The Shapley Value in the Non Differentiable Case.
STANFORD UNIV CA INST FOR MATHEMATICAL STUDIES IN THE SOCIAL SCIENCES
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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 bvNA. 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.
- Statistics and Probability