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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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File URL: http://hdl.handle.net/10.1111/j.1467-9779.2011.01525.x
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Article provided by Association for Public Economic Theory in its journal Journal of Public Economic Theory.

Volume (Year): 13 (2011)
Issue (Month): 6 (December)
Pages: 921-933

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Handle: RePEc:bla:jpbect:v:13:y:2011:i:6:p:921-933
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  1. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
  2. 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.
  3. Samir Kamat & Frank Page & Myrna Wooders, 2004. "Networks and Farsighted Stability," Econometric Society 2004 North American Winter Meetings 561, Econometric Society.
  4. Klaus Bettina & Klijn Flip, 2007. "Smith and Rawls Share a Room," Research Memorandum 026, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  5. Vannetelbosch, Vincent J. & Mauleon, Ana & Vergote, Wouter, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
  6. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
  7. 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.
  8. Klaus Bettina & Klijn Flip & Walzl Markus, 2008. "Stochastic Stability for Roommate Markets," Research Memorandum 010, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  9. Effrosyni Diamantoudi & Licun Xue, 2003. "Farsighted stability in hedonic games," Social Choice and Welfare, Springer, vol. 21(1), pages 39-61, 08.
  10. 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.
  11. 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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