Vector Measure Games Based on Measures with Values in an Infinite Dimensional Vector Space
Games and Economic Behavior 24 (1998), 25–46
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 pNA∞ has a representation that satisfies this condition. These results yield a characterization of pNA∞ as the set of all differentiable games whose derivative satisfies a certain continuity condition.
C71, D46, D51