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The core of roommate problems: size and rank-fairness within matched pairs

Author

Listed:
  • Paula Jaramillo

    (Universidad de Los Andes)

  • Çaǧatay Kayı

    (Universidad del Rosario)

  • Flip Klijn

    (Institute for Economic Analysis (CSIC) and Barcelona GSE)

Abstract

This paper deals with roommate problems (Gale and Shapley, Am Math Mon 69(1):9–15, 1962) that are solvable, i.e., have a non-empty core (set of stable matchings). We study rank-fairness within pairs 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 & 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.
    • Handle: RePEc:spr:jogath:v:48:y:2019:i:1:d:10.1007_s00182-018-0651-9
    DOI: 10.1007/s00182-018-0651-9
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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. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, vol. 48(1), pages 18-28, July.
    5. 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.
    6. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    7. 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.
    8. Bettina Klaus & Flip Klijn, 2010. "Smith and Rawls share a room: stability and medians," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 647-667, October.
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    Cited by:

    1. 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.
    2. 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.
    3. Flip Klijn & Markus Walzl & Christopher Kah, 2021. "Almost mutually best in matching markets: rank gaps and size of the core," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 797-816, November.

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    More about this item

    Keywords

    Matching; Roommate problem; Stability; Core; Rank-fairness; 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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