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Size versus fairness in the assignment problem

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  • Bogomolnaia, Anna
  • Moulin, Herve

Abstract

When not all objects are acceptable to all agents, maximizing the number of objects actually assigned is an important design concern. We compute the guaranteed size ratio of the Probabilistic Serial mechanism, i.e., the worst ratio of the actual expected size to the maximal feasible size. It converges decreasingly to 1−1e≃63.2% as the maximal size increases. It is the best ratio of any Envy-Free assignment mechanism.

Suggested Citation

  • Bogomolnaia, Anna & Moulin, Herve, 2015. "Size versus fairness in the assignment problem," Games and Economic Behavior, Elsevier, vol. 90(C), pages 119-127.
    • Handle: RePEc:eee:gamebe:v:90:y:2015:i:c:p:119-127
    DOI: 10.1016/j.geb.2014.11.006
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    Cited by:

    1. Kondratev, Aleksei Y. & Nesterov, Alexander S., 2022. "Minimal envy and popular matchings," European Journal of Operational Research, Elsevier, vol. 296(3), pages 776-787.
    2. Basteck, Christian & Ehlers, Lars, 2023. "Strategy-proof and envy-free random assignment," Journal of Economic Theory, Elsevier, vol. 209(C).
    3. Demeulemeester, Tom & Goossens, Dries & Hermans, Ben & Leus, Roel, 2023. "A pessimist’s approach to one-sided matching," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1087-1099.
    4. Mustafa Oğuz Afacan & Inácio Bó & Bertan Turhan, 2023. "Assignment maximization," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 25(1), pages 123-138, February.
    5. Huang, Chao & Tian, Guoqiang, 2017. "Guaranteed size ratio of ordinally efficient and envy-free mechanisms in the assignment problem," Games and Economic Behavior, Elsevier, vol. 105(C), pages 1-8.
    6. Chang, Hee-In & Chun, Youngsub, 2017. "Probabilistic assignment of indivisible objects when agents have the same preferences except the ordinal ranking of one object," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 80-92.
    7. Noda, Shunya, 2023. "A planner-optimal matching mechanism and its incentive compatibility in a restricted domain," Games and Economic Behavior, Elsevier, vol. 141(C), pages 364-379.
    8. Mustafa Oğuz Afacan & Umut Dur, 2023. "Strategy‐proof size improvement: is it possible?," Scandinavian Journal of Economics, Wiley Blackwell, vol. 125(2), pages 321-338, April.
    9. Kitahara, Minoru & Okumura, Yasunori, 2019. "On the number of employed in the matching model," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 63-69.
    10. Haris Aziz & Florian Brandl, 2021. "Efficient, Fair, and Incentive-Compatible Healthcare Rationing," Papers 2102.04384, arXiv.org, revised Sep 2021.
    11. Noda, Shunya, 2020. "Size versus truncation robustness in the assignment problem," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 1-5.

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    More about this item

    Keywords

    Envy-freeness; Random assignment; Probabilistic serial;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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