A new basis and the Shapley value

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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

ASJC Scopus subject areas

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

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