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Stable sets in matching problems with coalitional sovereignty and path dominance

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  • Jean-Jacques Herings, P.
  • Mauleon, Ana
  • Vannetelbosch, Vincent

Abstract

We study von Neumann Morgenstern stable sets for one-to-one matching problems under the assumption of coalitional sovereignty (C), 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 (P) along the lines of van Deemen (1991) and Page and Wooders (2009). This results in the pairwise CP vNM set in the case of pairwise deviations and the CP vNM set in the case of coalitional deviations. We obtain a unique prediction for both types of stable sets: the set of matchings that belong to the core.

Suggested Citation

  • Jean-Jacques Herings, P. & Mauleon, Ana & Vannetelbosch, Vincent, 2017. "Stable sets in matching problems with coalitional sovereignty and path dominance," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 14-19.
    • Handle: RePEc:eee:mateco:v:71:y:2017:i:c:p:14-19
    DOI: 10.1016/j.jmateco.2017.03.003
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    Cited by:

    1. Ata Atay & Sylvain Funck & Ana Mauleon & Vincent Vannetelbosch, 2023. "Matching markets with farsighted couples," UB School of Economics Working Papers 2023/445, University of Barcelona School of Economics.
    2. 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).
    3. Atay, Ata & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "A bargaining set for roommate problems," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    4. Núñez, Marina & Vidal-Puga, Juan, 2022. "Stable cores in information graph games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 353-367.
    5. Ata Atay & Ana Mauleon & Vincent Vannetelbosch, 2022. "Limited Farsightedness in Priority-Based Matching," Papers 2212.07427, arXiv.org.
    6. Thomas Demuynck & P. Jean‐Jacques Herings & Riccardo D. Saulle & Christian Seel, 2019. "The Myopic Stable Set for Social Environments," Econometrica, Econometric Society, vol. 87(1), pages 111-138, January.
    7. Okada, Akira, 2021. "Stable matching and protocol-free equilibrium," Games and Economic Behavior, Elsevier, vol. 128(C), pages 193-201.
    8. Mauleon, Ana & Sempere-Monerris, Jose J. & Vannetelbosch, Vincent, 2023. "R&D network formation with myopic and farsighted firms," Journal of Economic Behavior & Organization, Elsevier, vol. 208(C), pages 203-229.
    9. Pierre de Callataÿ & Ana Mauleon & Vincent Vannetelbosch, 2023. "Myopic-farsighted absorbing networks," Theory and Decision, Springer, vol. 94(3), pages 405-422, April.
    10. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2020. "Matching with myopic and farsighted players," Journal of Economic Theory, Elsevier, vol. 190(C).
    11. Mauleon, Ana & Roehl, Nils & Vannetelbosch, Vincent, 2019. "Paths to stability for overlapping group structures," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 19-24.
    12. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, V., 2020. "Do Stable Outcomes Survive in Marriage Problems with Myopic and Farsighted Players?," Research Memorandum 031, Maastricht University, Graduate School of Business and Economics (GSBE).
    13. Hirai, Toshiyuki & Watanabe, Naoki, 2018. "von Neumann–Morgenstern stable sets of a patent licensing game: The existence proof," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 1-12.
    14. Ata Atay & Ana Mauleon & Vincent Vannetelbosch, 2022. "School choice with farsighted students," UB School of Economics Working Papers 2022/437, University of Barcelona School of Economics.
    15. Herings, P. Jean-Jacques & Kóczy, László Á., 2021. "The equivalence of the minimal dominant set and the myopic stable set for coalition function form games," Games and Economic Behavior, Elsevier, vol. 127(C), pages 67-79.
    16. Bando, Keisuke & Kawasaki, Ryo, 2021. "Stability properties of the core in a generalized assignment problem," Games and Economic Behavior, Elsevier, vol. 130(C), pages 211-223.
    17. Vicki Knoblauch, 2020. "Von Neumann–Morgenstern stable set rationalization of choice functions," Theory and Decision, Springer, vol. 89(3), pages 369-381, October.
    18. Luo, Chenghong & Mauleon, Ana & Vannetelbosch, Vincent, 2022. "Friendship networks with farsighted agents," LIDAM Discussion Papers CORE 2022021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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    More about this item

    Keywords

    Matching problems; Stable sets; Enforceability; Coalitional sovereignty; Path dominance;
    All these keywords.

    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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