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The singleton core in the college admissions problem and its application to the National Resident Matching Program (NRMP)

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  • Ma, Jinpeng

Abstract

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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  • Ma, Jinpeng, 2010. "The singleton core in the college admissions problem and its application to the National Resident Matching Program (NRMP)," Games and Economic Behavior, Elsevier, vol. 69(1), pages 150-164, May.
  • Handle: RePEc:eee:gamebe:v:69:y:2010:i:1:p:150-164
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    References listed on IDEAS

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    1. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
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    3. 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.
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    7. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 197-218.
    8. 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.
    9. 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.
    10. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
    11. 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.
    12. Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-570, May.
    13. Jinpeng Ma, 2002. "original papers : Stable matchings and the small core in Nash equilibrium in the college admissions problem," Review of Economic Design, Springer;Society for Economic Design, vol. 7(2), pages 117-134.
    14. 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.
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    Cited by:

    1. Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2014. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 793-811, April.
    2. repec:spr:joecth:v:64:y:2017:i:1:d:10.1007_s00199-016-0997-9 is not listed on IDEAS
    3. Itai Ashlagi & Flip Klijn, 2012. "Manipulability in matching markets: conflict and coincidence of interests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 23-33, June.
    4. repec:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-017-0573-y is not listed on IDEAS
    5. Assaf Romm, 2014. "Implications of capacity reduction and entry in many-to-one stable matching," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 851-875, December.
    6. Parag A. Pathak & Tayfun Sönmez, 2013. "School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation," American Economic Review, American Economic Association, vol. 103(1), pages 80-106, February.
    7. David Pérez-Castrillo & Marilda Sotomayor, 2017. "The outcome of competitive equilibrium rules in buyer–seller markets when the agents play strategically," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 99-119, June.
    8. Tayfun Sonmez & Parag Pathak (MIT), 2011. "Admissions Reform at Chicago's Selective High Schools: Comparing Mechanisms by their Vulnerability to Manipulation," EcoMod2011 2954, EcoMod.
    9. repec:bpj:bejtec:v:17:y:2017:i:2:p:9:n:10 is not listed on IDEAS
    10. Alcalde, José, 2017. "Beyond the Spanish MIR with Consent: (Hidden) Cooperation and Coordination in Matching," QM&ET Working Papers 17-1, University of Alicante, D. Quantitative Methods and Economic Theory.

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