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Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2021, Volume 13, Issue 1, Pages 5–27
(Mi mgta273)
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Nonadditive integration and some solutions of cooperative games
Valery A. Vasil'evab a Sobolev Institute of Mathematics, Siberian Branch of RAS, Novosibirsk
b Novosibirsk State University
Abstract:
In the paper, we propose three schemes of nonadditive integration based on several extensions of nonadditive set function and integrand to the appropriate symmetric power of the original measurable space. A survey on the integral representation of some classic objects of the cooperative game theory, derived by nonadditive integration, is given. A universal approach for investigation of both finite and infinite games is developed. We pay a particular attention to the Shapley value, Owen multilinear extension, and support function of the core of a convex cooperative game.
Keywords:
nonadditive integration, polynomial cooperative game, Shapley functional, generalized Owen extension, support function of the core.
Received: 20.10.2020 Revised: 28.01.2021 Accepted: 09.03.2021
Citation:
Valery A. Vasil'ev, “Nonadditive integration and some solutions of cooperative games”, Mat. Teor. Igr Pril., 13:1 (2021), 5–27
Linking options:
https://www.mathnet.ru/eng/mgta273 https://www.mathnet.ru/eng/mgta/v13/i1/p5
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Abstract page: | 183 | Full-text PDF : | 88 | References: | 27 |
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