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

GÉRARD HAMIACHE

Université Lille Nord de France, EQUIPPE-Lille 3, Domaine universitaire du Pont de Bois, B.P. 60149, 59653 Villeneuve d'Ascq Cedex, France

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https://doi.org/10.1142/S0219198910002581Cited by:17 (Source: Crossref)

Abstract

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.

Keywords:

JEL: 91A12

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