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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.

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  • 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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    Cited by:

    1. Basteck, Christian & Ehlers, Lars, 2023. "Strategy-proof and envy-free random assignment," Journal of Economic Theory, Elsevier, vol. 209(C).
    2. Basteck, Christian, 2018. "Fair solutions to the random assignment problem," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 163-172.
    3. Basteck, Christian & Ehlers, Lars H., 2022. "Strategy-proof and envy-free random assignment," Discussion Papers, Research Unit: Market Behavior SP II 2022-208, WZB Berlin Social Science Center.
    4. Shende, Priyanka & Purohit, Manish, 2023. "Strategy-proof and envy-free mechanisms for house allocation," Journal of Economic Theory, Elsevier, vol. 213(C).
    5. Rasoul Ramezanian & Mehdi Feizi, 2021. "Ex-post favoring ranks: a fairness notion for the random assignment problem," Review of Economic Design, Springer;Society for Economic Design, vol. 25(3), pages 157-176, September.
    6. Jingsheng Yu & Jun Zhang, 2020. "Efficient and fair trading algorithms in market design environments," Papers 2005.06878, arXiv.org, revised May 2021.
    7. Basteck, Christian & Ehlers, Lars, 2021. "Strategy-Proof and Envy-Free Random Assignment," Rationality and Competition Discussion Paper Series 307, CRC TRR 190 Rationality and Competition.

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