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Dominance invariant one-to-one matching problems

Author

Listed:
  • MAULEON, Ana
  • MOLIS, Elena
  • VANNETELBOSCH , Vincent J
  • VERGOTE, Wouter

Abstract

Solution concepts in social environments use either a direct or indirect dominance relationship, depending on whether it is assumed that agents are myopic or farsighted. Direct dominance implies indirect dominance, but not the reverse. Hence, the predicted outcomes when assuming myopic (direct) or farsighted (in- direct) agents could be very different. In this paper, we characterize dominance invariant one-to-one matching problems when preferences are strict. That is, we obtain the conditions on preference profiles such that indirect dominance implies direct dominance in these problems and give them an intuitive interpretation. Whenever some of the conditions are not satisfied, it is important to know the kind of agents that are being investigated in order to use the appropriate stability concept. Furthermore, we characterize dominance invariant one-to-one matching problems having a non-empty core. Finally, we show that, if the core of a dominance invariant one-to-one matching problem is not empty, it contains a unique matching, the dominance invariant stable matching, in which all agents who mutually top rank each other are matched to one another and all other agents remain unmatched.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • MAULEON, Ana & MOLIS, Elena & VANNETELBOSCH , Vincent J & VERGOTE, Wouter, 2014. "Dominance invariant one-to-one matching problems," LIDAM Reprints CORE 2638, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2638
    Note: In : International Journal of Game Theory, 43(4), 925-943, 2014
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    Cited by:

    1. Ata Atay & Sylvain Funck & Ana Mauleon & Vincent Vannetelbosch, 2025. "Matching markets with farsighted couples," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 64(3), pages 465-481, May.
    2. Mert Kimya, 2023. "Coalition Formation Under Dominance Invariance," Dynamic Games and Applications, Springer, vol. 13(2), pages 480-496, June.
    3. Atay, Ata & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "A bargaining set for roommate problems," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    4. Kimya, Mert, 2020. "Farsighted Objections and Maximality in One-to-one Matching Problems," Working Papers 2020-14, University of Sydney, School of Economics.
    5. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2020. "Matching with myopic and farsighted players," Journal of Economic Theory, Elsevier, vol. 190(C).
    6. Kimya, Mert, 2022. "Farsighted objections and maximality in one-to-one matching problems," Journal of Economic Theory, Elsevier, vol. 204(C).
    7. Francis Bloch & Ana Mauleon & Vincent Vannetelbosch, 2023. "Preface to the Special issue on “Group Formation and Farsightedness”," Dynamic Games and Applications, Springer, vol. 13(2), pages 435-439, June.
    8. Kimya, Mert, 2021. "Coalition Formation Under Dominance Invariance," Working Papers 2021-06, University of Sydney, School of Economics.
    9. 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.
    10. Kimya, Mert, 2021. "Coalition Formation Under Dominance Invariance," Working Papers 202106, University of Sydney, School of Economics.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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