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Rank Gaps and the Size of the Core for Roommate Problems

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Listed:
  • Paula Jaramillo
  • Ça?atay Kayi
  • Flip Klijn

Abstract

This paper deals with roommate problems (Gale and Shapley, 1962) that are solvable, i.e., have a non-empty core (set of stable matchings). We study the assortativeness of stable matchings and the size of the core by means of maximal and average rank gaps. We provide upper bounds in terms of maximal and average disagreements in the agents’ rankings. Finally, we show that most of our bounds are tight.

Suggested Citation

  • Paula Jaramillo & Ça?atay Kayi & Flip Klijn, 2017. "Rank Gaps and the Size of the Core for Roommate Problems," Documentos de Trabajo 15499, Universidad del Rosario.
    • Handle: RePEc:col:000092:015499
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    References listed on IDEAS

    as
    1. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
    2. 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.
    3. Jens Gudmundsson, 2014. "When do stable roommate matchings exist? A review," Review of Economic Design, Springer;Society for Economic Design, vol. 18(2), pages 151-161, June.
    4. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
    5. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    6. José Alcalde, 1994. "Exchange-proofness or divorce-proofness? Stability in one-sided matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 275-287, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Matching; roommate problem; stability; core; rank gap; bound;
    All these keywords.

    JEL classification:

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

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