IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v322y2025i2p713-724.html
   My bibliography  Save this article

Do stable outcomes survive in marriage problems with myopic and farsighted players?

Author

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

Abstract

We consider marriage problems where myopic and farsighted players interact and analyze these problems by means of the myopic-farsighted stable set. We require that coalition members are only willing to deviate if they all strictly benefit from doing so. Our first main result establishes the equivalence of myopic-farsighted stable sets based on arbitrary coalitional deviations and those based on pairwise deviations.

Suggested Citation

  • Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2025. "Do stable outcomes survive in marriage problems with myopic and farsighted players?," European Journal of Operational Research, Elsevier, vol. 322(2), pages 713-724.
    • Handle: RePEc:eee:ejores:v:322:y:2025:i:2:p:713-724
    DOI: 10.1016/j.ejor.2024.12.043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221724009858
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2024.12.043?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Newton, Jonathan & Sawa, Ryoji, 2015. "A one-shot deviation principle for stability in matching problems," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1-27.
    2. , & , J. & ,, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
    3. Dutta, Bhaskar & Vohra, Rajiv, 2017. "Rational expectations and farsighted stability," Theoretical Economics, Econometric Society, vol. 12(3), September.
    4. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2020. "Matching with myopic and farsighted players," Journal of Economic Theory, Elsevier, vol. 190(C).
    5. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2009. "Farsightedly stable networks," Games and Economic Behavior, Elsevier, vol. 67(2), pages 526-541, November.
    6. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent J., 2004. "Rationalizability for social environments," Games and Economic Behavior, Elsevier, vol. 49(1), pages 135-156, October.
    7. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    8. Kimya, Mert, 2020. "Equilibrium coalitional behavior," Theoretical Economics, Econometric Society, vol. 15(2), May.
    9. 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.
    10. 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.
    11. Alvin E. Roth, 1985. "Conflict and Coincidence of Interest in Job Matching: Some New Results and Open Questions," Mathematics of Operations Research, INFORMS, vol. 10(3), pages 379-389, August.
    12. Dutta, Bhaskar & Vartiainen, Hannu, 2020. "Coalition formation and history dependence," Theoretical Economics, Econometric Society, vol. 15(1), January.
    13. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    14. Anesi, Vincent, 2010. "Noncooperative foundations of stable sets in voting games," Games and Economic Behavior, Elsevier, vol. 70(2), pages 488-493, November.
    15. Jean-Jacques HERINGS & Ana MAULEON & Vincent VANNETELBOSCH, 2017. "Stable sets in matching problems with coalitional sovereignty path dominance," LIDAM Reprints CORE 2861, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. José Alcalde, 1994. "Exchange-proofness or divorce-proofness? Stability in one-sided matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 275-287, December.
    17. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    18. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
    19. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 603-627.
    20. Vartiainen, Hannu, 2011. "Dynamic coalitional equilibrium," Journal of Economic Theory, Elsevier, vol. 146(2), pages 672-698, March.
    21. Atay, Ata & Mauleon, Ana & Vannetelbosch, Vincent, 2025. "School choice with farsighted students," Games and Economic Behavior, Elsevier, vol. 149(C), pages 148-163.
    22. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, vol. 14(1), pages 90-123, May.
    23. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
    24. Delorme, Maxence & García, Sergio & Gondzio, Jacek & Kalcsics, Jörg & Manlove, David & Pettersson, William, 2019. "Mathematical models for stable matching problems with ties and incomplete lists," European Journal of Operational Research, Elsevier, vol. 277(2), pages 426-441.
    25. Diebold, Franz & Bichler, Martin, 2017. "Matching with indifferences: A comparison of algorithms in the context of course allocation," European Journal of Operational Research, Elsevier, vol. 260(1), pages 268-282.
    26. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
    27. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. Kenzo Imamura & Hideo Konishi, 2023. "Assortative Matching with Externalities and Farsighted Agents," Dynamic Games and Applications, Springer, vol. 13(2), pages 497-509, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2020. "Matching with myopic and farsighted players," Journal of Economic Theory, Elsevier, vol. 190(C).
    2. Mert Kimya, 2023. "Coalition Formation Under Dominance Invariance," Dynamic Games and Applications, Springer, vol. 13(2), pages 480-496, June.
    3. Bloch, Francis & van den Nouweland, Anne, 2020. "Farsighted stability with heterogeneous expectations," Games and Economic Behavior, Elsevier, vol. 121(C), pages 32-54.
    4. 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.
    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. Kimya, Mert, 2021. "Coalition Formation Under Dominance Invariance," Working Papers 202106, University of Sydney, School of Economics.
    7. Kimya, Mert, 2021. "Coalition Formation Under Dominance Invariance," Working Papers 2021-06, University of Sydney, School of Economics.
    8. Kimya, Mert, 2022. "Farsighted objections and maximality in one-to-one matching problems," Journal of Economic Theory, Elsevier, vol. 204(C).
    9. Ata Atay & Ana Mauleon & Vincent Vannetelbosch, 2022. "Limited Farsightedness in Priority-Based Matching," Papers 2212.07427, arXiv.org.
    10. 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.
    11. Kimya, Mert, 2020. "Equilibrium coalitional behavior," Theoretical Economics, Econometric Society, vol. 15(2), May.
    12. Atay, Ata & Mauleon, Ana & Vannetelbosch, Vincent, 2025. "School choice with farsighted students," Games and Economic Behavior, Elsevier, vol. 149(C), pages 148-163.
    13. Korpela, Ville & Lombardi, Michele & Vartiainen, Hannu, 2021. "Implementation in largest consistent set via rights structures," Games and Economic Behavior, Elsevier, vol. 128(C), pages 202-212.
    14. Bloch, Francis & van den Nouweland, Anne, 2021. "Myopic and farsighted stable sets in 2-player strategic-form games," Games and Economic Behavior, Elsevier, vol. 130(C), pages 663-683.
    15. 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.
    16. Korpela, Ville & Lombardi, Michele & Vartiainen, Hannu, 2019. "Implementation with foresighted agents," MPRA Paper 102496, University Library of Munich, Germany.
    17. Cai, Xinyue & Kimya, Mert, 2023. "Stability of alliance networks," Games and Economic Behavior, Elsevier, vol. 140(C), pages 401-409.
    18. 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.
    19. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    20. Dutta, Bhaskar & Vartiainen, Hannu, 2020. "Coalition formation and history dependence," Theoretical Economics, Econometric Society, vol. 15(1), January.

    More about this item

    Keywords

    Marriage problems; Core; 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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:322:y:2025:i:2:p:713-724. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.