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Coincidence of the Shapley value with other solutions satisfying covariance

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  • Yokote, Koji
  • Funaki, Yukihiko
  • Kamijo, Yoshio

Abstract

We identify the necessary and sufficient condition under which the Shapley value coincides with the prenucleolus for general TU games. For 0-normalized 3-person games, the coincidence holds if and only if the game is symmetric or satisfies the PS property (Kar et al., 2009). We also identify the necessary and sufficient coincidence condition in the following allocation problems: the airport games (Littlechild and Owen, 1973), the bidder collusion games (Graham et al., 1990) and the polluted river games (Ni and Wang, 2007). The coincidence between the Shapley value and the CIS and ENSC values is discussed as well.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matsoc:v:89:y:2017:i:c:p:1-9
    DOI: 10.1016/j.mathsocsci.2017.05.005
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    References listed on IDEAS

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    1. Kar, Anirban & Mitra, Manipushpak & Mutuswami, Suresh, 2009. "On the coincidence of the prenucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 16-25, January.
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    8. Orshan, Gooni, 1993. "The Prenucleolus and the Reduced Game Property: Equal Treatment Replaces Anonymity," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 241-248.
    9. 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).
    10. Yokote, Koji & Funaki, Yukihiko & Kamijo, Yoshio, 2016. "A new basis and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 21-24.
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    Cited by:

    1. Kjell Hausken, 2020. "The Shapley value of coalitions to other coalitions," Palgrave Communications, Palgrave Macmillan, vol. 7(1), pages 1-10, December.
    2. 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.
    3. Shin Kobayashi, 2021. "A Characterization of the Shapley Value based on “Equal Excess"," Working Papers 2120, Waseda University, Faculty of Political Science and Economics.
    4. Takaaki Abe & Satoshi Nakada, 2018. "Generalized Potentials, Value, and Core," Discussion Paper Series DP2018-19, Research Institute for Economics & Business Administration, Kobe University.

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