A new basis and the Shapley value

Koji Yokote*, Yukihiko Funaki, Yoshio Kamijo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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
Publication statusPublished - 2016 Mar 1

ASJC Scopus subject areas

  • Sociology and Political Science
  • General Social Sciences
  • General Psychology
  • Statistics, Probability and Uncertainty


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