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


  • Koji Yokote

    () (Graduate School of Economics, Waseda University)

  • Yukihiko Funaki

    () (Faculty of Political Science and Economics, Waseda University)


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 T obtains payoff. We consider the intermediate between the two games. We introduce a game in which a coalition including k players in T obtains 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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    Cited by:

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

    More about this item


    basis; Shapley value; prenucleolus; coincidence condition;

    JEL classification:

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

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