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Social Choice and Welfare

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01-10-2013 | Original Paper

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

Authors: Farhad Hüsseinov, Nobusumi Sagara

Published in: Social Choice and Welfare | Issue 4/2013

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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.

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Title: Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities
Authors: Farhad Hüsseinov
Nobusumi Sagara
Publication date: 01-10-2013
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 4/2013
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-012-0714-y

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