Geodesic
Strong coalitional equilibria in games under uncertainty
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 2, pp. 189-207

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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, saddle point, equilibrium.
Mots-clés : Germeier convolution 
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     title = {Strong coalitional equilibria in games under uncertainty},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VUU_2020_30_2_a3/}
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V. I. Zhukovskiy; L. V. Zhukovskaya; K. N. Kudryavtsev; M. Larbani. Strong coalitional equilibria in games under uncertainty. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 2, pp. 189-207. http://geodesic.mathdoc.fr/item/VUU_2020_30_2_a3/