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Group Robust Stability in Matching Markets

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  • Mustafa Oguz Afacan

    (Department of Economics, Stanford University)

Abstract

We propose a group robust stability notion which requires robustness against a combined manipulation, first misreporting of preferences and then rematching, by any group of students in a school choice type of matching markets. Our first result shows that there is no group robustly stable mechanism even under acyclic priority structures (Ergin (2002)). Then, we define a weak version of group robust stability, called weak group robust stability. Our main theorem shows that there is a weakly group robustly stable mechanism if and only if the priority structure is acyclic, and in that case it coincides with the student-optimal stable mechanism. Hence this result generalizes the main theorem of Kojima (2010). Then as a real-world practice, we add uncertainty regarding an acceptance of an appeal of students to rematch after the announced matching. In that setting, we show that under some conditions along with the acyclicity, the student-optimal stable mechanism is group robustly stable under uncertainty.

Suggested Citation

  • Mustafa Oguz Afacan, 2010. "Group Robust Stability in Matching Markets," Discussion Papers 09-019, Stanford Institute for Economic Policy Research.
  • Handle: RePEc:sip:dpaper:09-019
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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. ,, 2011. "Robust stability in matching markets," Theoretical Economics, Econometric Society, vol. 6(2), May.
    3. 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.
    4. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541, Elsevier.
    5. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    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.
    7. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    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.
    9. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
    10. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    11. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
    12. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    13. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
    14. Sonmez, Tayfun, 1999. "Can Pre-arranged Matches Be Avoided in Two-Sided Matching Markets?," Journal of Economic Theory, Elsevier, vol. 86(1), pages 148-156, May.
    15. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
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    Cited by:

    1. 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.
    2. Feng Zhang & Liwei Zhong, 2021. "Three-sided matching problem with mixed preferences," Journal of Combinatorial Optimization, Springer, vol. 42(4), pages 928-936, November.
    3. 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.
    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. Afacan, Mustafa Oǧuz, 2013. "Application fee manipulations in matching markets," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 446-453.
    6. Chen, Yajing, 2014. "When is the Boston mechanism strategy-proof?," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 43-45.
    7. Feng Zhang & Liwei Zhong, 0. "Three-sided matching problem with mixed preferences," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-9.
    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

    group stability mechansim; group robust stability; student-optimal stable mechanism;
    All these keywords.

    JEL classification:

    • A10 - General Economics and Teaching - - General Economics - - - General

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