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Several bases of a game space and an application to the Shapley value

Author

Listed:
  • Koji Yokote

    (Graduate School of Economics, Waseda University)

  • Yukihiko Funaki

    (Faculty of Political Science and Economics, Waseda University)

Abstract

We introduce several bases of the set of TU games. Given a coalition T, Yokote et al. (2013) introduced the commander game in which a coalition including 1 player in T obtains payoff. On the other hand, Shapley (1953) introduced the unanimity game in which a coalition including all players in To btains payoff. We consider the intermediate between the two games. We introduce a game in which a coalition including k players in To btains payoff, where 1 ≤ k ≤| T |. We show that, if there is a specific relationship between the size of coalition T and k, we can construct a new basis. By using the new basis, we give sufficient conditions under which the Shapley value coincides with the prenucleolus.

Suggested Citation

  • Koji Yokote & Yukihiko Funaki, 2015. "Several bases of a game space and an application to the Shapley value," Working Papers 1419, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:1419
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    File URL: http://www.waseda.jp/fpse/winpec/assets/uploads/2015/06/No.E1419Yokote_Funaki.pdf
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    References listed on IDEAS

    as
    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.
    2. Chang, Chih & Tseng, Ying-Chih, 2011. "On the coincidence property," Games and Economic Behavior, Elsevier, vol. 71(2), pages 304-314, March.
    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).
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    Cited by:

    1. Sylvain Béal & Mihai Manea & Eric Rémila & Phillippe Solal, 2018. "Games With Identical Shapley Values," Working Papers 2018-03, CRESE.

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    More about this item

    Keywords

    basis; Shapley value; prenucleolus; coincidence condition;
    All these keywords.

    JEL classification:

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

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