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Asymptotic existence of proportionally fair allocations

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  • Suksompong, Warut

Abstract

Fair division has long been an important problem in the economics literature. In this note, we consider the existence of proportionally fair allocations of indivisible goods, i.e., allocations of indivisible goods in which every agent gets at least her proportionally fair share according to her own utility function. We show that when utilities are additive and utilities for individual goods are drawn independently at random from a distribution, proportionally fair allocations exist with high probability if the number of goods is a multiple of the number of agents or if the number of goods grows asymptotically faster than the number of agents.

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  • Suksompong, Warut, 2016. "Asymptotic existence of proportionally fair allocations," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 62-65.
    • Handle: RePEc:eee:matsoc:v:81:y:2016:i:c:p:62-65
    DOI: 10.1016/j.mathsocsci.2016.03.007
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    Cited by:

    1. Manurangsi, Pasin & Suksompong, Warut, 2017. "Asymptotic existence of fair divisions for groups," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 100-108.
    2. Suksompong, Warut, 2018. "Approximate maximin shares for groups of agents," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 40-47.
    3. Pasin Manurangsi & Warut Suksompong, 2020. "Closing Gaps in Asymptotic Fair Division," Papers 2004.05563, arXiv.org.

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