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A note on the relation between the Shapley value and the core of 3-player transferable utility games

Author

Listed:
  • Pierre Dehez

    (UCLouvain)

  • Pier Mario Pacini

    (University of Pisa)

Abstract

We reconsider the necessary and sufficient conditions under which the Shapley value of a 3-player superadditive game belongs to the core. We then compute the proportion of games whose Shapley value belongs to the core within the set of balanced superadditive games. value of a 3-player superadditive game belongs to the core. We then compute the proportion of games whose Shapley value belongs to the core within the set of balanced superadditive games. value of a 3-player superadditive game belongs to the core. We then compute the proportion of games whose Shapley value belongs to the core within the set of balanced superadditive games. value of a 3-player superadditive game belongs to the core. We then compute the proportion of games whose Shapley value belongs to the core within the set of balanced superadditive games.

Suggested Citation

  • Pierre Dehez & Pier Mario Pacini, 2024. "A note on the relation between the Shapley value and the core of 3-player transferable utility games," Economics Bulletin, AccessEcon, vol. 44(2), pages 611-619.
    • Handle: RePEc:ebl:ecbull:eb-24-00283
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    References listed on IDEAS

    as
    1. Zhao, Jingang, 2018. "Three little-known and yet still significant contributions of Lloyd Shapley," Games and Economic Behavior, Elsevier, vol. 108(C), pages 592-599.
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    Cited by:

    1. Pierre Dehez, 2024. "Axiomatization of the core of positive games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 219-228, December.

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    More about this item

    Keywords

    Core; Shapley value;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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