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 so-called 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 (n-handed 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