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Group Robust Stability in Matching Markets

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  • Mustafa Oguz Afacan

    () (Department of Economics, Stanford University)

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    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.

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    Bibliographic Info

    Paper provided by Stanford Institute for Economic Policy Research in its series Discussion Papers with number 09-019.

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    Date of creation: Jun 2010
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    Handle: RePEc:sip:dpaper:09-019

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    Related research

    Keywords: group stability mechansim; group robust stability; student-optimal stable mechanism;

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    References

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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. Atila Abdulkadiroglu & Tayfun Smez, 2003. "School Choice: A Mechanism Design Approach," Discussion Papers 0203-18, Columbia University, Department of Economics.
    3. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
    4. 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, vol. 33(1), pages 115-128, January.
    5. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
    6. 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.
    7. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    8. 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.
    9. 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.
    10. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
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