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Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities

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  • Farhad Hüsseinov
  • Nobusumi Sagara

Abstract

This paper studies the existence of Pareto optimal, envy-free allocations of a heterogeneous, divisible commodity for a finite number of individuals. We model the commodity as a measurable space and make no convexity assumptions on the preferences of individuals. We show that if the utility function of each individual is uniformly continuous and strictly monotonic with respect to set inclusion, and if the partition matrix range of the utility functions is closed, a Pareto optimal envy-free partition exists. This result follows from the existence of Pareto optimal envy-free allocations in an extended version of the original allocation problem. Copyright Springer-Verlag Berlin Heidelberg 2013

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  • Farhad Hüsseinov & Nobusumi Sagara, 2013. "Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 923-940, October.
    • Handle: RePEc:spr:sochwe:v:41:y:2013:i:4:p:923-940
    DOI: 10.1007/s00355-012-0714-y
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    2. Erel Segal-Halevi & Shmuel Nitzan & Avinatan Hassidim & Yonatan Aumann, 2020. "Envy-Free Division of Land," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 896-922, August.
    3. Erel Segal-Halevi & Shmuel Nitzan, 2014. "Cake Cutting – Fair and Square," Working Papers 2014-01, Bar-Ilan University, Department of Economics.
    4. Erel Segal-Halevi & Shmuel Nitzan, 2019. "Fair cake-cutting among families," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 709-740, December.

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