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Matching of like rank and the size of the core in the marriage problem

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  • Holzman, Ron
  • Samet, Dov

Abstract

When men and women are objectively ranked in a marriage problem, say by beauty, then pairing individuals of equal rank is the only stable matching. We generalize this observation by providing bounds on the size of the rank gap between mates in a stable matching in terms of the size of the ranking sets. Using a metric on the set of matchings, we provide bounds on the diameter of the core – the set of stable matchings – in terms of the size of the ranking sets and in terms of the size of the rank gap. We conclude that when the set of rankings is small, so are the core and the rank gap in stable matchings. We construct examples showing that our bounds are essentially tight, and that certain natural variants of the bounds fail to hold.

Suggested Citation

  • Holzman, Ron & Samet, Dov, 2014. "Matching of like rank and the size of the core in the marriage problem," Games and Economic Behavior, Elsevier, vol. 88(C), pages 277-285.
  • Handle: RePEc:eee:gamebe:v:88:y:2014:i:c:p:277-285
    DOI: 10.1016/j.geb.2014.10.003
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    References listed on IDEAS

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    1. James W. Boudreau & Vicki Knoblauch, 2010. "Marriage Matching and Intercorrelation of Preferences," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 12(3), pages 587-602, June.
    2. Clark Simon, 2006. "The Uniqueness of Stable Matchings," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-28, December.
    3. Caldarelli, G. & Capocci, A., 2001. "Beauty and distance in the stable marriage problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(1), pages 325-331.
    4. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-627, June.
    5. Eeckhout, Jan, 2000. "On the uniqueness of stable marriage matchings," Economics Letters, Elsevier, vol. 69(1), pages 1-8, October.
    6. 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 & Cagatay Kayi & Flip Klijn, 2017. "Rank Gaps and the Size of the Core for Roommate Problems," DOCUMENTOS CEDE 015610, UNIVERSIDAD DE LOS ANDES-CEDE.
    2. Peng, Zixuan & Shan, Wenxuan & Guan, Feng & Yu, Bin, 2016. "Stable vessel-cargo matching in dry bulk shipping market with price game mechanism," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 95(C), pages 76-94.

    More about this item

    Keywords

    Marriage problem; Stable matching; Core; Correlated preferences; Assortative matching;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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