A Generalized Model of Hierarchically Controlled Dynamical System

The idea of the paper is to combine in the same model several concepts from game theory, graph theory, and controlled dynamical systems theory, namely: 1) a directed graph without contours and loops; 2) a game of $n$ players in normal form; 3) a cooperative game; 4) a dynamical system controlled by several subjects. The combination permits to describe complex dynamical systems with hierarchical structure (particularly organizational and environmental systems) more completely and to take into consideration different interactive and interdependent aspects of the systems. Some examples are considered such as environmental control, corruption modeling, and linear multistage games with hierarchical matrices.