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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

Suggested Citation

  • 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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