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Robust stability in matching markets

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    (Department of Economics, Stanford University)

Abstract

In a matching problem between students and schools, a mechanism is said to be robustly stable if it is stable, strategy-proof, and immune to a combined manipulation, where a student first misreports her preferences and then blocks the matching that is produced by the mechanism. We find that even when school priorities are publicly known and only students can behave strategically, there is a priority structure for which no robustly stable mechanism exists. Our main result shows that there exists a robustly stable mechanism if and only if the priority structure of schools is acyclic (Ergin, 2002), and in that case, the student-optimal stable mechanism is the unique robustly stable mechanism.

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  • ,, 2011. "Robust stability in matching markets," Theoretical Economics, Econometric Society, vol. 6(2), May.
    • Handle: RePEc:the:publsh:780
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    References listed on IDEAS

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    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. Chakraborty, Archishman & Citanna, Alessandro & Ostrovsky, Michael, 2010. "Two-sided matching with interdependent values," Journal of Economic Theory, Elsevier, vol. 145(1), pages 85-105, January.
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    Cited by:

    1. Chen, Siwei & Heo, Eun Jeong, 2021. "Acyclic priority profiles in school choice: Characterizations," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 22-30.
    2. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    3. Archishman Chakraborty & Alessandro Citanna & Michael Ostrovsky, 2015. "Group stability in matching with interdependent values," Review of Economic Design, Springer;Society for Economic Design, vol. 19(1), pages 3-24, March.
    4. Han, Xiang, 2018. "Stable and efficient resource allocation under weak priorities," Games and Economic Behavior, Elsevier, vol. 107(C), pages 1-20.
    5. 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.
    6. 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).
    7. Mustafa Afacan, 2014. "Fictitious students creation incentives in school choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 493-514, August.
    8. Afacan, Mustafa Og̃uz & Dur, Umut Mert, 2017. "When preference misreporting is Harm[less]ful?," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 16-24.
    9. Eun Jeong Heo, 2019. "Preference profiles for efficiency, fairness, and consistency in school choice problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 243-266, March.
    10. Yusuke Narita, 2021. "Comment on “Efficient Resource Allocation on the Basis of Priorities”," Econometrica, Econometric Society, vol. 89(4), pages 15-17, July.
    11. Oğuz Afacan, Mustafa, 2012. "Group robust stability in matching markets," Games and Economic Behavior, Elsevier, vol. 74(1), pages 394-398.
    12. Afacan, Mustafa Oǧuz, 2013. "Application fee manipulations in matching markets," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 446-453.
    13. Kumano, Taro, 2013. "Strategy-proofness and stability of the Boston mechanism: An almost impossibility result," Journal of Public Economics, Elsevier, vol. 105(C), pages 23-29.
    14. Matsui, Akihiko & Murakami, Megumi, 2022. "Deferred acceptance algorithm with retrade," Mathematical Social Sciences, Elsevier, vol. 120(C), pages 50-65.
    15. Afacan, Mustafa Oǧuz, 2016. "Enrollment manipulations in school choice," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 119-125.
    16. Chen, Yajing, 2014. "When is the Boston mechanism strategy-proof?," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 43-45.
    17. Siwei Chen & Yajing Chen & Chia-Ling Hsu, 2021. "New axioms for top trading cycles," Papers 2104.09157, arXiv.org, revised Jun 2021.
    18. Ning Sun & Zaifu Yang, 2016. "A Theory of Marriage with Mutually Consented Divorces," Discussion Papers 16/14, Department of Economics, University of York.

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    More about this item

    Keywords

    Matching; stability; strategy-proofness; robust stability; acyclicity;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • J44 - Labor and Demographic Economics - - Particular Labor Markets - - - Professional Labor Markets and Occupations

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