Vector Measure Games Based on Measures with Values in an Infinite Dimensional Vector Space

Igal Milchtaich

Games and Economic Behavior 24 (1998), 25–46

Abstract

The definition of vector measure game is generalized in this paper to include all
cooperative games of the form `f` ∘ `μ`, where `μ` is a nonatomic vector measure of
bounded variation that takes values in a Banach space. It is shown that if `f` is
weakly continuously differentiable on the closed convex hull of the range of `μ` then
the vector measure game `f` ∘ `μ` is in `pNA _{∞}` and its value is given by the diagonal
formula. Moreover, every game in

JEL classification

C71, D46, D51