A MATRIX APPROACH TO THE ASSOCIATED CONSISTENCY WITH AN APPLICATION TO THE SHAPLEY VALUE

被引：20

作者：

Hamiache, Gerard ^{[1
]}

机构：

[1] Univ Lille Nord France, EQUIPPE Lille 3, Domaine Univ Pont Bois, BP 60149, F-59653 Villeneuve, France

来源：

INTERNATIONAL GAME THEORY REVIEW | 2010年 / 12卷 / 02期

关键词：

Shapley value; matrix; consistency; associated game;

D O I：

10.1142/S0219198910002581

中图分类号：

O1 [数学];

学科分类号：

0701 [数学]; 070101 [基础数学];

摘要：

In an article by Hamiache (IJGT, 2001) an axiomatization of the Shapley value has been proposed. Three axioms were called on, inessential game, continuity and associated consistency. This present article proposes a new proof, based on elementary linear algebra. Games are represented by vectors. Associated games are the results of matrix operations. The eigenvalues of the involved matrices are computed and it is shown that they are diagonalizable. The present contribution offers a powerful tool allowing further generalizations of the Shapley value, which were difficult to consider on the basis of the previous proof.

引用

页码：175 / 187

页数：13