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Fair solutions to the random assignment problem

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  • Basteck, Christian

Abstract

We study the problem of assigning indivisible goods to individuals where each is to receive one good. To guarantee fairness in the absence of monetary compensation, we consider random assignments that individuals evaluate according to first order stochastic dominance (sd). In particular, we find that solutions which guarantee sd-no-envy (e.g. the Probabilistic Serial) are incompatible even with the weak sd-core from equal division. Solutions on the other hand that produce assignments in the strong sd-core from equal division (e.g. Hylland and Zeckhauser’s Walrasian Equilibria from Equal Incomes) are incompatible with the strong sd-equal-division-lower-bound. As an alternative, we present a solution, based on Walrasian equilibria, that is sd-efficient, in the weak sd-core from equal division, and satisfies the strong sd-equal-division-lower-bound.

Suggested Citation

  • Basteck, Christian, 2018. "Fair solutions to the random assignment problem," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 163-172.
  • Handle: RePEc:eee:mateco:v:79:y:2018:i:c:p:163-172
    DOI: 10.1016/j.jmateco.2018.02.006
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    References listed on IDEAS

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    1. Stergios Athanassoglou & Jay Sethuraman, 2011. "House allocation with fractional endowments," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 481-513, August.
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    14. Heo, Eun Jeong, 2014. "Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 40-47.
    15. Basteck, Christian, 2018. "Fair solutions to the random assignment problem," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 163-172.
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    1. repec:eee:mateco:v:79:y:2018:i:c:p:163-172 is not listed on IDEAS
    2. Basteck, Christian, 2018. "Fair solutions to the random assignment problem," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 163-172.

    More about this item

    Keywords

    Probabilistic serial; Walrasian equilibrium; Sd-efficiency; Sd-envy-freeness; Sd-core from equal division; Sd-equal-division-lower-bound;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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