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Stable Matching with Proportionality Constraints

Author

Listed:
  • Thành Nguyen

    (Krannert School of Management, Purdue University, West Lafayette, Indiana 47907)

  • Rakesh Vohra

    (Department of Economics, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

Abstract

The problem of finding stable matches that meet distributional concerns is usually formulated by imposing side constraints whose “right-hand sides” are absolute numbers specified before the preferences or number of agents on the “proposing” side are known. In many cases, it is more natural to express the relevant constraints as proportions. We treat such constraints as soft but provide ex post guarantees on how well the constraints are satisfied while preserving stability. Our technique requires an extension of Scarf’s lemma, which is of independent interest.

Suggested Citation

  • Thành Nguyen & Rakesh Vohra, 2019. "Stable Matching with Proportionality Constraints," Operations Research, INFORMS, vol. 67(6), pages 1503-1519, November.
    • Handle: RePEc:inm:oropre:v:67:y:2019:i:6:p:1503-1519
    DOI: 10.1287/opre.2019.1909
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    References listed on IDEAS

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    6. Glenn Ellison & Parag A. Pathak, 2021. "The Efficiency of Race-Neutral Alternatives to Race-Based Affirmative Action: Evidence from Chicago's Exam Schools," American Economic Review, American Economic Association, vol. 111(3), pages 943-975, March.
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    Cited by:

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    5. Aygün, Orhan & Turhan, Bertan, 2021. "How to De-reserve Reserves," ISU General Staff Papers 202104130700001123, Iowa State University, Department of Economics.
    6. Chao Huang, 2022. "Two-sided matching with firms' complementary preferences," Papers 2205.05599, arXiv.org, revised May 2022.
    7. Reischmann, Tobias & Klein, Thilo & Giegerich, Sven, 2021. "An iterative deferred acceptance mechanism for decentralized, fast and fair childcare assignment," ZEW Discussion Papers 21-095, ZEW - Leibniz Centre for European Economic Research.
    8. Priyank Arora & Wei Wei & Senay Solak, 2021. "Improving Outcomes in Child Care Subsidy Voucher Programs under Regional Asymmetries," Production and Operations Management, Production and Operations Management Society, vol. 30(12), pages 4435-4454, December.
    9. Kong, Qianqian & Peters, Hans, 2023. "Power indices for networks, with applications to matching markets," European Journal of Operational Research, Elsevier, vol. 306(1), pages 448-456.
    10. Jalota, Devansh & Pavone, Marco & Qi, Qi & Ye, Yinyu, 2023. "Fisher markets with linear constraints: Equilibrium properties and efficient distributed algorithms," Games and Economic Behavior, Elsevier, vol. 141(C), pages 223-260.
    11. Imamura, Kenzo & Kawase, Yasushi, 2024. "Efficient matching under general constraints," Games and Economic Behavior, Elsevier, vol. 145(C), pages 197-207.
    12. Hai Nguyen & Thành Nguyen & Alexander Teytelboym, 2021. "Stability in Matching Markets with Complex Constraints," Management Science, INFORMS, vol. 67(12), pages 7438-7454, December.
    13. Chao Huang, 2021. "Unidirectional substitutes and complements," Papers 2108.12572, arXiv.org.
    14. Tobias Reischmann & Thilo Klein & Sven Giegerich, 2021. "A deferred acceptance mechanism for decentralized, fast, and fair childcare assignment," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 6(1), pages 59-100, December.
    15. Orhan Aygun & Bertan Turhan, 2020. "Designing Direct Matching Mechanism for India with Comprehensive Affirmative Action," Papers 2004.13264, arXiv.org, revised Dec 2021.
    16. Chao Huang, 2022. "Firm-worker hypergraphs," Papers 2211.06887, arXiv.org, revised Nov 2023.
    17. Chao Huang, 2023. "Concave many-to-one matching," Papers 2309.04181, arXiv.org.

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