IDEAS home Printed from https://ideas.repec.org/a/ebl/ecbull/eb-25-00361.html

Comparing the nucleolus and the Shapley value of 3-player transferable utility games

Author

Listed:
  • Pierre Dehez

    (UCLouvain)

  • Pier Mario Pacini

    (University of Pisa)

Abstract

We propose a simplified version of the formulas defining the nucleolus of a 3-player transferable utility game proposed by Legros (1981) and study its relation to the Shapley value.

Suggested Citation

  • Pierre Dehez & Pier Mario Pacini, 2025. "Comparing the nucleolus and the Shapley value of 3-player transferable utility games," Economics Bulletin, AccessEcon, vol. 45(3), pages 1588-1597.
    • Handle: RePEc:ebl:ecbull:eb-25-00361
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/Pubs/EB/2025/Volume45/EB-25-V45-I3-P138.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Pierre Dehez & Pier Mario Pacini, 2025. "Corrigendum to "A note on the relation between the Shapley value and the core of 3-player transferable utility games"," Economics Bulletin, AccessEcon, vol. 45(1), pages 138-138.
    2. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    Full references (including those not matched with items on IDEAS)

    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. Youngsub Chun & Boram Park, 2016. "The airport problem with capacity constraints," Review of Economic Design, Springer;Society for Economic Design, vol. 20(3), pages 237-253, September.
    2. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2022. "Monotonicity in sharing the revenues from broadcasting sports leagues," European Journal of Operational Research, Elsevier, vol. 297(1), pages 338-346.
    3. María Gómez-Rúa, 2013. "Sharing a polluted river through environmental taxes," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 4(2), pages 137-153, June.
    4. Ryusuke Shinohara, 2014. "Participation and demand levels for a joint project," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 925-952, December.
    5. Cristina Fernández & Peter Borm & Ruud Hendrickx & Stef Tijs, 2005. "Drop out monotonic rules for sequencing situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 501-504, July.
    6. Hervé Moulin & Yves Sprumont, 2007. "Fair allocation of production externalities : recent results," Revue d'économie politique, Dalloz, vol. 117(1), pages 7-36.
    7. Csóka, Péter & Illés, Ferenc & Solymosi, Tamás, 2022. "On the Shapley value of liability games," European Journal of Operational Research, Elsevier, vol. 300(1), pages 378-386.
    8. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2002. "Convex Fuzzy Games and Participation Monotonic Allocation Schemes," Discussion Paper 2002-13, Tilburg University, Center for Economic Research.
    9. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2020. "Allocating extra revenues from broadcasting sports leagues," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 65-73.
    10. Gustavo Bergantiños & Juan D. Moreno-Ternero, 2022. "On the axiomatic approach to sharing the revenues from broadcasting sports leagues," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 321-347, February.
    11. Dehez, Pierre & Ferey, Samuel, 2013. "How to share joint liability: A cooperative game approach," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 44-50.
    12. repec:dau:papers:123456789/7891 is not listed on IDEAS
    13. Gustavo Bergantiños & Juan D. Moreno-Ternero, 2024. "Axiomatic characterizations of the core and the Shapley value of the broadcasting game," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 977-988, September.
    14. Chessa, Michela & Hanaki, Nobuyuki & Lardon, Aymeric & Yamada, Takashi, 2023. "An experiment on the Nash program: A comparison of two strategic mechanisms implementing the Shapley value," Games and Economic Behavior, Elsevier, vol. 141(C), pages 88-104.
    15. G Reinhardt & M Dada, 2005. "Allocating the gains from resource pooling with the Shapley Value," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(8), pages 997-1000, August.
    16. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    17. Munich, Léa, 2024. "Schedule situations and their cooperative game theoretic representations," European Journal of Operational Research, Elsevier, vol. 316(2), pages 767-778.
    18. Yokote, Koji & Funaki, Yukihiko & Kamijo, Yoshio, 2017. "Coincidence of the Shapley value with other solutions satisfying covariance," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 1-9.
    19. René Brink & Yukihiko Funaki & Yuan Ju, 2013. "Reconciling marginalism with egalitarianism: consistency, monotonicity, and implementation of egalitarian Shapley values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 693-714, March.
    20. José Alcalde & Matthias Dahm, 2007. "Tullock and Hirshleifer: a meeting of the minds," Review of Economic Design, Springer;Society for Economic Design, vol. 11(2), pages 101-124, September.
    21. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Tvede, Mich & Østerdal, Lars Peter, 2017. "Sharing the proceeds from a hierarchical venture," Games and Economic Behavior, Elsevier, vol. 102(C), pages 98-110.

    More about this item

    Keywords

    ;
    ;
    ;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining 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:ebl:ecbull:eb-25-00361. 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: John P. Conley (email available below). General contact details of provider: .

    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.