TY - JOUR
T1 - A new basis and the Shapley value
AU - Yokote, Koji
AU - Funaki, Yukihiko
AU - Kamijo, Yoshio
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/3/1
Y1 - 2016/3/1
N2 - 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.
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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U2 - 10.1016/j.mathsocsci.2015.12.003
DO - 10.1016/j.mathsocsci.2015.12.003
M3 - Article
AN - SCOPUS:84956482426
SN - 0165-4896
VL - 80
SP - 21
EP - 24
JO - Mathematical social sciences
JF - Mathematical social sciences
ER -