
Accession Number : ADA136471
Title : The Shapley Value in the Non Differentiable Case.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CA INST FOR MATHEMATICAL STUDIES IN THE SOCIAL SCIENCES
Personal Author(s) : Mertens,J F
PDF Url : ADA136471
Report Date : Sep 1983
Pagination or Media Count : 92
Abstract : In their book Values of Non Atomic Games, Aumann and Shapley (1974) define the Shapley value for non atomic games, and prove existence and uniqueness of it for a number of important spaces of games like pNA and bv'NA. They also show that this value obeys the socalled diagonal formula, expressing the value of each infinitesimal player as his marginal contribution to the coalition of all players preceding him in a random ordering of the players. The basic definitions are given in Section 1 of this document. Section 2 defines the probability distribution over perturbations and shows its uniqueness. An explicit formula for the value of games of the type discussed above (nhanded glove markets, majority in several different houses) is derived in Section 3.
Descriptors : *Game theory, *Value, Probability distribution functions, Perturbations, Set theory, Operators(Mathematics), Linearity, Symmetry, Computations
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE