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On the existence of Pareto Efficient and envy-free allocations

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  • Cole, Richard
  • Tao, Yixin

Abstract

Envy-freeness and Pareto Efficiency are two major goals in welfare economics. The existence of an allocation that satisfies both conditions has been studied for a long time. Whether items are indivisible or divisible, it is impossible to achieve envy-freeness and Pareto Efficiency ex post even in the case of two people and two items. In contrast, in this work, we prove that, for any cardinal utility functions (including complementary utilities for example) and for any number of items and players, there always exists an ex ante mixed allocation which is envy-free and Pareto Efficient, assuming the allowable assignments satisfy an anonymity property. The problem remains open in the divisible case.

Suggested Citation

  • Cole, Richard & Tao, Yixin, 2021. "On the existence of Pareto Efficient and envy-free allocations," Journal of Economic Theory, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:jetheo:v:193:y:2021:i:c:s0022053121000247
    DOI: 10.1016/j.jet.2021.105207
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    References listed on IDEAS

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    Cited by:

    1. Guy Barokas, 2022. "Revealed desirability: a novel instrument for social welfare," Theory and Decision, Springer, vol. 93(4), pages 649-661, November.

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    More about this item

    Keywords

    Pareto Efficient; Envy-free; Fair allocation; Communication complexity;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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