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Almost Mutually Best in Matching Markets: Rank-Fairness and Size of the Core

Author

Listed:
  • Christopher Kah
  • Flip Klijn
  • Markus Walzl

Abstract

This paper studies the one-to-one two-sided marriage model (Gale and Shapley, 1962). If agents' preferences exhibit mutually best, there is a unique stable matching that is trivially rank-fair (i.e., in each matched pair the agents assign one another the same rank). We study in how far this result is robust for matching markets that are "close" to mutually best. Without a restriction on preference profiles, we find that natural "distances" to mutually best neither bound the size of the core nor the rank-unfairness of stable matchings. However, for matching markets that satisfy horizontal heterogeneity, "local" distances to mutually best provide bounds for the size of the core and the rank- unfairness of stable matchings.

Suggested Citation

  • Christopher Kah & Flip Klijn & Markus Walzl, 2019. "Almost Mutually Best in Matching Markets: Rank-Fairness and Size of the Core," Working Papers 1115, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1115
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    References listed on IDEAS

    as
    1. 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.
    2. Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2019. "The core of roommate problems: size and rank-fairness within matched pairs," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 157-179, March.
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    7. Eeckhout, Jan, 2000. "On the uniqueness of stable marriage matchings," Economics Letters, Elsevier, vol. 69(1), pages 1-8, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    matching; mutually best; horizontal heterogeneity; stable matching; core; rank-fairness;
    All these keywords.

    JEL classification:

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

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