TY - JOUR

T1 - Vector measure games based on measures with values in an infinite dimensional vector space

AU - Milchtaich, Igal

PY - 1998/7

Y1 - 1998/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0039413600&partnerID=8YFLogxK

U2 - 10.1006/game.1998.0657

DO - 10.1006/game.1998.0657

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AN - SCOPUS:0039413600

SN - 0899-8256

VL - 24

SP - 25

EP - 46

JO - Games and Economic Behavior

JF - Games and Economic Behavior

IS - 1-2

ER -