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Some things couples always wanted to know about stable matchings (but were afraid to ask)

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  • Bettina Klaus
  • Flip Klijn
  • Jordi Massó

Abstract

In this note we study the National Resident Matching Program (NRMP) algorithm in the US market for physicians. We report on two problems that concern the presence of couples, a feature explicitly incorporated in the new NRMP algorithm (cf. Roth and Peranson, 1999). First, we show that the new NRMP algorithm may not find an existing stable matching, even when couples' preferences are "responsive," i.e., when Gale and Shapleyís (1962) deferred acceptance algorithm (on which the old NRMP algorithm is based) is applicable. Second, we demonstrate that the new NRMP algorithm may also be manipulated by couples acting as singles.
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Suggested Citation

  • Bettina Klaus & Flip Klijn & Jordi Massó, 2007. "Some things couples always wanted to know about stable matchings (but were afraid to ask)," Review of Economic Design, Springer;Society for Economic Design, vol. 11(3), pages 175-184, November.
    • Handle: RePEc:spr:reecde:v:11:y:2007:i:3:p:175-184
    DOI: 10.1007/s10058-006-0017-9
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    References listed on IDEAS

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    1. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
    2. 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.
    3. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
    4. 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.
    5. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    6. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
    7. 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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    Citations

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    Cited by:

    1. Klaus, Bettina & Klijn, Flip, 2007. "Paths to stability for matching markets with couples," Games and Economic Behavior, Elsevier, vol. 58(1), pages 154-171, January.
    2. Lars Ehlers & Jordi Massó, 2004. "Incomplete Information and Small Cores in Matching Markets," Working Papers 147, Barcelona School of Economics.
    3. repec:ebl:ecbull:v:3:y:2004:i:45:p:1-11 is not listed on IDEAS
    4. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
    5. Aslan, Fatma & Lainé, Jean, 2020. "Competitive equilibria in Shapley–Scarf markets with couples," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 66-78.
    6. Alfredo Salgado-Torres, 2012. "A simple decentralized matching mechanism in markets with couples," Economics Bulletin, AccessEcon, vol. 32(3), pages 2044-2055.
    7. Bettina Klaus & Flip Klijn, 2007. "Fair and efficient student placement with couples," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 177-207, October.
    8. Dogan, Onur & Laffond, Gilbert & Lainé, Jean, 2011. "The Core of Shapley-Scarf markets with couples," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 60-67, January.
    9. David Cantala, 2011. "Agreement toward stability in matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 293-316, December.
    10. Péter Biró & Flip Klijn, 2013. "Matching With Couples: A Multidisciplinary Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-18.
    11. Rouzbeh Ghouchani & Szilvia Pápai, 2022. "Preference aggregation for couples," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 889-923, November.
    12. Peter Biro & Tamas Fleiner & Rob Irving, 2013. "Matching Couples with Scarf's Algorithm," CERS-IE WORKING PAPERS 1330, Institute of Economics, Centre for Economic and Regional Studies.
    13. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    14. Jay Sethuraman & Chung-Piaw Teo & Liwen Qian, 2006. "Many-to-One Stable Matching: Geometry and Fairness," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 581-596, August.
    15. Nicolò, Antonio & Sen, Arunava & Yadav, Sonal, 2019. "Matching with partners and projects," Journal of Economic Theory, Elsevier, vol. 184(C).
    16. Britta Hoyer & Nadja Stroh-Maraun, 2020. "Stability in Weighted College Admissions Problems," Working Papers Dissertations 63, Paderborn University, Faculty of Business Administration and Economics.

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    More about this item

    Keywords

    Matching; Stability; Couples; C78; D78; J41;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • J41 - Labor and Demographic Economics - - Particular Labor Markets - - - Labor Contracts

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