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Decentralized rationing problems and the proportional rule

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  • Izquierdo, Josep M.
  • Timoner, Pere

Abstract

Decentralized rationing problems are those in which the resource is not directly assigned to agents, but first allocated to groups of agents and then divided among their members. Within this framework, we define the decentralized proportional rule. We characterize it as the only solution that satisfies equal treatment of equals, provided claims are rational numbers. Adding a continuity property the result is extended to the general domain of all decentralized rationing problems. Finally, we prove that the proportional rule is the only solution that assigns the same allocation regardless of whether the resource is distributed directly to agents or in a decentralized manner (with agents grouped).

Suggested Citation

  • Izquierdo, Josep M. & Timoner, Pere, 2019. "Decentralized rationing problems and the proportional rule," Economics Letters, Elsevier, vol. 175(C), pages 88-91.
    • Handle: RePEc:eee:ecolet:v:175:y:2019:i:c:p:88-91
    DOI: 10.1016/j.econlet.2018.12.034
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    References listed on IDEAS

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    1. Juan D. Moreno-Ternero, 2009. "The proportional rule for multi-issue bankruptcy problems," Economics Bulletin, AccessEcon, vol. 29(1), pages 474-481.
    2. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    3. Silvia Lorenzo-Freire & Balbina Casas-Méndez & Ruud Hendrickx, 2010. "The two-stage constrained equal awards and losses rules for multi-issue allocation situations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 465-480, December.
    4. Josep Maria Izquierdo Aznar & Pere Timoner Lledó, 2016. "Decentralized rationing problems," UB School of Economics Working Papers 2016/345, University of Barcelona School of Economics.
    5. Gustavo Bergantiños & Leticia Lorenzo & Silvia Lorenzo-Freire, 2011. "New characterizations of the constrained equal awards rule in multi-issue allocation situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 311-325, December.
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    Cited by:

    1. Gallo, Oihane & Klaus, Bettina, 2024. "Stable partitions for proportional generalized claims problems," Games and Economic Behavior, Elsevier, vol. 147(C), pages 485-516.

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    More about this item

    Keywords

    Rationing; Claims problem; Proportional rule; A priori unions; Multi-issue allocation; Non manipulability;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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