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On stable and efficient mechanisms for priority-based allocation problems

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  • Rong, Kang
  • Tang, Qianfeng
  • Zhang, Yongchao

Abstract

For school choice (priority-based allocation) problems, when the priority structure is acyclic, the associated student-proposing deferred acceptance algorithm is Pareto efficient and group strategy-proof (Ergin, 2002). We reveal a hidden iterative removal structure behind such deferred acceptance algorithms. A nonempty set of students is called a top fair set (TFS) if when all students apply to their most preferred schools and all schools accept the best applicants up to their quotas, students in the set are always accepted, regardless of other students' preferences. We provide an elimination process to find the maximal TFS, if any TFS exists. We show that for any priority structure, iterative removal of TFS is equivalent to the associated deferred acceptance algorithm if and only if the latter is a Pareto efficient mechanism.

Suggested Citation

  • Rong, Kang & Tang, Qianfeng & Zhang, Yongchao, 2020. "On stable and efficient mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:jetheo:v:187:y:2020:i:c:s0022053120300193
    DOI: 10.1016/j.jet.2020.105014
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    Cited by:

    1. Siwei Chen & Yajing Chen & Chia‐Ling Hsu, 2023. "New axioms for top trading cycles," Bulletin of Economic Research, Wiley Blackwell, vol. 75(4), pages 1064-1077, October.
    2. Estelle Cantillon & Li Chen & Juan S. Pereyra, 2022. "Respecting priorities versus respecting preferences in school choice: When is there a trade-off?," Papers 2212.02881, arXiv.org, revised Jan 2024.
    3. Estelle Cantillon & Li Chen & Juan Sebastian Pereyra Barreiro, 2022. "Respecting priorities versus respecting preferences in school choice: When is there a trade-off ?," Working Papers ECARES 2022-39, ULB -- Universite Libre de Bruxelles.
    4. Siwei Chen & Yajing Chen & Chia-Ling Hsu, 2021. "New axioms for top trading cycles," Papers 2104.09157, arXiv.org, revised Jun 2021.

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    More about this item

    Keywords

    Deferred acceptance algorithm; Pareto efficiency; School choice; Stability; Strategy-proofness;
    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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