The singleton core in the college admissions problem and its application to the National Resident Matching Program (NRMP)
We show that in the marriage problem the student-optimal algorithm may in fact generate an equilibrium outcome that is college-optimal and student-pessimal in terms of the true preferences even though it is student-optimal and college-pessimal in terms of the submitted preferences. In the college admissions problem, the student-optimal algorithm generates either a matching that is not stable for the true preferences or a matching that is college-optimal and student-pessimal in terms of the true preferences. Thus, our results show that, in the absence of certain match variations, the newly designed student-optimal algorithm adopted by the NRMP since 1998 either may be bias in favor of hospitals in terms of the true preferences or fails to produce a true stable matching. We also discuss when the core is large and when the core is a singleton at a Nash equilibrium.
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- Roth, Alvin E & Vande Vate, John H, 1991. "Incentives in Two-Sided Matching with Random Stable Mechanisms," Economic Theory, Springer, vol. 1(1), pages 31-44, January.
- 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.
- Mongell, Susan & Roth, Alvin E, 1991. "Sorority Rush as a Two-Sided Matching Mechanism," American Economic Review, American Economic Association, vol. 81(3), pages 441-64, June.
- Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-50, March.
- Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
- Elliott Peranson & Alvin E. Roth, 1999.
"The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design,"
American Economic Review,
American Economic Association, vol. 89(4), pages 748-780, September.
- Alvin E. Roth & Elliott Peranson, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," NBER Working Papers 6963, National Bureau of Economic Research, Inc.
- Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer, vol. 9(2), pages 197-218.
- Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
- 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.
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
- Crawford, Vincent P., 2005. "The Flexible-Salary Match: A Proposal to Increase the Salary Flexibility of the National Resident Matching Program," University of California at San Diego, Economics Working Paper Series qt2gw114b2, Department of Economics, UC San Diego.
- Jinpeng Ma, 2002. "original papers : Stable matchings and the small core in Nash equilibrium in the college admissions problem," Review of Economic Design, Springer, vol. 7(2), pages 117-134.
- Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
- Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-70, May.
- Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
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