On the Core and Shapley Value for Regular Polynomial Games Full article
| Journal |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2022, Volume: 63, Number: 1, Pages: 65-78 Pages count : 14 DOI: 10.1134/S0037446622010050 | ||
| Tags | $ (v,c) $-integral; 519.83; generalized Owen extension; polynomial cooperative game; Shapley value; support function of the core | ||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Sobolev Institute of Mathematics | 0314-2019-0018 |
| 2 | Russian Foundation for Basic Research | 19-10-00910 |
Abstract:
Considering some classes of polynomial cooperative games, we describethe integral representation of the Shapley values and the support functionsof their cores. Also, we analyze the relationship between the Shapley valuesand the polar forms of homogeneous polynomial games. The found formula for the supportfunction of the core of a convex game is applied for the dual descriptionof the Harsanyi sets of finite cooperative games. The main peculiarity of the proposedapproach to the study of optimal solutions of game theory is a systematic useof the extensions of polynomial set functions to the corresponding measures on symmetricpowers of the initial measure spaces. © 2022, Pleiades Publishing, Ltd.
Cite:
Vasil’ev V.A.
On the Core and Shapley Value for Regular Polynomial Games
Siberian Mathematical Journal. 2022. V.63. N1. P.65-78. DOI: 10.1134/S0037446622010050 WOS Scopus РИНЦ OpenAlex
On the Core and Shapley Value for Regular Polynomial Games
Siberian Mathematical Journal. 2022. V.63. N1. P.65-78. DOI: 10.1134/S0037446622010050 WOS Scopus РИНЦ OpenAlex
Original:
Васильев В.А.
О ядре и значении Шепли для регулярных полиномиальных игр
Сибирский математический журнал. 2022. Т.63. №1. С.77–94. DOI: 10.33048/smzh.2022.63.105 РИНЦ
О ядре и значении Шепли для регулярных полиномиальных игр
Сибирский математический журнал. 2022. Т.63. №1. С.77–94. DOI: 10.33048/smzh.2022.63.105 РИНЦ
Identifiers:
| Web of science: | WOS:000749276800005 |
| Scopus: | 2-s2.0-85123621358 |
| Elibrary: | 48145724 |
| OpenAlex: | W4210528149 |