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The stability of the roommate problem revisited

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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.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2010007.

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Date of creation: 01 Feb 2010
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Handle: RePEc:cor:louvco:2010007

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Keywords: roommate problem; core; absorbing sets;

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  1. 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.
  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.
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  8. EHLERS, Lars, 2005. "Von Neumann-Morgenstern Stable Sets in Matching Problems," Cahiers de recherche 2005-11, Universite de Montreal, Departement de sciences economiques.
  9. Abeledo, Hernan & Isaak, Garth, 1991. "A characterization of graphs that ensure the existence of stable matchings," Mathematical Social Sciences, Elsevier, vol. 22(1), pages 93-96, August.
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  12. 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.
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  15. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
  16. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, April.
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Cited by:
  1. MAULEON, Ana & MOLIS, Elena & VANNETELBOSCH, Vincent & VERGOTE, Wouter, 2011. "Absolutely stable roommate problems," CORE Discussion Papers 2011029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Bettina Klaus & Flip Klijn & Markus Walzl, 2008. "Stochastic Stability for Roommate Markets," Working Papers 357, Barcelona Graduate School of Economics.
  3. Péter Biró & Gethin Norman, 2013. "Analysis of stochastic matching markets," International Journal of Game Theory, Springer, vol. 42(4), pages 1021-1040, November.

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