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Farsighted Stability for Roommate Markets

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  • Bettina Klaus
  • Flip Klijn
  • Markus Walzl

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 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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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. HERINGS, Jean-Jacques & MAULEON, Ana & VANNETELBOSCH, Vincent, . "Farsightedly stable networks," CORE Discussion Papers RP -2171, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. 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).
  3. Bettina Klaus & Flip Klijn, 2004. "Paths to Stability for Matching Markets with Couples," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 604.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 01 Dec 2005.
  4. Effrosyni Diamantoudi & Licun Xue, . "Farsighted Stability in Hedonic Games," Economics Working Papers, School of Economics and Management, University of Aarhus 2000-12, School of Economics and Management, University of Aarhus.
  5. Vannetelbosch, Vincent J. & Mauleon, Ana & Vergote, Wouter, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, Econometric Society, vol. 6(3), September.
  6. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
  7. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
  8. 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.
  9. E. Inarra & C. Larrea & E. Molis, 2008. "Random paths to P-stability in the roommate problem," International Journal of Game Theory, Springer, Springer, vol. 36(3), pages 461-471, March.
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Cited by:
  1. MAULEON, Ana & MOLIS, Elena & VANNETELBOSCH, Vincent & VERGOTE, Wouter, 2011. "Absolutely stable roommate problems," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2011029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Florian M. Biermann, 2011. "A Measure to Compare Matchings in Marriage Markets," Working Papers 2011.41, Fondazione Eni Enrico Mattei.
  3. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers 2014.48, Fondazione Eni Enrico Mattei.
  4. MAULEON, Ana & MOLIS, Elena & VANNETELBOSCH, Vincent & VERGOTE , Wouter, 2013. "Dominance invariant one-to-one matching problems," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2013052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. N. Roketskiy, 2012. "Farsightedly Stable Matchings," Working Papers 12-26, NET Institute.

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