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Optimal Priority-Based Allocation Mechanisms

Author

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  • Peng Shi

    (Marshall School of Business, University of Southern California, Los Angeles, California 90089)

Abstract

This paper develops a tractable methodology for designing an optimal priority system for assigning agents to heterogeneous items while accounting for agents’ choice behavior. The space of mechanisms being optimized includes deferred acceptance and top trading cycles as special cases. In contrast to previous literature, I treat the inputs to these mechanisms, namely the priority distribution of agents and quotas of items, as parameters to be optimized. The methodology is based on analyzing large market models of one-sided matching using techniques from revenue management and solving a certain assortment planning problem whose objective is social welfare. I apply the methodology to school choice and show that restricting choices may be beneficial to student welfare. Moreover, I compute optimized choice sets and priorities for elementary school choice in Boston.

Suggested Citation

  • Peng Shi, 2022. "Optimal Priority-Based Allocation Mechanisms," Management Science, INFORMS, vol. 68(1), pages 171-188, January.
    • Handle: RePEc:inm:ormnsc:v:68:y:2022:i:1:p:171-188
    DOI: 10.1287/mnsc.2020.3925
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    References listed on IDEAS

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    Cited by:

    1. Peng Shi, 2025. "Optimal Match Recommendations in Two-sided Marketplaces with Endogenous Prices," Management Science, INFORMS, vol. 71(9), pages 7431-7448, September.
    2. Ali Aouad & Daniela Saban, 2023. "Online Assortment Optimization for Two-Sided Matching Platforms," Management Science, INFORMS, vol. 69(4), pages 2069-2087, April.
    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. Marco Pariguana & Maria Elenda Ortega-Hesles, 2023. "School Admissions, Mismatch and Graduation," Edinburgh School of Economics Discussion Paper Series 311, Edinburgh School of Economics, University of Edinburgh.
    5. Kazuki Sekiya & Suguru Otani & Yuki Komatsu & Sachio Ohkawa & Shunya Noda, 2026. "Integrating Predictive Models into Two-Sided Recommendations: A Matching-Theoretic Approach," Papers 2602.19689, arXiv.org.
    6. Ata Atay & Ana Mauleon & Vincent Vannetelbosch, 2025. "Limited Farsightedness in Priority‐Based Matching," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 27(4), August.
    7. Combe, Julien & Nora, Vladyslav & Tercieux, Olivier, 2025. "Dynamic assignment without money: optimality of spot mechanisms," Theoretical Economics, Econometric Society, vol. 20(1), January.
    8. Will Ma, 2023. "When Is Assortment Optimization Optimal?," Management Science, INFORMS, vol. 69(4), pages 2088-2105, April.
    9. Clark, Damon & Coate, Stephen, 2025. "An efficiency case for equity-based school priorities," Journal of Public Economics, Elsevier, vol. 250(C).

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