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On fair division of a homogeneous good

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  • Feige, Uriel
  • Tennenholtz, Moshe

Abstract

We consider the problem of dividing a homogeneous divisible good among n players. Each player holds a private non-negative utility function that depends only on the amount of the good that he receives. We define the fair share of a player P to be the average utility that a player could receive if all players had the same utility function as P. We present a randomized allocation mechanism in which every player has a dominant strategy for maximizing his expected utility. Every player that follows his dominant strategy is guaranteed to receive an expected utility of at least n/(2n−1) of his fair share. This is best possible in the sense that there is a collection of utility functions with respect to which no allocation mechanism can guarantee a larger fraction of the fair share. In interesting special cases our allocation mechanism does offer a larger fraction of the fair share.

Suggested Citation

  • Feige, Uriel & Tennenholtz, Moshe, 2014. "On fair division of a homogeneous good," Games and Economic Behavior, Elsevier, vol. 87(C), pages 305-321.
    • Handle: RePEc:eee:gamebe:v:87:y:2014:i:c:p:305-321
    DOI: 10.1016/j.geb.2014.02.009
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    References listed on IDEAS

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    1. Hervé Moulin, 2002. "The proportional random allocation of indivisible units," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 381-413.
    2. Moulin, Herve, 1990. "Uniform externalities : Two axioms for fair allocation," Journal of Public Economics, Elsevier, vol. 43(3), pages 305-326, December.
    3. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Cited by:

    1. Moshe Babaioff & Uriel Feige, 2024. "Share-Based Fairness for Arbitrary Entitlements," Papers 2405.14575, arXiv.org.

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    More about this item

    Keywords

    Fairness; Fair share; Bin packing; Random allocations;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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