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

Abstract

The definition of vector measure game is generalized in this paper to include all cooperative games of the formf∘μ, where μ is a nonatomic vector measure of bounded variation that takes values in a Banach space. It is shown that iffis weakly continuously differentiable on the closed convex hull of the range of μ then the vector measure gamef∘μ is inpNA∞and its value is given by the diagonal formula. Moreover, every game inpNA∞has a representation that satisfies this condition. These results yield a characterization ofpNA∞as the set of all differentiable games whose derivative satisfies a certain continuity condition.Journal of Economic LiteratureClassification Numbers: C71, D46, D51.