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Farsighted Stability for Roommate Markets

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Author Info

  • Bettina-Elisabeth Klaus

    () (Harvard Business School, Negotiation, Organizations & Markets Unit)

  • Flip Klijn

    () (Institute for Economic Analysis (CSIC))

  • Markus Walzl

    () (Department of Economics, Bamberg University)

Abstract

Using a bi-choice graph technique (Klaus and Klijn, 2009), we show that a matching for a roommate market indirectly dominates another matching if and only if no blocking pair of the former is matched in the latter (Proposition 1). Using this characterization of indirect dominance, we investigate von Neumann-Morgenstern farsightedly stable sets. We show that a singleton is von Neumann-Morgenstern farsightedly stable if and only if the matching is stable (Theorem 1). We also present roommate markets with no and with a non-singleton von Neumann-Morgenstern farsightedly stable set (Examples 1 and 2).

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Bibliographic Info

Paper provided by Harvard Business School in its series Harvard Business School Working Papers with number 09-135.

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Length: 18 pages
Date of creation: May 2009
Date of revision:
Handle: RePEc:hbs:wpaper:09-135

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Related research

Keywords: core; farsighted stability; one- and two-sided matching; roommate markets; von Neumann-Morgenstern stability.;

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References

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  1. 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.
  2. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2009. "Farsightedly stable networks," Open Access publications from Maastricht University urn:nbn:nl:ui:27-22854, Maastricht University.
  3. Bettina Klaus & Flip Klijn, 2004. "Paths to Stability for Matching Markets with Couples," UFAE and IAE Working Papers 604.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 01 Dec 2005.
  4. Klaus, Bettina & Klijn, Flip, 2007. "Smith and Rawls Share a Room," Research Memoranda 026, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
  5. MAULEON, Ana & VANNETELBOSCH, Vincent & VERGOTE, Wouter, 2008. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," CORE Discussion Papers 2008016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  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. Effrosyni Diamantoudi & Licun Xue, 2003. "Farsighted stability in hedonic games," Social Choice and Welfare, Springer, vol. 21(1), pages 39-61, 08.
  8. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
  9. 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.
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Citations

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Cited by:
  1. N. Roketskiy, 2012. "Farsightedly Stable Matchings," Working Papers 12-26, NET Institute.
  2. Florian M. Biermann, 2011. "A Measure to compare Matchings in Marriage Markets," Discussion Paper Series dp575, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  3. 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).

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