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Contributions to Game Theory and Management, 2013, том 6, страницы 434–446
(Mi cgtm138)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
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
Аннотация:
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).
Ключевые слова:
Shapley value, nonatomic polynomial game, generalized Owen extension, polar form, polar representation formula.
Образец цитирования:
Valeri A. Vasil'ev, “Polar Representation of Shapley Value: Nonatomic Polynomial Games”, Contributions to Game Theory and Management, 6 (2013), 434–446
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/cgtm138 https://www.mathnet.ru/rus/cgtm/v6/p434
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Страница аннотации: | 263 | PDF полного текста: | 77 | Список литературы: | 65 |
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