Mean field model of a game for power

Our aim is to model a game for power as a dynamical process, where an excess of power possessed by a player allows him to gain even more power. Such a positive feedback is often termed as the Matthew effect. Analytical and numerical methods allow to identify a set of fixed points of the model dynamics. The positions of the unstable fixed points give an insight on the basins of attraction of the stable fixed points. The results are interpreted in terms of modeling of coercive power.Comment: 16 pages, 6 figure

Dynamical systems of conflict in terms of structural measures

We investigate the dynamical systems modeling conflict processes between a pair of opponents. We assume that opponents are given on a common space by distributions (probability measures) having the similar or self-similar structure. Our main result states the existence of the controlled conflict in which one of the opponents occupies almost whole conflicting space. Besides, we compare conflicting effects stipulated by the rough structural approximation under controlled redistributions of starting measures.Comment: Published in Methods of Functional Analysis and Topology (MFAT), available at http://mfat.imath.kiev.ua/article/?id=84