A new basis and the Shapley value

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    The purpose of this paper is to introduce a new basis of the set of all TU games. Shapley (1953) introduced the unanimity game in which cooperation of all players in a given coalition yields payoff. We introduce the commander game in which only one player in a given coalition yields payoff. The set of the commander games forms a basis and has two properties. First, when we express a game by a linear combination of the basis, the coefficients related to singletons coincide with the Shapley value. Second, the basis induces the null space of the Shapley value.

    Original languageEnglish
    Pages (from-to)21-24
    Number of pages4
    JournalMathematical Social Sciences
    Volume80
    DOIs
    Publication statusPublished - 2016 Mar 1

    Fingerprint

    Shapley Value
    coalition
    Game
    Coalitions
    TU Game
    Null Space
    Linear Combination
    Express
    Shapley value
    Coefficient

    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Social Sciences(all)
    • Psychology(all)
    • Sociology and Political Science

    Cite this

    A new basis and the Shapley value. / Yokote, Koji; Funaki, Yukihiko; Kamijo, Yoshio.

    In: Mathematical Social Sciences, Vol. 80, 01.03.2016, p. 21-24.

    Research output: Contribution to journalArticle

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