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Weak stability and Pareto efficiency in school choice

Author

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  • Qianfeng Tang

    (Shanghai University of Finance and Economics)

  • Yongchao Zhang

    (Shanghai University of Finance and Economics)

Abstract

We study the trade-off between stability and students’ welfare in school choice problems. We call a matching weakly stable if none of its blocking pairs can be matched in a more stable matching—one with a weakly smaller set of blocking pairs. A matching is said to be self-constrained efficient if for students it is not Pareto dominated by any more stable matching, and it is self-constrained optimal if it weakly Pareto dominates all such matchings. We show that the following are equivalent for any matching: (1) It is weakly stable and self-constrained efficient; (2) it is self-constrained optimal; (3) it is an efficiency-adjusted deferred acceptance mechanism (EADAM) outcome under some consenting constraints; and (4) it is exactly the EADAM outcome when its own set of blocking pairs is used as consenting constraint.

Suggested Citation

  • Qianfeng Tang & Yongchao Zhang, 2021. "Weak stability and Pareto efficiency in school choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 533-552, March.
    • Handle: RePEc:spr:joecth:v:71:y:2021:i:2:d:10.1007_s00199-020-01255-3
    DOI: 10.1007/s00199-020-01255-3
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    References listed on IDEAS

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    1. José Alcalde & Antonio Romero-Medina, 2017. "Fair student placement," Theory and Decision, Springer, vol. 83(2), pages 293-307, August.
    2. Atila Abdulkadiroğlu & Yeon-Koo Che & Parag A. Pathak & Alvin E. Roth & Olivier Tercieux, 2020. "Efficiency, Justified Envy, and Incentives in Priority-Based Matching," American Economic Review: Insights, American Economic Association, vol. 2(4), pages 425-442, December.
    3. Klijn, Flip & Masso, Jordi, 2003. "Weak stability and a bargaining set for the marriage model," Games and Economic Behavior, Elsevier, vol. 42(1), pages 91-100, January.
    4. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match," NBER Working Papers 14864, National Bureau of Economic Research, Inc.
    5. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    6. Pereyra, Juan Sebastián, 2013. "A dynamic school choice model," Games and Economic Behavior, Elsevier, vol. 80(C), pages 100-114.
    7. Bando, Keisuke, 2014. "On the existence of a strictly strong Nash equilibrium under the student-optimal deferred acceptance algorithm," Games and Economic Behavior, Elsevier, vol. 87(C), pages 269-287.
    8. Lars Ehlers & Thayer Morrill, 2020. "(Il)legal Assignments in School Choice," Review of Economic Studies, Oxford University Press, vol. 87(4), pages 1837-1875.
    9. Pablo Guillen & Onur Kesten, 2012. "Matching Markets With Mixed Ownership: The Case For A Real‐Life Assignment Mechanism," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 1027-1046, August.
    10. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    11. Troyan, Peter & Delacrétaz, David & Kloosterman, Andrew, 2020. "Essentially stable matchings," Games and Economic Behavior, Elsevier, vol. 120(C), pages 370-390.
    12. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-689, June.
    13. Dur, Umut & Gitmez, A. Arda & Yılmaz, Özgür, 2019. "School choice under partial fairness," Theoretical Economics, Econometric Society, vol. 14(4), November.
    14. Tang, Qianfeng & Yu, Jingsheng, 2014. "A new perspective on Kesten's school choice with consent idea," Journal of Economic Theory, Elsevier, vol. 154(C), pages 543-561.
    15. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    16. José Alcalde Pérez & Antonio Romero-Medina, 2011. "Fair School Placement," Working Papers. Serie AD 2011-22, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    17. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
    18. Kesten, Onur & Kurino, Morimitsu, 2019. "Strategy-proof improvements upon deferred acceptance: A maximal domain for possibility," Games and Economic Behavior, Elsevier, vol. 117(C), pages 120-143.
    19. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    20. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
    21. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
    22. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
    23. Yan Chen & Onur Kesten, 2017. "Chinese College Admissions and School Choice Reforms: A Theoretical Analysis," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 99-139.
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    Cited by:

    1. Minoru Kitahara & Yasunori Okumura, 2023. "School Choice with Multiple Priorities," Papers 2308.04780, arXiv.org, revised Oct 2023.
    2. de Callatay, Pierre & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "Minimally Farsighted Unstable Networks," LIDAM Discussion Papers CORE 2021012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Mustafa Oguz Afacan & Umut Dur & A. Arda Gitmez & Ozgur Y{i}lmaz, 2022. "Improving the Deferred Acceptance with Minimal Compromise," Papers 2205.00032, arXiv.org, revised Sep 2023.

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    More about this item

    Keywords

    Deferred acceptance algorithm; Pareto efficiency; School choice; Stability;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • I20 - Health, Education, and Welfare - - Education - - - General

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