Group Robust Stability in Matching Markets
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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- 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.
- 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.
- Paul Milgrom, 2003.
"Matching with Contracts,"
03003, Stanford University, Department of Economics.
- Atila Abdulkadiroglu & Tayfun Sönmez, 2003.
"School Choice: A Mechanism Design Approach,"
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- Pathak, Parag A. & Abdulkadiroglu, Atila & Roth, Alvin, 2005.
"The New York City High School Match,"
2562765, Harvard University Department of Economics.
- Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
- Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
- 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.
- 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.
- 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.
- Ruth Mart?ez & Jordi MassóAuthor-Email: firstname.lastname@example.org & Alejandro Neme & Jorge Oviedo, 2003. "On group strategy-proof mechanisms for a many-to-one matching model," UFAE and IAE Working Papers 577.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
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