Polar Representation of Shapley Value: Nonatomic Polynomial Games
Abstract
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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References
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Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
