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Weak stability and a bargaining set for the marriage model

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  • Klijn, Flip
  • Masso, Jordi

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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Suggested Citation

  • Klijn, Flip & Masso, Jordi, 2003. "Weak stability and a bargaining set for the marriage model," Games and Economic Behavior, Elsevier, vol. 42(1), pages 91-100, January.
  • Handle: RePEc:eee:gamebe:v:42:y:2003:i:1:p:91-100
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    References listed on IDEAS

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    1. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    2. 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.
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    Cited by:

    1. Alfredo Salgado-Torres, 2011. "A solution concept for housing market problems with externalities," Economics Bulletin, AccessEcon, vol. 31(1), pages 623-630.
    2. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    3. Takumi Kongo, 2013. "On non-bossy matching rules in two-sided matching problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(4), pages 303-311, December.
    4. Atay, Ata & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "A bargaining set for roommate problems," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    5. Kimya, Mert, 2020. "Farsighted Objections and Maximality in One-to-one Matching Problems," Working Papers 2020-14, University of Sydney, School of Economics.
    6. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
    7. Damiano, Ettore & Lam, Ricky, 2005. "Stability in dynamic matching markets," Games and Economic Behavior, Elsevier, vol. 52(1), pages 34-53, July.
    8. 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.
    9. José Alcalde & Antonio Romero-Medina, 2017. "Fair student placement," Theory and Decision, Springer, vol. 83(2), pages 293-307, August.
    10. Florian M. Biermann, 2011. "A Measure to compare Matchings in Marriage Markets," Discussion Paper Series dp575, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    11. Morimitsu Kurino, 2020. "Credibility, efficiency, and stability: a theory of dynamic matching markets," The Japanese Economic Review, Springer, vol. 71(1), pages 135-165, January.
    12. Mauleon, Ana & Vannetelbosch, Vincent J. & Vergote, Wouter, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
    13. Péter Biró & Flip Klijn, 2013. "Matching With Couples: A Multidisciplinary Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-18.
    14. Federico Echenique, 2008. "What Matchings Can Be Stable? The Testable Implications of Matching Theory," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 757-768, August.
    15. Lahiri, Somdeb, 2007. "A weak bargaining set for contract choice problems," Research in Economics, Elsevier, vol. 61(4), pages 185-190, December.
    16. Hirata, Daisuke & Kasuya, Yusuke & Tomoeda, Kentaro, 2019. "Stability against Robust Deviations in the Roommate Problem," Discussion Papers 2019-03, Graduate School of Economics, Hitotsubashi University.
    17. Echenique, Federico & Oviedo, Jorge, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    18. Qianfeng Tang & Yongchao Zhang, 2021. "Weak stability and Pareto efficiency in school choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 533-552, March.
    19. Kadam, Sangram V. & Kotowski, Maciej H., 2018. "Time horizons, lattice structures, and welfare in multi-period matching markets," Games and Economic Behavior, Elsevier, vol. 112(C), pages 1-20.
    20. Bando, Keisuke, 2012. "Many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 14-20.
    21. Kimya, Mert, 2020. "Farsighted Objections and Maximality in One-to-one Matching Problems," Working Papers 202014, University of Sydney, School of Economics, revised Jul 2021.
    22. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers 2014.48, Fondazione Eni Enrico Mattei.

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    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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