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Perfectly Fair Allocations with Indivisibilities


  • Ning Sun

    (Yokohama National University)

  • Zaifu Yang

    (Yokohama National University)


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.

Suggested Citation

  • Ning Sun & Zaifu Yang, 2001. "Perfectly Fair Allocations with Indivisibilities," Cowles Foundation Discussion Papers 1318, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1318

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    Cited by:

    1. Talman, A.J.J. & Yang, Z.F., 2012. "On a parameterized system of nonlinear equations with economic applications," Other publications TiSEM 8233343d-0b60-428d-a20b-6, Tilburg University, School of Economics and Management.

    More about this item


    Perfectly fair allocation; indivisibility; discrete optimization; multi-person decision; existence theorem; optimality preserved matrix;

    JEL classification:

    • D3 - Microeconomics - - Distribution
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D6 - Microeconomics - - Welfare Economics
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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