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The stability of the roommate problem revisited

Author

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  • INARRA, Elena

    (University of the Basque Country, Dep. Ftos. A. Económico I, E-48007 Bilbao, Spain)

  • LARREA, Conchi

    (University of the Basque Country, Dpto Economía Aplicada IV (Mathematics), E-48007 Bilbao, Spain)

  • MOLIS, Elena

    (Facultés Universitaires Saint-Louis, CEREC, B-1000 Bruxelles, Belgium and Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

Abstract

The lack of stability in some matching problems suggests that alternative solution concepts to the core might be a step towards furthering our understanding of matching market performance. We propose absorbing sets as a solution for the class of roommate problems with strict preferences. This solution, which always exists, either gives the matchings in the core or predicts other matchings when the core is empty. Furthermore, it satisfies the interesting property of outer stability. We also determine the matchings in absorbing sets and find that in the case of multiple absorbing sets a similar structure is shared by all.

Suggested Citation

  • INARRA, Elena & LARREA, Conchi & MOLIS, Elena, 2010. "The stability of the roommate problem revisited," LIDAM Discussion Papers CORE 2010007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2010007
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    References listed on IDEAS

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    1. Kalai, Ehud & Pazner, Elisha A & Schmeidler, David, 1976. "Collective Choice Correspondences as Admissible Outcomes of Social Bargaining Processes," Econometrica, Econometric Society, vol. 44(2), pages 233-240, March.
    2. E. Inarra & C. Larrea & E. Molis, 2008. "Random paths to P-stability in the roommate problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 461-471, March.
    3. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    4. 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.
    5. 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.
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    Cited by:

    1. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
    2. Gudmundsson , Jens, 2014. "Sequences in Pairing Problems: A New Approach to Reconcile Stability with Strategy-Proofness for Elementary Matching Problems," Working Papers 2014:40, Lund University, Department of Economics.
    3. MAULEON, Ana & MOLIS, Elena & VANNETELBOSCH, Vincent & VERGOTE, Wouter, 2011. "Absolutely stable roommate problems," LIDAM Discussion Papers CORE 2011029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Hakan İnal, 2014. "A Generalization of the Lone Wolf Theorem," Metroeconomica, Wiley Blackwell, vol. 65(4), pages 541-547, November.

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    More about this item

    Keywords

    roommate problem; core; absorbing sets;
    All these keywords.

    JEL classification:

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

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