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

Author

Listed:
  • Dehez, Pierre

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Pacini, Pier Mario

    (University of Pisa)

Abstract

We reconsider 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

  • Dehez, Pierre & Pacini, Pier Mario, 2025. "Comparing the nucleolus and the Shapley value of 3-player transferable utility games," LIDAM Discussion Papers CORE 2025001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2025001
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    References listed on IDEAS

    as
    1. Graham, Daniel A & Marshall, Robert C & Richard, Jean-Francois, 1990. "Differential Payments within a Bidder Coalition and the Shapley Value," American Economic Review, American Economic Association, vol. 80(3), pages 493-510, June.
    2. 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.
    3. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

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    JEL classification:

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

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