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Absorbing sets in roommate problems

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  • Iñarra, E.
  • Larrea, C.
  • Molis, E.
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    Abstract

    We analyze absorbing sets as a solution for roommate problems with strict preferences. This solution provides the set of stable matchings when it is non-empty and some matchings with interesting properties otherwise. In particular, all matchings in an absorbing set have the greatest number of agents with no incentive to change partners. These “satisfied” agents are paired in the same stable manner. In the case of multiple absorbing sets we find that any two such sets differ only in how satisfied agents are matched with each other.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0899825613000730
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    Bibliographic Info

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 81 (2013)
    Issue (Month): C ()
    Pages: 165-178

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    Handle: RePEc:eee:gamebe:v:81:y:2013:i:c:p:165-178

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    Web page: http://www.elsevier.com/locate/inca/622836

    Related research

    Keywords: Roommate problem; Stability; Absorbing sets;

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    References

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    1. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    2. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    3. 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.
    4. Péter Biró & Katarína Cechlárová & Tamás Fleiner, 2008. "The dynamics of stable matchings and half-matchings for the stable marriage and roommates problems," International Journal of Game Theory, Springer, vol. 36(3), pages 333-352, March.
    5. Bettina Klaus & Flip Klijn & Markus Walzl, 2008. "Stochastic Stability for Roommate Markets," Working Papers 357, Barcelona Graduate School of Economics.
    6. EHLERS, Lars, 2005. "Von Neumann-Morgenstern Stable Sets in Matching Problems," Cahiers de recherche 12-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    7. E. Inarra & C. Larrea & E. Molis, 2008. "Random paths to P-stability in the roommate problem," International Journal of Game Theory, Springer, vol. 36(3), pages 461-471, March.
    8. Kalai, Ehud & Schmeidler, David, 1977. "An admissible set occurring in various bargaining situations," Journal of Economic Theory, Elsevier, vol. 14(2), pages 402-411, April.
    9. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
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    Cited by:
    1. MAULEON, Ana & MOLIS, Elena & VANNETELBOSCH, Vincent & VERGOTE , Wouter, 2013. "Dominance invariant one-to-one matching problems," CORE Discussion Papers 2013052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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