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Group robust stability in matching markets

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  • Oğuz Afacan, Mustafa

Abstract

We introduce the notion of group robust stability which requires robustness against a combined manipulation, first misreporting preferences and then rematching, by any group of students in the school choice type of matching markets. Our first result shows that there is no group robustly stable mechanism even under acyclic priority structures. Next, we define a weak version of group robust stability, called weak group robust stability. Our main theorem, then, proves that there is a weakly group robustly stable mechanism if and only if the priority structure of schools is acyclic, and in that case, it coincides with the student-optimal stable mechanism.

Suggested Citation

  • Oğuz Afacan, Mustafa, 2012. "Group robust stability in matching markets," Games and Economic Behavior, Elsevier, vol. 74(1), pages 394-398.
    • Handle: RePEc:eee:gamebe:v:74:y:2012:i:1:p:394-398
    DOI: 10.1016/j.geb.2011.06.004
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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.
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    6. Ruth Martínez & Jordi Massó & Alejdanro Neme & Jorge Oviedo, 2004. "On group strategy-proof mechanisms for a many-to-one matching model," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 115-128, January.
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    8. 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.
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    Cited by:

    1. Feng Zhang & Liwei Zhong, 2021. "Three-sided matching problem with mixed preferences," Journal of Combinatorial Optimization, Springer, vol. 42(4), pages 928-936, November.
    2. 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.
    3. Afacan, Mustafa Oǧuz, 2013. "Application fee manipulations in matching markets," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 446-453.
    4. Chen, Yajing, 2014. "When is the Boston mechanism strategy-proof?," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 43-45.
    5. Feng Zhang & Liwei Zhong, 0. "Three-sided matching problem with mixed preferences," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-9.
    6. 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.
    7. 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.
    8. Siwei Chen & Yajing Chen & Chia-Ling Hsu, 2021. "New axioms for top trading cycles," Papers 2104.09157, arXiv.org, revised Jun 2021.
    9. Liwei Zhong & Yanqin Bai, 2019. "Three-sided stable matching problem with two of them as cooperative partners," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 286-292, January.

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    More about this item

    Keywords

    Matching; Stability; Group robust stability; Group strategy-proofness; Acyclicity; Combined manipulation;
    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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