Vector measure games based on measures with values in an infinite dimensional vector space

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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 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. Journal of Economic Literature Classification Numbers: C71, D46, D51.

Original languageEnglish
Pages (from-to)25-46
Number of pages22
JournalGames and Economic Behavior
Volume24
Issue number1-2
DOIs
StatePublished - Jul 1998
Externally publishedYes

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