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Robust stability in matching markets

Author

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  • Kojima, Fuhito

    () (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.

Suggested Citation

  • Kojima, Fuhito, 2011. "Robust stability in matching markets," Theoretical Economics, Econometric Society, vol. 6(2), May.
  • Handle: RePEc:the:publsh:780
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    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20110257/5199/184
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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. 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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    Citations

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    Cited by:

    1. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    2. 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.
    3. repec:eee:gamebe:v:107:y:2018:i:c:p:1-20 is not listed on IDEAS
    4. 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.
    5. repec:eee:mateco:v:72:y:2017:i:c:p:16-24 is not listed on IDEAS
    6. Oğuz Afacan, Mustafa, 2012. "Group robust stability in matching markets," Games and Economic Behavior, Elsevier, vol. 74(1), pages 394-398.
    7. Afacan, Mustafa Oǧuz, 2013. "Application fee manipulations in matching markets," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 446-453.
    8. 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.
    9. Afacan, Mustafa Oǧuz, 2016. "Enrollment manipulations in school choice," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 119-125.
    10. Chen, Yajing, 2014. "When is the Boston mechanism strategy-proof?," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 43-45.
    11. Ning Sun & Zaifu Yang, 2016. "A Theory of Marriage with Mutually Consented Divorces," Discussion Papers 16/14, Department of Economics, University of York.

    More about this item

    Keywords

    Matching; stability; strategy-proofness; robust stability; acyclicity;

    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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