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

Igal Milchtaich

The following generalization of a theorem of Aumann and Shapley is proved: A vector measure game of the form f°%, where % is a nonatomic banach-space measure of bounded variation and f is a weakly continuously differentiable real-valued function defined on the closed convex hull of the range of % such that f(0)=0, is in pNA. If the game is monotonic, then the conclusion holds even if at 0 f is only continuous, and not differentiable. The value of the game is given by the diagonal formula. These results are used for giving a new, relatively short, proof to the result that, under certain conditions, a market game is in pNA.

December, 1995
Published in: 
Games and Economic Behavior 24 (1998), 25-46