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Farsighted Stability for Roommate Markets

  • Bettina Klaus
  • Flip Klijn
  • Markus Walzl

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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Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 385.

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Date of creation: May 2009
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Handle: RePEc:bge:wpaper:385
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  1. MAULEON, Ana & VANNETELBOSCH, Vincent J. & VERGOTE, Wouter, . "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," CORE Discussion Papers RP 2337, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Page Jr, Frank H & Wooders, Myrna H. & Kamat, Samir, 2002. "Networks And Farsighted Stability," The Warwick Economics Research Paper Series (TWERPS) 660, University of Warwick, Department of Economics.
  3. Bettina Klaus & Flip Klijn & Markus Walzl, 2008. "Stochastic Stability for Roommate Markets," Working Papers 357, Barcelona Graduate School of Economics.
  4. Effrosyni Diamantoudi & Licun Xue, . "Farsighted Stability in Hedonic Games," Economics Working Papers 2000-12, Department of Economics and Business Economics, Aarhus University.
  5. 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.
  6. Klaus, Bettina & Klijn, Flip, 2007. "Paths to stability for matching markets with couples," Games and Economic Behavior, Elsevier, vol. 58(1), pages 154-171, January.
  7. Jean-Jacques, HERINGS & Ana, MAULEON & Vincent, VANNETELBOSCH, 2006. "Farsightedly stable networks," Discussion Papers (ECON - Département des Sciences Economiques) 2006046, Université catholique de Louvain, Département des Sciences Economiques.
  8. Bettina Klaus & Flip Klijn, 2007. "Smith and Rawls Share a Room," UFAE and IAE Working Papers 706.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  9. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
  10. 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.
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