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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. Caterina Calsamiglia & Guillaume Haeringer & Flip Klijn, 2010. "Constrained School Choice: An Experimental Study," American Economic Review, American Economic Association, vol. 100(4), pages 1860-1874, September.
    2. 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.
    3. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-2271, August.
    4. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
    5. 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.
    6. Christopher P. Chambers & M. Bumin Yenmez, 2017. "Choice and Matching," American Economic Journal: Microeconomics, American Economic Association, vol. 9(3), pages 126-147, August.
    7. Turhan, Bertan, 2019. "Welfare and incentives in partitioned school choice markets," Games and Economic Behavior, Elsevier, vol. 113(C), pages 199-208.
    8. Yajing Chen, 2017. "New axioms for deferred acceptance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 393-408, February.
    9. 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.
    10. 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.
    11. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
    12. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    13. Marek Pycia, 2012. "Stability and Preference Alignment in Matching and Coalition Formation," Econometrica, Econometric Society, vol. 80(1), pages 323-362, January.
    14. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    15. Tayfun Sönmez, 2013. "Bidding for Army Career Specialties: Improving the ROTC Branching Mechanism," Journal of Political Economy, University of Chicago Press, vol. 121(1), pages 186-219.
    16. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
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    Cited by:

    1. Haeringer, Guillaume & Iehlé, Vincent, 2021. "Gradual college admission," Journal of Economic Theory, Elsevier, vol. 198(C).
    2. 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.
    3. Atila Abdulkadiroglu & Tommy Andersson, 2022. "School Choice," NBER Working Papers 29822, National Bureau of Economic Research, Inc.
    4. Turhan, Bertan, 2019. "Welfare and incentives in partitioned school choice markets," Games and Economic Behavior, Elsevier, vol. 113(C), pages 199-208.
    5. 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.
    6. Laura Doval, 2019. "Dynamically Stable Matching," Papers 1906.11391, arXiv.org, revised Feb 2021.
    7. Vincent Iehlé, 2016. "Gradual College Admisssion," Post-Print halshs-02367006, HAL.

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