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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, Volume 30, Issue 2, Pages 189–207
DOI: https://doi.org/10.35634/vm200204
(Mi vuu719)
 

This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Strong coalitional equilibria in games under uncertainty

V. I. Zhukovskiya, L. V. Zhukovskayab, K. N. Kudryavtsevcd, M. Larbanie

a Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991, Russia
b Central Economics and Mathematics Institute, Russian Academy of Science, Nakhimovsky pr., 32, Moscow, 117418, Russia
c South Ural State University, pr. Lenina, 76, Chelyabinsk, 454080, Russia
d Chelyabinsk State University, ul. Brat’ev Kashirinykh, 129, Chelyabinsk, 454001, Russia
e School of Mathematics and Statistics, Carleton University, Ottawa, Canada
Full-text PDF (254 kB) Citations (2)
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Abstract: The Strong Coalitional Equilibrium (SCE) is introduced for normal form games under uncertainty. This concept is based on the synthesis of the notions of individual rationality, collective rationality in normal form games without side payments, and a proposed coalitional rationality. For presentation simplicity, SCE is presented for 4-person games under uncertainty. Sufficient conditions for the existence of SCE in pure strategies are established via the saddle point of the Germeir's convolution function. Finally, following the approach of Borel, von Neumann and Nash, a theorem of existence of SCE in mixed strategies is proved under common minimal mathematical conditions for normal form games (compactness and convexity of players' strategy sets, compactness of uncertainty set and continuity of payoff functions).
Keywords: normal form game, uncertainty, guarantee, mixed strategies, Germeier convolution, saddle point, equilibrium.
Received: 16.04.2020
Bibliographic databases:
Document Type: Article
UDC: 519.83
MSC: 91A06, 91B50
Language: English
Citation: V. I. Zhukovskiy, L. V. Zhukovskaya, K. N. Kudryavtsev, M. Larbani, “Strong coalitional equilibria in games under uncertainty”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:2 (2020), 189–207
Citation in format AMSBIB
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\by V.~I.~Zhukovskiy, L.~V.~Zhukovskaya, K.~N.~Kudryavtsev, M.~Larbani
\paper Strong coalitional equilibria in games under uncertainty
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2020
\vol 30
\issue 2
\pages 189--207
\mathnet{http://mi.mathnet.ru/vuu719}
\crossref{https://doi.org/10.35634/vm200204}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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    References:24
     
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