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Stable Sets in Matching Problems with Coalitional Sovereignty and Path Dominance

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  • HERINGS, P. Jean-Jacques
  • MAULEON, Ana
  • VANNETELBOSCH, Vincent

Abstract

We study von Neumann Morgenstern stable sets for one-to-one matching problems under the assumption of coalitional sovereignty, meaning that a deviating coalition of players does not have the power to arrange the matches of agents outside the coalition. We study both the case of pairwise and coalitional deviations. We argue further that dominance has to be replaced by path dominance along the lines of van Deemen (1991) and Page and Wooders (2009). This results in the pairwise myopic vNM set and the myopic vNM set, respectively. We obtain a unique prediction for both types of stable sets: the set of matchings that belong to the core. We also show that the pairwise and coalitional analogues of the level-1 farsighted set yield the core as the unique prediction.

Suggested Citation

  • HERINGS, P. Jean-Jacques & MAULEON, Ana & VANNETELBOSCH, Vincent, 2016. "Stable Sets in Matching Problems with Coalitional Sovereignty and Path Dominance," CORE Discussion Papers 2016010, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2016010
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    References listed on IDEAS

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    5. Konishi, Hideo & Unver, M. Utku, 2006. "Credible group stability in many-to-many matching problems," Journal of Economic Theory, Elsevier, vol. 129(1), pages 57-80, July.
    6. 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.
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    Cited by:

    1. Demuynck, Thomas & Herings, P. Jean-Jacques & Saulle, Riccardo & Seel, Christian, 2018. "The Myopic Stable Set for Social Environments (RM/17/002-revised)," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).
    2. Thomas Demuynck & Jean-Jacques Herings & Riccardo Saulle & Christian Seel, 2017. "The Myopic Stable Set for Social Environments," Working Papers ECARES ECARES 2017-02, ULB -- Universite Libre de Bruxelles.

    More about this item

    Keywords

    Matching problems; stable sets; coalitional sovereignty;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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