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Perfectly Fair Allocations with Indivisibilities

  • Ning Sun

    (Yokohama National University)

  • Zaifu Yang

    (Yokohama National University)

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    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.

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    File URL: http://cowles.econ.yale.edu/P/cd/d13a/d1318.pdf
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    Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1318.

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    Length: 17 pages
    Date of creation: Aug 2001
    Date of revision:
    Handle: RePEc:cwl:cwldpp:1318
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