Geodesic
Stability analysis of equilibrium position of von Neumann’s model under interval uncertainty
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, no. 2 (2012), pp. 99-111

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There is discussed the problem of stability analysis of equilibrium position under interval settings. In case of multiplicative uncertainty both primal and dual Frobenius vectors are obtained by exact von Neumann’s model with matrices of interval centers. Interval of the Frobenius number in case of interval von Neumann’s model are obtained by finding equilibrium for two exact von Neumann’s models with exact matrices of interval upper and lower bounds. There are introduced definitions of weak and strong solutions, which are used to obtain robust estimates of equilibrium position of interval von Neumann’s model.
Keywords: product strategy, linear programming, von Neumann’s model, interval analysis, game theory, bilinear systems, computer, software, interval uncertainty. 
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     title = {Stability analysis of equilibrium position of von {Neumann{\textquoteright}s} model under interval uncertainty},
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Anatoly V. Panyukov; Alina T. Latipova. Stability analysis of equilibrium position of von Neumann’s model under interval uncertainty. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, no. 2 (2012), pp. 99-111. http://geodesic.mathdoc.fr/item/VYURV_2012_2_a8/