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Individually rational rules for the division problem when the number of units to be allotted is endogenous

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  • Gustavo Bergantiños
  • Jordi Massó
  • Alejandro Neme

Abstract

We study individually rational rules to be used to allot, among a group of agents, a perfectly divisible good that is freely available only in whole units. A rule is individually rational if, at each preference profile, each agent finds that her allotment is at least as good as any whole unit of the good. We study and characterize two individually rational and efficient families of rules, whenever agents' preferences are symmetric single‐peaked on the set of possible allotments. Rules in the two families are in addition envy‐free, but they differ on whether envy‐freeness is considered on losses or on awards. Our main result states that (a) the family of constrained equal losses rules coincides with the class of all individually rational and efficient rules that satisfy justified envy‐freeness on losses and (b) the family of constrained equal awards rules coincides with the class of all individually rational and efficient rules that satisfy envy‐freeness on awards.

Suggested Citation

  • Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2021. "Individually rational rules for the division problem when the number of units to be allotted is endogenous," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(2), pages 376-401, April.
    • Handle: RePEc:bla:jpbect:v:23:y:2021:i:2:p:376-401
    DOI: 10.1111/jpet.12492
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    References listed on IDEAS

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    1. Bergantiños, Gustavo & Massó, Jordi & Neme, Alejandro, 2015. "The division problem under constraints," Games and Economic Behavior, Elsevier, vol. 89(C), pages 56-77.
    2. Thomson, William, 1995. "Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 229-246, March.
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    14. Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2012. "The division problem with voluntary participation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 371-406, March.
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    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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