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Matching with myopic and farsighted players

Author

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  • HERINGS P. Jean-Jacques

    (Universiteit Maastricht)

  • MAULEON Ana

    (Université Saint-Louis, Bruxelles and CORE, UCL)

  • VANNETELBOSCH Vincent

    (Université catholique de Louvain, CORE, Belgium)

Abstract

We study stable sets for marriage problems under the assumption that players can be both myopic and farsighted. We introduce the new notion of the myopic-farsighted stable set, which is based on the notion of a myopic-farsighted improving path. A myopic-farsighted stable set is the set of match-ings such that there is no myopic-farsighted improving path from any match-ing in the set to another matching in the set (internal stability) and there is a myopic-farsighted improving path from any matching outside the set to some matching in the set (external stability). For the special cases where all players are myopic and where all players are farsighted, our concept pre-dicts the set of matchings in the core. When all men are myopic and the top choice of each man is a farsighted woman, we show that the singleton consist-ing of the woman-optimal stable matching is a myopic-farsighted stable set. The same result holds when all women are farsighted. We present examples where this is the unique myopic-farsighted stable set as well as examples of myopic-farsighted stable sets consisting of a core element di erent from the woman-optimal matching or even of a non-core element.

Suggested Citation

  • HERINGS P. Jean-Jacques & MAULEON Ana & VANNETELBOSCH Vincent, 2017. "Matching with myopic and farsighted players," LIDAM Discussion Papers CORE 2017014, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2017014
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    Cited by:

    1. Mert Kimya, 2023. "Coalition Formation Under Dominance Invariance," Dynamic Games and Applications, Springer, vol. 13(2), pages 480-496, June.
    2. de Callatay, Pierre & Mauleon, Ana & Vannetelbosch, Vincent, 2023. "Local Farsightedness in Network Formation," LIDAM Discussion Papers CORE 2023003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. P. Jean-Jacques Herings & Ana Mauleon & Vincent Vannetelbosch, 2023. "Social Rationalizability with Mediation," Dynamic Games and Applications, Springer, vol. 13(2), pages 440-461, June.
    4. Kimya, Mert, 2020. "Equilibrium coalitional behavior," Theoretical Economics, Econometric Society, vol. 15(2), May.
    5. Atay, Ata & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "A bargaining set for roommate problems," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    6. Kimya, Mert, 2020. "Farsighted Objections and Maximality in One-to-one Matching Problems," Working Papers 2020-14, University of Sydney, School of Economics.
    7. Ana Mauleon & Simon Schopohl & Akylai Taalaibekova & Vincent Vannetelbosch, 2022. "Coordination on networks with farsighted and myopic agents," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(3), pages 509-536, November.
    8. Pierre de Callataÿ & Ana Mauleon & Vincent Vannetelbosch, 2023. "Myopic-farsighted absorbing networks," Theory and Decision, Springer, vol. 94(3), pages 405-422, April.
    9. Mariya Teteryatnikova, 2021. "Cautious farsighted stability in network formation games with streams of payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 829-865, December.
    10. 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.
    11. 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.
    12. Bayer, Péter & Herings, P. Jean-Jacques & Peeters, Ronald, 2021. "Farsighted manipulation and exploitation in networks," Journal of Economic Theory, Elsevier, vol. 196(C).
    13. Ata Atay & Ana Mauleon & Vincent Vannetelbosch, 2022. "Limited Farsightedness in Priority-Based Matching," Papers 2212.07427, arXiv.org.
    14. Kimya, Mert, 2021. "Coalition Formation Under Dominance Invariance," Working Papers 202106, University of Sydney, School of Economics.
    15. Kenzo Imamura & Hideo Konishi, 2023. "Assortative Matching with Externalities and Farsighted Agents," Dynamic Games and Applications, Springer, vol. 13(2), pages 497-509, June.
    16. Imamura, Kenzo & Konishi, Hideo & Pan, Chen-Yu, 2023. "Stability in matching with externalities: Pairs competition and oligopolistic joint ventures," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 270-286.
    17. Chenghong Luo & Ana Mauleon & Vincent Vannetelbosch, 2021. "Network formation with myopic and farsighted players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1283-1317, June.
    18. Hirai, Toshiyuki & Watanabe, Naoki & Muto, Shigeo, 2019. "Farsighted stability in patent licensing: An abstract game approach," Games and Economic Behavior, Elsevier, vol. 118(C), pages 141-160.
    19. Bloch, Francis & van den Nouweland, Anne, 2020. "Farsighted stability with heterogeneous expectations," Games and Economic Behavior, Elsevier, vol. 121(C), pages 32-54.
    20. Ana Mauleon & Jose J. Sempere-Monerris & Vincent Vannetelbosch, 2023. "Limited Farsightedness in R &D Network Formation," Dynamic Games and Applications, Springer, vol. 13(2), pages 549-565, June.
    21. Kimya, Mert, 2022. "Farsighted objections and maximality in one-to-one matching problems," Journal of Economic Theory, Elsevier, vol. 204(C).
    22. de Callatay, Pierre & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "Minimally Farsighted Unstable Networks," LIDAM Discussion Papers CORE 2021012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    23. Kimya, Mert, 2021. "Coalition Formation Under Dominance Invariance," Working Papers 2021-06, University of Sydney, School of Economics.
    24. 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

    Marriage problems; stable sets; myopic and farsighted players.;
    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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