A new basis and the Shapley value

Koji Yokote; Yukihiko Funaki; Yoshio Kamijo

doi:10.1016/j.mathsocsci.2015.12.003

A new basis and the Shapley value

Koji Yokote^*, Yukihiko Funaki, Yoshio Kamijo

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 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 language	English
Pages (from-to)	21-24
Number of pages	4
Journal	Mathematical social sciences
Volume	80
DOIs	https://doi.org/10.1016/j.mathsocsci.2015.12.003
Publication status	Published - 2016 Mar 1

ASJC Scopus subject areas

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

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10.1016/j.mathsocsci.2015.12.003

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AB - 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.

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A new basis and the Shapley value

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