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Stable partitions for proportional generalized claims problems

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  • Gallo, Oihane
  • Klaus, Bettina

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 θ 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) θ-size coalitions emerge. For CEA and CEL we provide algorithms to construct such a stable partition formed by (mostly) θ-size coalitions.

Suggested Citation

  • Gallo, Oihane & Klaus, Bettina, 2024. "Stable partitions for proportional generalized claims problems," Games and Economic Behavior, Elsevier, vol. 147(C), pages 485-516.
    • Handle: RePEc:eee:gamebe:v:147:y:2024:i:c:p:485-516
    DOI: 10.1016/j.geb.2024.07.011
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    More about this item

    Keywords

    Claims problems; Coalition formation; Stable partitions;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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