Exit-and-Join Dynamics: Decentralized Coalition Formation (2026)

Quanyan Zhu submitted Exit-and-Join Dynamics for Decentralized Coalition Formation to arXiv on 18 Jun 2026, arXiv:2606.19683. The paper models coalition formation as a decentralized dynamical process driven by unilateral exit-and-join decisions, and presents equilibrium characterizations plus numerical experiments that test finite-time stabilization, cost sensitivity, and a convex-game benchmark.

What does the paper introduce?

The paper introduces a decentralized dynamical model where agents make unilateral exit-and-join decisions and evaluate local moves using the Aumann-Dreze value. Payoffs are computed within each agent's current coalition rather than through a global negotiation, and a terminal partition is defined as a coalition structure with no admissible, individually profitable exit-and-join deviation.

Quanyan Zhu frames the model to directly connect cooperative payoff allocation procedures with noncooperative best-response behavior. The submission is listed under Artificial Intelligence, Multiagent Systems, and Systems and Control, with MSC classes 91A12, 91A43, 68T05, 91D30 and ACM classes I.2.11; I.2.6; J.4.

How does the model work?

Agents evaluate local moves using the Aumann-Dreze value, computing payoffs inside their current coalition and then making unilateral exit-or-join decisions; dynamics proceed as a sequence of these local unilateral moves. The paper shows that a terminal partition corresponds exactly to a coalition structure with no admissible, individually profitable exit-and-join deviation, tying the local decision rule to a global notion of stability.

The analysis in the paper includes equilibrium characterizations and identifies conditions under which the dynamics admit scalar Lyapunov or exact-potential representations. The author also analyzes how switching costs and acceptance costs affect local stability, making costs an explicit parameter in the dynamical behavior. Those analytical results are complemented by numerical experiments described in the text and available in the paper's PDF and TeX source.

What technical results and experiments are presented?

The paper establishes equilibrium characterizations and gives sufficient conditions for the dynamics to admit scalar Lyapunov or exact-potential representations, and it analyzes the role of switching and acceptance costs on local stability. Numerical experiments test finite-time stabilization, cost sensitivity, and a special convex-game benchmark.

The submission metadata records the version [v1] and a file size of 76 KB on arXiv. The document is available as a PDF and TeX source, and the arXiv-issued DOI is https://doi.org/10.48550/arXiv.2606.19683.

Why it matters

Linking cooperative payoff allocations like the Aumann-Dreze value with unilateral, noncooperative best responses provides a bridge between two common modeling perspectives in coalition theory. Making switching and acceptance costs explicit gives designers of decentralized multiagent systems concrete levers to shape stability and convergence, and the identification of Lyapunov or exact-potential structures offers standard tools to certify dynamics in specific classes of games.

Those are practical benefits for systems where global negotiation is infeasible and agents must rely on local information and unilateral moves to form coalitions.

What to watch

Examine the paper's numerical experiments for details on finite-time stabilization, sensitivity to switching and acceptance costs, and the convex-game benchmark described in the text. The PDF and TeX source linked on the arXiv page contain the experimental setups and results that will clarify how the analytical conditions play out in examples.

Reference: Quanyan Zhu, Exit-and-Join Dynamics for Decentralized Coalition Formation, arXiv:2606.19683, submitted 18 Jun 2026.