Citation:
Milchtaich, I. . (1995). Vector Measure Games Based on Measures with Values in an Infinite Dimensional Vector Space. Discussion Papers. presented at the 12, Games and Economic Behavior 24 (1998), 25-46. Retrieved from /files/dp89.pdf
Abstract:
The following generalization of a theorem of Aumann and Shapley is proved: A vector measure game of the form f'$^\circ$%, 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.