Perfectly Fair Allocations with Indivisibilities
AbstractOne 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.
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Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1318.
Length: 17 pages
Date of creation: Aug 2001
Date of revision:
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2001-11-27 (All new papers)
- NEP-CDM-2001-11-27 (Collective Decision-Making)
- NEP-ENT-2001-11-27 (Entrepreneurship)
- NEP-NET-2001-11-27 (Network Economics)
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