In this paper we introduce a modification of the concept of Equilibrium in Secure Strategies (EinSS), which takes into account the non-uniform attitudes of players to security in non-cooperative games. In particular, we examine an asymmetric attitude of players to mutual threats in the simplest case, when all players are strictly ordered by their relation to security. Namely, we assume that the players can be reindexed so that each player i in his behavior takes into account the threats posed by players j > i but ignores the threats of players j < i provided that these threats are effectively contained by some counterthreats. A corresponding equilibrium will be called a Chain EinSS. The conceptual meaning of this equilibrium is illustrated by two continuous games that have no pure Nash equilibrium or (conventional) EinSS. The Colonel Blotto two-player game (Borel 1953; Owen 1968) for two battlefields with different price always admits a Chain EinSS with intuitive interpretation. The product competition of many players on a segment (Eaton, Lipsey 1975; Shaked 1975) with the linear distribution of consumer preferences always admits a unique Chain EinSS solution (up to a permutation of players). Finally, we compare Chain EinSS with Stackelberg equilibrium.

The anisotropic norm of the linear discrete stationary system is the measure of the system output sensitivity to a random input with the mean anisotropy bounded by some nonnegative value a. The mean anisotropy characterizes the degree of predictability of the stochastic signal. The anisotropic norm of a system is the induced norm with the extreme cases of H2 norm and H∞ norm, respectively, under a → 0 and a → ∞. The lower bound of the anisotropic norm of the linear discrete stationary system was established in the present paper using the methods of linear algebra.

Abstract—We find an estimate on the norm of the operator that describes the dynamics of a linear two-layered one-dimensional unilaterally bounded heat transfer object with nonperfect heat contact between the layers. Based on this estimate, we find a sufficient causality and stability condition for the closed system arising when the object is closed with feedback.

Modern problems of optimization, estimation, signal and image processing, pattern recognition, etc., deal with huge-dimensional data; this necessitates elaboration of efficient methods of processing such data. The idea of building low-dimensional approximations to huge data arrays is in the heart of the modern data analysis. One of the most appealing methods of compact data representation is the statistical method referred to as the principal component analysis; however, it is sensitive to uncertainties in the available data and to the presence of outliers. In this paper, robust versions of the principle component analysis approach are proposed along with numerical methods for their implementation.