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Absolutely stable roommate problems

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  • MAULEON, Ana

    ()
    (CEREC, Facultés universitaires Saint-Louis, B-1000 Brussels, Belgium; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • MOLIS, Elena

    (Universidad de Granada, E-18011 Granada, Spain)

  • VANNETELBOSCH, Vincent

    ()
    (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • VERGOTE, Wouter

    ()
    (CEREC, Facultés universitaires Saint-Louis, B-1000 Brussels, Belgium; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

Abstract

Different solution concepts (core, stable sets, largest consistent set, ...) can be defined using either a direct or an indirect dominance relation. Direct dominance implies indirect dominance, but not the reverse. Hence, the predicted outcomes when assuming myopic (direct) or farsighted (indirect) agents could be very different. In this paper, we characterize absolutely stable roommate problems when preferences are strict. That is, we obtain the conditions on preference profiles such that indirect dominance implies direct dominance in roommate problems. Furthermore, we characterize absolutely stable roommate problems having a non-empty core. Finally, we show that, if the core of an absolutely stable roommate problem is not empty, it contains a unique matching in which all agents who mutually top rank each other are matched to one another and all other agents remain unmatched.

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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 2011029.

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Date of creation: 01 Jul 2011
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Handle: RePEc:cor:louvco:2011029

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Related research

Keywords: roommate problems; direct dominance; indirect dominance;

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References

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  1. José Alcalde, 1994. "Exchange-proofness or divorce-proofness? Stability in one-sided matching markets," Review of Economic Design, Springer, vol. 1(1), pages 275-287, December.
  2. Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999. "Core in a Simple Coalition Formation Game," Boston College Working Papers in Economics 449, Boston College Department of Economics.
  3. EHLERS, Lars, 2005. "Von Neumann-Morgenstern Stable Sets in Matching Problems," Cahiers de recherche 2005-11, Universite de Montreal, Departement de sciences economiques.
  4. INARRA, Elena & LARREA, Conchi & MOLIS, Elena, 2010. "The stability of the roommate problem revisited," CORE Discussion Papers 2010007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Ana, MAULEON & Vincent, VANNETELBOSCH & Wouter, VERGOTE, 2008. "Von Neuman-Morgenstern farsightedly stable sets in two-sided matching," Discussion Papers (ECON - Département des Sciences Economiques) 2008013, Université catholique de Louvain, Département des Sciences Economiques.
  6. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, November.
  7. Bettina Klaus & Flip Klijn & Markus Walzl, 2009. "Farsighted Stability for Roommate Markets," Working Papers 385, Barcelona Graduate School of Economics.
  8. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
  9. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
  10. Effrosyni Diamantoudi & Eiichi Miyagawa & Licun Xue, 2002. "Random paths to stability in the roommate problem," Discussion Papers 0102-65, Columbia University, Department of Economics.
  11. Duranton, Gilles & Martin, Philippe & Mayer, Thierry & Mayneris, Florian, 2010. "The Economics of Clusters: Lessons from the French Experience," OUP Catalogue, Oxford University Press, number 9780199592203.
  12. Effrosyni Diamantoudi & Licun Xue, 2003. "Farsighted stability in hedonic games," Social Choice and Welfare, Springer, vol. 21(1), pages 39-61, 08.
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