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When does an additional stage improve welfare in centralized assignment?

Author

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  • Battal Doğan

    (University of Bristol)

  • M. Bumin Yenmez

    (Boston College)

Abstract

We study multistage centralized assignment systems to allocate scarce resources based on priorities in the context of school choice. We characterize schools’ capacity-priority profiles under which an additional stage of assignment may improve student welfare when the deferred acceptance algorithm is used at each stage. If the capacity-priority profile is acyclic, then no student prefers any subgame-perfect Nash equilibrium (SPNE) outcome of the 2-stage system to the truthful dominant-strategy equilibrium outcome of the 1-stage system. If the capacity-priority profile is not acyclic, then an SPNE outcome of the 2-stage system may Pareto dominate the truthful dominant-strategy equilibrium outcome of the 1-stage system. If students are restricted to playing truncation strategies, an additional stage unambiguously improves student welfare: no student prefers the truthful dominant-strategy equilibrium outcome of the 1-stage system to any SPNE outcome of the 2-stage system.

Suggested Citation

  • Battal Doğan & M. Bumin Yenmez, 2023. "When does an additional stage improve welfare in centralized assignment?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1145-1173, November.
    • Handle: RePEc:spr:joecth:v:76:y:2023:i:4:d:10.1007_s00199-023-01488-y
    DOI: 10.1007/s00199-023-01488-y
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    Cited by:

    1. Tommy Andersson & Umut Dur & Sinan Ertemel & Onur Kesten, 2024. "Sequential school choice with public and private schools," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(2), pages 231-276, September.
    2. Haeringer, Guillaume & Iehlé, Vincent, 2021. "Gradual college admission," Journal of Economic Theory, Elsevier, vol. 198(C).
    3. Jiarui Xie, 2024. "Games under the Tiered Deferred Acceptance Mechanism," Papers 2406.00455, arXiv.org, revised Oct 2024.
    4. Atila Abdulkadiroglu & Tommy Andersson, 2022. "School Choice," NBER Working Papers 29822, National Bureau of Economic Research, Inc.
    5. Turhan, Bertan, 2019. "Welfare and incentives in partitioned school choice markets," Games and Economic Behavior, Elsevier, vol. 113(C), pages 199-208.
    6. Doval, Laura, 2022. "Dynamically stable matching," Theoretical Economics, Econometric Society, vol. 17(2), May.
    7. Vincent Iehlé, 2016. "Gradual College Admisssion," Post-Print halshs-02367006, HAL.
    8. repec:hhs:lunewp:2023_012 is not listed on IDEAS
    9. Doğan, Battal & Yenmez, M. Bumin, 2019. "Unified versus divided enrollment in school choice: Improving student welfare in Chicago," Games and Economic Behavior, Elsevier, vol. 118(C), pages 366-373.

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