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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. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, Elsevier, vol. 134(1), pages 537-547, May.
  2. Effrosyni Diamantoudi & Eiichi Miyagawa & Licun Xue, 2002. "Random paths to stability in the roommate problem," Discussion Papers, Columbia University, Department of Economics 0102-65, Columbia University, Department of Economics.
  3. HERINGS, Jean-Jacques & MAULEON, Ana & VANNETELBOSCH, Vincent, 2006. "Farsightedly stable networks," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2006092, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Vincent Vannetelbosch & Ana Mauleon & Wouter Vergote, 2008. "Von Neumann-Morgenstern Farsightedly Stable Sets in Two-Sided Matching," Working Papers, Fondazione Eni Enrico Mattei 2008.29, Fondazione Eni Enrico Mattei.
  5. Bettina Klaus & Flip Klijn, 2004. "Paths to Stability for Matching Markets with Couples," Working Papers 156, Barcelona Graduate School of Economics.
  6. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2008. "Stochastic Stability for Roommate Markets," Research Memorandum, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) 010, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  7. 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.
  8. Bettina Klaus & Flip Klijn, 2007. "Smith and Rawls Share a Room," Working Papers 315, Barcelona Graduate School of Economics.
  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. Florian M. Biermann, 2011. "A Measure to compare Matchings in Marriage Markets," Working Papers, International School of Economics at TSU, Tbilisi, Republic of Georgia 005-11, International School of Economics at TSU, Tbilisi, Republic of Georgia.
  2. 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).
  3. 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).
  4. N. Roketskiy, 2012. "Farsightedly Stable Matchings," Working Papers, NET Institute 12-26, NET Institute.
  5. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers, Fondazione Eni Enrico Mattei 2014.48, Fondazione Eni Enrico Mattei.

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