Geodesic
Polar Representation of Shapley Value: Nonatomic Polynomial Games
Contributions to game theory and management, Tome 6 (2013), pp. 434-446.

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The paper deals with polar representation formula for the Shapley value, established in (Vasil’ev, 1998). Below, we propose a new, simplified proof of the formula for nonatomic polynomial games. This proof relies on the coincidence of generalized Owen extension and multiplicative Aumann-Shapley expansion for polynomial games belonging to $pNA$ (Vasil’ev, 2009). The coincidence mentioned makes it possible to calculate Aumann-Shapley expansion in a straightforward manner, and to complete new proof of the polar representation formula for nonatomic case by exploiting the generalized Owen integral formula, established in (Aumann and Shapley, 1974).
Keywords: Shapley value, nonatomic polynomial game, generalized Owen extension, polar form, polar representation formula. 
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Valeri A. Vasil'ev. Polar Representation of Shapley Value: Nonatomic Polynomial Games. Contributions to game theory and management, Tome 6 (2013), pp. 434-446. http://geodesic.mathdoc.fr/item/CGTM_2013_6_a33/

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