Stable partitions for proportional generalized claims problems

TL;DR

This paper studies how agents with claims on limited resources form stable coalitions under proportional sharing rules, identifying conditions for stable partitions with minimal coalition sizes and providing algorithms for specific rules.

Contribution

It characterizes the structure of stable partitions in claims problems with minimal coalition sizes and offers algorithms for CEA and CEL rules.

Findings

Stable partitions with mostly θ-sized coalitions emerge under certain rules.

Algorithms are provided for constructing stable partitions with CEA and CEL.

Continuous, resource monotonic, and consistent rules lead to stable coalition structures.

Abstract

We consider a set of agents who have claims on an endowment that is not large enough to cover all claims. Agents can form coalitions but a minimal coalition size $\theta$ is required to have positive coalitional funding that is proportional to the sum of the claims of its members. We analyze the structure of stable partitions when coalition members use well-behaved rules to allocate coalitional endowments, e.g., the well-known constrained equal awards rule (CEA) or the constrained equal losses rule (CEL).For continuous, (strictly) resource monotonic, and consistent rules, stable partitions with (mostly) $\theta$-size coalitions emerge. For CEA and CEL we provide algorithms to construct such a stable partition formed by $\theta$-size coalitions.