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Weak Stability and a Bargaining Set for the Marriage Model

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  • Klijn, F.
  • Masso, J.

    (Tilburg University, Center for Economic Research)

Abstract

In this note we introduceweak stability, a relaxation of the concept of stability for the marriage model by assuming that the agents are no longer myopic in choosing a blocking pair. The new concept is based on threats within blocking pairs: an individually rational matching is weakly stable if for every blocking pair one of themembers can find a more attractive partner with whom he forms another blocking pair for the original matching. Our main result is that under the assumption of strict preferences, the set of weakly stable and weakly efficient matchings coincides with the bargaining set of Zhou (1994) for this context.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1999-114.

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Date of creation: 1999
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Handle: RePEc:dgr:kubcen:1999114

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Keywords: matching; (weak) stability; bargaining set;

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References

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  1. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
  2. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
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Cited by:
  1. Peter Biro & Flip Klijn, 2011. "Matching with Couples: a Multidisciplinary Survey," IEHAS Discussion Papers 1139, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  2. 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).
  3. Federico Echenique & Jorge Oviedo, 2004. "A Theory of Stability in Many-to-many Matching Markets," Game Theory and Information 0401002, EconWPA.
  4. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers 2014.48, Fondazione Eni Enrico Mattei.
  5. Somdeb Lahiri, 2006. "A Weak Bargaining Set for Contract Choice Problems," Working Papers 2006.19, Fondazione Eni Enrico Mattei.
  6. Lahiri, S., 2004. "Stable outcomes for contract choice problems," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 15(4), pages 409-418.
  7. Bando, Keisuke, 2012. "Many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 14-20.
  8. 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.
  9. Bettina Klaus & Flip Klijn, 2004. "Stable Matchings and Preferences of Couples," Working Papers 117, Barcelona Graduate School of Economics.
  10. Damiano, Ettore & Lam, Ricky, 2005. "Stability in dynamic matching markets," Games and Economic Behavior, Elsevier, vol. 52(1), pages 34-53, July.

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