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 Section Mathematics Title Strong coalitional equilibria in games under uncertainty Author(-s) Zhukovskii V.I.a, Zhukovskaya L.V.b, Kudryavtsev K.N.cd, Larbani M.e Affiliations Lomonosov Moscow State Universitya, Central Economics and Mathematics Institute, Russian Academy of Scienceb, Chelyabinsk State Universityc, South Ural State Universityd, Carleton Universitye 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 UDC 519.83 MSC 91A06, 91B50 DOI 10.35634/vm200204 Received 16 April 2020 Language English Citation Zhukovskii V.I., Zhukovskaya L.V., Kudryavtsev K.N., Larbani M. Strong coalitional equilibria in games under uncertainty, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 2, pp. 189-207. References Nash J. Equillibrium points in $n$-person games, Proc. Nat. Academ. Sci. USA, 1950, vol. 36, no. 1, pp. 48-49. https://doi.org/10.1073/pnas.36.1.48 Nash J. 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