalition formation driven by local exit-and-join decisions reaches equilibrium when no agent can profitably deviate unilaterally.
• →The Aumann-Dreze value enables payoff evaluation within immediate coalitions, eliminating need for global information or central coordination.
• →Transaction costs and switching fees significantly influence which coalition structures achieve stable equilibrium in dynamic processes.
• →The framework bridges cooperative game theory with noncooperative best-response dynamics, creating unified equilibrium characterizations.
• →Mathematical representations through Lyapunov functions enable predictability and design of stable multi-agent systems without simulation.