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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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    Cited by:

    1. Rodríguez-Álvarez, Carmelo & Romero-Medina, Antonio, 2024. "School choice with transferable student characteristics," Games and Economic Behavior, Elsevier, vol. 143(C), pages 103-124.
    2. Pierre Callataÿ & Ana Mauleon & Vincent Vannetelbosch, 2024. "Minimal farsighted instability," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 493-523, June.
    3. Minoru Kitahara & Yasunori Okumura, 2023. "School Choice with Multiple Priorities," Papers 2308.04780, arXiv.org, revised Oct 2024.
    4. 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).
    5. 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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