IDEAS home Printed from https://ideas.repec.org/p/col/000089/015610.html
   My bibliography  Save this paper

Rank Gaps and the Size of the Core for Roommate Problems

Author

Listed:
  • Paula Jaramillo
  • Cagatay 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 & Cagatay Kayi & Flip Klijn, 2017. "Rank Gaps and the Size of the Core for Roommate Problems," Documentos CEDE 15610, Universidad de los Andes, Facultad de Economía, CEDE.
  • Handle: RePEc:col:000089:015610
    as

    Download full text from publisher

    File URL: https://repositorio.uniandes.edu.co/bitstream/handle/1992/8725/dcede2017-36.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Ana Mauleon & Elena Molis & Vincent Vannetelbosch & Wouter Vergote, 2014. "Dominance invariant one-to-one matching problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 925-943, November.
    3. Azar Abizada, 2019. "Exchange-stability in roommate problems," Review of Economic Design, Springer;Society for Economic Design, vol. 23(1), pages 3-12, June.
    4. Papai, Szilvia, 2004. "Unique stability in simple coalition formation games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 337-354, August.
    5. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers CIE 74, Paderborn University, CIE Center for International Economics.
    6. Péter Biró & Elena Inarra & Elena Molis, 2014. "A new solution for the roommate problem: The Q-stable matchings," CERS-IE WORKING PAPERS 1422, Institute of Economics, Centre for Economic and Regional Studies.
    7. Agust'in G. Bonifacio & Elena Inarra & Pablo Neme, 2020. "Stable decompositions of coalition formation games," Papers 2009.11689, arXiv.org, revised Dec 2021.
    8. Niclas Boehmer & Edith Elkind, 2020. "Stable Roommate Problem with Diversity Preferences," Papers 2004.14640, arXiv.org.
    9. Biró, Péter & Iñarra, Elena & Molis, Elena, 2016. "A new solution concept for the roommate problem: Q-stable matchings," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 74-82.
    10. Gutin, Gregory Z. & Neary, Philip R. & Yeo, Anders, 2023. "Unique stable matchings," Games and Economic Behavior, Elsevier, vol. 141(C), pages 529-547.
    11. Jaeok Park, 2017. "Competitive equilibrium and singleton cores in generalized matching problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 487-509, May.
    12. 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.
    13. Mauleon, Ana & Roehl, Nils & Vannetelbosch, Vincent, 2019. "Paths to stability for overlapping group structures," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 19-24.
    14. Alison Watts, 2007. "Formation of segregated and integrated groups," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 505-519, April.
    15. Klaus, B.E. & Klijn, F. & Walzl, M., 2007. "The evolution of roommate networks: a comment on Jackson and Watts JET (2002)," Research Memorandum 012, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    16. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
    17. Mauleon, Ana & Roehl, Nils & Vannetelbosch, Vincent, 2018. "Constitutions and groups," Games and Economic Behavior, Elsevier, vol. 107(C), pages 135-152.
    18. Alcalde, Jose & Revilla, Pablo, 2004. "Researching with whom? Stability and manipulation," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 869-887, December.
    19. Konishi, Hideo & Unver, M. Utku, 2006. "Credible group stability in many-to-many matching problems," Journal of Economic Theory, Elsevier, vol. 129(1), pages 57-80, July.
    20. Atay, Ata & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "A bargaining set for roommate problems," Journal of Mathematical Economics, Elsevier, vol. 94(C).

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:col:000089:015610. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Universidad De Los Andes-Cede (email available below). General contact details of provider: https://edirc.repec.org/data/ceandco.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.