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Contributions to Game Theory and Management, 2013, Volume 6, Pages 434–446
(Mi cgtm138)
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This article is cited in 1 scientific paper (total in 1 paper)
Polar Representation of Shapley Value: Nonatomic Polynomial Games
Valeri A. Vasil'ev Sobolev Institute of Mathematics,
Russian Academy of Sciences, Siberian Branch,
Prosp. Acad. Koptyuga 4, Novosibirsk, 630090, Russia
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.
Citation:
Valeri A. Vasil'ev, “Polar Representation of Shapley Value: Nonatomic Polynomial Games”, Contributions to Game Theory and Management, 6 (2013), 434–446
Linking options:
https://www.mathnet.ru/eng/cgtm138 https://www.mathnet.ru/eng/cgtm/v6/p434
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Abstract page: | 249 | Full-text PDF : | 73 | References: | 51 |
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