TY - JOUR

T1 - Properties of solutions of cooperative games with transferable utilities

AU - Smirnova, N. V.

AU - Tarashnina, S. I.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - We understand a solution of a cooperative TU-game as the α-prenucleoli set, α ∈ R, which is a generalization of the notion of the [0, 1]-prenucleolus. We show that the set of all α-nucleoli takes into account the constructive power with the weight α and the blocking power with the weight (1 − α) for all possible values of the parameter α. The further generalization of the solution by introducing two independent parameters makes no sense. We prove that the set of all α-prenucleoli satisfies properties of duality and independence with respect to the excess arrangement. For the considered solution we extend the covariance propertywith respect to strategically equivalent transformations.

AB - We understand a solution of a cooperative TU-game as the α-prenucleoli set, α ∈ R, which is a generalization of the notion of the [0, 1]-prenucleolus. We show that the set of all α-nucleoli takes into account the constructive power with the weight α and the blocking power with the weight (1 − α) for all possible values of the parameter α. The further generalization of the solution by introducing two independent parameters makes no sense. We prove that the set of all α-prenucleoli satisfies properties of duality and independence with respect to the excess arrangement. For the considered solution we extend the covariance propertywith respect to strategically equivalent transformations.

KW - duality

KW - prenucleolus

KW - SM-nucleolus

KW - TU-game

KW - [0, 1]-prenucleolus

KW - α-prenucleoli set

UR - http://www.scopus.com/inward/record.url?scp=84971255077&partnerID=8YFLogxK

U2 - 10.3103/S1066369X16060086

DO - 10.3103/S1066369X16060086

M3 - Article

AN - SCOPUS:84971255077

VL - 60

SP - 63

EP - 74

JO - Russian Mathematics

JF - Russian Mathematics

SN - 1066-369X

IS - 6

ER -