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On the existence of a strictly strong Nash equilibrium under the student-optimal deferred acceptance algorithm

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  • Bando, Keisuke

Abstract

This study analyzes a preference revelation game in the student-optimal deferred acceptance algorithm in a college admission problem. We assume that each college's true preferences are known publicly, and analyze the strategic behavior of students. We demonstrate the existence of a strictly strong Nash equilibrium in the preference revelation game through a simple algorithm that finds it. Specifically, (i) the equilibrium outcome from our algorithm is the same matching as in the efficiency-adjusted deferred acceptance algorithm and (ii) in a one-to-one matching market, it coincides with the student-optimal von Neumann–Morgenstern (vNM) stable matching. We also show that (i) when a strict core allocation in a housing market derived from a college admission market exists, it can be supported by a strictly strong Nash equilibrium, and (ii) there exists a strictly strong Nash equilibrium under the college-optimal deferred acceptance algorithm if and only if the student-optimal stable matching is Pareto-efficient for students.

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  • 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.
    • Handle: RePEc:eee:gamebe:v:87:y:2014:i:c:p:269-287
    DOI: 10.1016/j.geb.2014.05.009
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    Cited by:

    1. BONKOUNGOU, Somouaoga, 2016. "Pareto dominance of deferred acceptance through early decision," Cahiers de recherche 2016-07, Universite de Montreal, Departement de sciences economiques.
    2. Chao Huang & Qianfeng Tang & Ziwei Wang, 2017. "Epsilon-stability in school choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 277-286, August.
    3. Ryo Shirakawa, 2022. "Coordinated Strategic Manipulations and Mechanisms in School Choice," Discussion Paper Series DP2022-25, Research Institute for Economics & Business Administration, Kobe University.
    4. Battal Doğan & M. Bumin Yenmez, 2023. "When does an additional stage improve welfare in centralized assignment?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1145-1173, November.
    5. Chen, Yiqiu & Möller, Markus, 2024. "Regret-free truth-telling in school choice with consent," Theoretical Economics, Econometric Society, vol. 19(2), May.
    6. Umut Dur & Onur Kesten, 2019. "Sequential versus simultaneous assignment systems and two applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(2), pages 251-283, September.
    7. Somouaoga BONKOUNGOU, 2016. "Pareto Dominance of Deferred Acceptance through Early Decision," Cahiers de recherche 11-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    8. Jaramillo, Paula & Kayı, Çaǧatay & Klijn, Flip, 2021. "School choice: Nash implementation of stable matchings through rank-priority mechanisms," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    9. Claudia Cerrone & Yoan Hermstrüwer & Onur Kesten, 2024. "School Choice with Consent: an Experiment," The Economic Journal, Royal Economic Society, vol. 134(661), pages 1760-1805.
    10. 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.
    11. Battal Dogan & Bumin Yenmez, 2017. "Unified Enrollment in School Choice: How to Improve Student Assignment in Chicago," Cahiers de Recherches Economiques du Département d'économie 17.10, Université de Lausanne, Faculté des HEC, Département d’économie.
    12. Dur, Umut & Gitmez, A. Arda & Yılmaz, Özgür, 2019. "School choice under partial fairness," Theoretical Economics, Econometric Society, vol. 14(4), November.
    13. Imamura, Kenzo & Kawase, Yasushi, 2024. "Efficient matching under general constraints," Games and Economic Behavior, Elsevier, vol. 145(C), pages 197-207.
    14. Yasushi Kawase & Keisuke Bando, 2021. "Subgame perfect equilibria under the deferred acceptance algorithm," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 503-546, June.
    15. 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.

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    More about this item

    Keywords

    Student-optimal deferred acceptance algorithm; Strictly strong Nash equilibrium; Efficiency-adjusted deferred acceptance algorithm; Student-optimal vNM stable matching;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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