Clustered federated learning benefits from organizing heterogeneous participants into coalitions that train coalition-specific models, but such clustering is sustainable only if participants prefer their assigned coalition and the required transfers are affordable. We develop a transferable-surplus model separating learning benefit, system cost, participant cost, and monetary transfers; an allocation rule converts coalition surplus into hedonic preferences, and weak budget feasibility guarantees nonnegative retained coordinator surplus. For symmetric pairwise allocations the induced game is an exact potential game: a Nash-stable partition exists, every strict better-response process converges, and with destination consent accepted better responses reach an individually stable partition. We characterize feasibility of bounded pair incentives and verify the exponentially many budget constraints in polynomial oracle time when retained slack is submodular. Decomposing welfare into participant potential and retained slack yields additive and multiplicative price-of-stability guarantees, the latter asymptotically tight; exact balance gives welfare-optimal stability only on the pairwise-representable class, and budget feasibility alone permits unbounded welfare loss. Global potential maximization equals weighted maximum-agreement correlation clustering, and approximation followed by stabilization satisfies an end-to-end welfare bound governed by retained slack and negative-edge mass, attained by an explicit construction. In a preregistered five-seed CIFAR-10 study the mechanism reaches the certified estimated-table welfare optimum on every primary instance, equal-surplus sharing has no Nash-stable outcome on three, and pairwise validation gain gives far more reliable pair signs than gradient alignment.
Modern agentic AI systems combine multiple large language model agents with heterogeneous skills, yet most architectures either fix communication in advance or allow full broadcast. Both can be inefficient because token cost, latency, redundancy, and error propagation increase with the number of active agents and communication links. We model agent selection and communication as a cooperative game with task-conditioned net utility $U(C\mid x)=V(C\mid x)-\sum_{i\in C}c_i$, separating coalition-level costs from agent activation costs. We propose a marginal-value activation rule and greedy router, extend the model to optimize communication edges with per-edge costs, and use estimated Shapley values to predict which agents are worth contacting before and during execution. We connect the problem to submodular maximization and prove two limited guarantees: a curvature-refined bound for a monotone, cardinality-constrained special case, and a tight $1/2$-approximation, with a correction for signed objectives, for an unconstrained non-monotone case via double greedy. Neither guarantee applies directly to the main router, which remains a heuristic. We also prove a Shapley-submodularity sandwich bound linking the error of marginal-value routing to a per-agent diminishing-returns quantity. In synthetic experiments, greedy routing achieves $99.5%$ of brute-force-optimal utility while activating $1.96$ of $8$ agents on average, compared with $38.8%$ for full broadcast. Performance is robust to activation cost and redundancy weight but falls to $66%$ under strong violations of submodularity or noisy value estimates. We distinguish the framework from Shapley pricing, hedonic coalition formation, and communication-graph pruning, and propose evaluation on real multi-agent LLM benchmarks.
This paper develops a multiscale model of coalition formation in which strategic exit-and-join decisions are coupled with tactical consensus dynamics inside coalitions. Coalition value is generated endogenously from within-coalition information aggregation, while Aumann-Dreze payoffs, switching frictions, and acceptance rules govern strategic reconfiguration. The framework introduces a fast-slow architecture in which transferable coalition value emerges from DeGroot-style consensus processes, while coalition structures evolve through incentive-driven exit-and-join dynamics. The analysis characterizes joint tactical-strategic equilibria, conditions for tactical and strategic unanimity, segregation, polarization, and cognitive barriers that sustain stable coalition structures. A fixed-point characterization and existence results are established for the coupled dynamics. Numerical experiments reveal an instability-consensus paradox: low or negative switching barriers may prevent strategic convergence while simultaneously promoting temporal mixing sufficient to achieve global tactical consensus. The results provide a unified perspective on coalition formation, consensus dynamics, information aggregation, and strategic stability in multi-agent systems.
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.