The problems of hierarchical management of stable advancement are incredibly timely issues. It's worth mentioning these three problematic areas as examples: firstly, the global, regional and local ecological problems; secondly, the businesses' and organizations' from various economical sectors management issues that can apply to private or public services; lastly, the problems of the government system. The effectiveness of managing the interaction of the central bank and commercial banks in regions and regions depends to a large extent on the degree of effectiveness of its information support, which, in turn, is provided by computer solution support systems. With their help, you can consider the various options for action, analyze the consequences of decisions taken, improve the skills of managers in decision-making related to management. In the work based on the game-theoretic and hierarchical approaches, a mathematical model of managing the population crediting is constructed, which takes into account the subjects of management of two levels. A solution support system that manages the interaction of the central bank and commercial banks is presented. Its structure, approaches to development and the order of work with it are described. Describes main approaches to the development of a system for supporting solutions for managing the interaction of central and commercial banks. The structure of the decision support system and its content. The order of work with the solution support system is specified.

Keywords: hierarchy, two-level control system, Stackelberg equilibrium

An original mathematical model describing different activities of actors in the vertical marketing system is presented. They are a provider, a agent, a trading enterprise are presented as a controlling subjects. The model is based on the game-theoretical and hierarchical approach. An equilibrium of Germeyer G1 game in terms of sustainable development is established. The method of impulsion is used as a method of hierarchical control to solve this model. The main system operation laws based on numerical experiments are presented.

Keywords: game theory, hierarchical, three-level control system, method of impulsion