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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
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
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
Linking options:
https://www.mathnet.ru/eng/vuu719 https://www.mathnet.ru/eng/vuu/v30/i2/p189
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