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Coordinated Strategic Manipulations and Mechanisms in School Choice

Author

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  • Ryo Shirakawa

    (Graduate School of Economics, The Univerity of Tokyo and Junior Research Fellow, Research Institute for Economics & Business Administration (RIEB), Kobe University, JAPAN)

Abstract

This study observes that no group strategy-proof mechanism satisfies even a fairly weak notion of stability in a school choice setting. In response to this result, we introduce two monotonicity axioms, which we call top-dropping monotonicity and extension monotonicity, as alternatives to group strategy-proofness. We prove that these two axioms are equivalent to the requirement that no group of students gains from a simple manipulation of their preferences. Replacing group strategy-proofness with the two axioms, we find that the Kesten's (2010) efficiency adjusted deferred acceptance mechanism is the unique mechanism satisfying the three criteria. We also provide several applications of the two monotonicity axioms, finding axiomatic characterizations of the deferred acceptance mechanism and a class of mechanisms in which stability and strategy-proofness are equivalent.

Suggested Citation

  • Ryo Shirakawa, 2022. "Coordinated Strategic Manipulations and Mechanisms in School Choice," Discussion Paper Series DP2022-25, Research Institute for Economics & Business Administration, Kobe University.
    • Handle: RePEc:kob:dpaper:dp2022-25
    as

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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2022-25.pdf
    File Function: First version, 2022
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    References listed on IDEAS

    as
    1. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
    2. 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.
    3. 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.
    4. Troyan, Peter & Delacrétaz, David & Kloosterman, Andrew, 2020. "Essentially stable matchings," Games and Economic Behavior, Elsevier, vol. 120(C), pages 370-390.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Matching; School choice; Strategy-proofness; Group strategy-proofness; Monotonicity; Deferred acceptance; Efficiency adjusted deferred acceptance;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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