On the Core of the Aubin Extension of an Almost Positive Game Full article
| Journal |
Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126 |
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| Output data | Year: 2025, Volume: 35, Number: 1, Pages: 79-86 Pages count : 8 DOI: 10.1134/s1055134425010067 | ||
| Tags | almost positive game, Shapley value, fuzzy game, Aubin extension, core, superdifferential of a fuzzy game | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0019 |
Abstract:
We analyze connections between the Shapley value and the core of the well-known Aubin extension of an almost positive cooperative game. Nonnegative Harsanyi dividends characterize such games up to an additive component. Since each almost positive game is convex, its core contain the Shapley value. We prove a stronger connection for the Aubin extension of such a game; namely, the core is a singleton consisting of the corresponding Shapley value. Aubin mentioned that, for certain classes of fuzzy cooperative games, it is possible to describe the core in terms of the superdifferential of the characteristic function. Our arguments are based on this fact.
Cite:
Vasil’ev V.A.
On the Core of the Aubin Extension of an Almost Positive Game
Siberian Advances in Mathematics. 2025. V.35. N1. P.79-86. DOI: 10.1134/s1055134425010067 Scopus РИНЦ OpenAlex
On the Core of the Aubin Extension of an Almost Positive Game
Siberian Advances in Mathematics. 2025. V.35. N1. P.79-86. DOI: 10.1134/s1055134425010067 Scopus РИНЦ OpenAlex
Original:
Васильев В.А.
О ядре расширения Обэна почти положительной игры
Математические труды. 2024. Т.27. №4. С.26–41. DOI: 10.25205/1560-750X-2024-27-4-26-41 РИНЦ
О ядре расширения Обэна почти положительной игры
Математические труды. 2024. Т.27. №4. С.26–41. DOI: 10.25205/1560-750X-2024-27-4-26-41 РИНЦ
Dates:
| Submitted: | Sep 18, 2024 |
| Accepted: | Oct 30, 2024 |
| Published print: | Mar 19, 2025 |
| Published online: | Jul 4, 2025 |
Identifiers:
| Scopus: | 2-s2.0-105009624987 |
| Elibrary: | 82581689 |
| OpenAlex: | W4412028603 |
Citing:
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