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arXiv · 1711.05973

Vector Representation of Preferences on $\sigma$-Algebras and Fair Division in Saturated Measure Spaces

Nobusumi Sagara
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Abstract

The purpose of this paper is twofold. First, we axiomatize preference relations on a $\sigma$-algebra of a saturated measure space represented by a vector measure and furnish a utility representation in terms of a nonadditive measure satisfying the appropriate requirement of continuity and convexity. Second, we investigate the fair division problems in which each individual has nonadditive preferences on a $\sigma$-algebra invoking our utility representation result. We show the existence of individually rational Pareto optimal partitions, Walrasian equilibria, core partitions, and Pareto optimal envy-free partitions.

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BibTeXRIS

Nobusumi Sagara. 2017-11-16. Vector Representation of Preferences on $\sigma$-Algebras and Fair Division in Saturated Measure Spaces. https://arxiv.org/abs/1711.05973

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