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When Does an Additional Stage Improve Welfare in Centralized Assignment?

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  • Battal Doğan
  • M. Bumin Yenmez

Abstract

We study multistage centralized assignments to allocate scarce resources based on priorities in the context of school choice. We characterize the capacity-priority profiles of schools 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 enrollment system to the truthful equilibrium outcome of the 1-stage enrolment system. If the capacity-priority profile is not acyclic, then an SPNE outcome of the 2-stage enrollment system may Pareto dominate the truthful equilibrium outcome of the 1-stage enrollment system.

Suggested Citation

  • Battal Doğan & M. Bumin Yenmez, 2018. "When Does an Additional Stage Improve Welfare in Centralized Assignment?," Bristol Economics Discussion Papers 18/704, School of Economics, University of Bristol, UK.
  • Handle: RePEc:bri:uobdis:18/704
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    References listed on IDEAS

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    1. Marilda Sotomayor, 2008. "The stability of the equilibrium outcomes in the admission games induced by stable matching rules," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 621-640, March.
    2. Manjunath, Vikram & Turhan, Bertan, 2016. "Two school systems, one district: What to do when a unified admissions process is impossible," Games and Economic Behavior, Elsevier, vol. 95(C), pages 25-40.
    3. Christopher P. Chambers & M. Bumin Yenmez, 2017. "Choice and Matching," American Economic Journal: Microeconomics, American Economic Association, vol. 9(3), pages 126-147, August.
    4. Turhan, Bertan, 2019. "Welfare and incentives in partitioned school choice markets," Games and Economic Behavior, Elsevier, vol. 113(C), pages 199-208.
    5. Federico Echenique & M. Bumin Yenmez, 2015. "How to Control Controlled School Choice," American Economic Review, American Economic Association, vol. 105(8), pages 2679-2694, August.
    6. Doğan, Battal & Klaus, Bettina, 2018. "Object allocation via immediate-acceptance: Characterizations and an affirmative action application," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 140-156.
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    Cited by:

    1. Vincent Iehlé, 2016. "Gradual College Admisssion," Post-Print halshs-02367006, HAL.
    2. 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.
    3. Laura Doval, 2019. "Dynamically Stable Matching," Papers 1906.11391, arXiv.org, revised Feb 2021.
    4. Turhan, Bertan, 2019. "Welfare and incentives in partitioned school choice markets," Games and Economic Behavior, Elsevier, vol. 113(C), pages 199-208.
    5. Andersson, Tommy & Dur, Umut & Ertemel, Sinan & Kesten , Onur, 2018. "Sequential School Choice with Public and Private Schools," Working Papers 2018:39, Lund University, Department of Economics.

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