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

Gerard Hamiache

International Game Theory Review (IGTR), 2010, vol. 12, issue 02, 175-187

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: Shapley value; matrix; consistency; associated game; 91A12 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (14)

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DOI: 10.1142/S0219198910002581

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