Perfectly Fair Allocations with Indivisibilities

Ning Sun and Zaifu Yang
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Ning Sun: Yokohama National University
Zaifu Yang: Yokohama National University

No 1318, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: One set of n objects of type I, another set of n objects of type II, and an amount M of money is to be completely allocated among n agents in such a way that each agent gets one object of each type with some amount of money. We propose a new solution concept to this problem called a perfectly fair allocation. It is a refinement of the concept of fair allocation. An appealing and interesting property of this concept is that every perfectly fair allocation is Pareto optimal. It is also shown that a perfectly fair allocation is envy free and gives each agent what he likes best, and that a fair allocation need not be perfectly fair. Furthermore, we give a necessary and sufficient condition for the existence of a perfectly fair allocation. Precisely, we show that there exists a perfectly fair allocation if and only if the valuation matrix is an optimality preserved matrix. Optimality preserved matrices are a class of new and interesting matrices. An extension of the model is also discussed.

Keywords: Perfectly fair allocation; indivisibility; discrete optimization; multi-person decision; existence theorem; optimality preserved matrix (search for similar items in EconPapers)
JEL-codes: D3 D31 D6 D61 D63 D7 D74 (search for similar items in EconPapers)
Pages: 17 pages
Date: 2001-08
New Economics Papers: this item is included in nep-cdm, nep-ent and nep-net
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Citations: View citations in EconPapers (2)

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