In the article a cognitive map of an organization whose activities are related to the sale of rolled metal products is presented. The constructed map is investigated analyzing the impulse processes occurring in the constructed system. It is assumed that the system may be affected by random factors such as economic and social crises, examples of which may be a lockdown during a pandemic, military actions in the country, sanctions, etc., as well as weather conditions, which, although accidental, are more predictable than economic and social cataclysms. The processes are investigated for impulse and absolute stability. The possibilities of increasing stability in the system are analyzed. The methods of increasing stability in the system are proposed in order to preserve profits in the rolled metal sales enterprise.

Keywords: cognitive map, metal rolling realization system, socio-economic cataclysms, weather conditions, impulse processes, impulse stability, absolute stability, petal sequence, characteristic polynomial, positive and negative cycles

The article is devoted to the study of administrative corruption in the model of combining general and private interests, taking into account the costs of controlling agents. As the subject of research, we considered mathematical models of a combination of general and private interests of a hierarchical structure such as "Principal-Agent" and "Supervisor-Agent". The administrative control mechanism was investigated for the case where the principal sets a lower constraint.

Keywords: models of the combination of general and private interests, corruption, resource allocation, hierarchical systems, management systems, the Germeier-Vatel idea, private and common interests, principal, agent, center, administrative mechanism

In this article the problem of purpose and non-purpose resource use is considered. In the system there are two elements each of which has some resource quality and he must allocate his own resource among public and private interests. Elements of the system may be equal one to other or they may be connected by leading-subordinating relationship. Besides, elements can enter into the coalition. By combining all various situations we obtain four possible cases. The first is when both elements are equal and don’t enter into the coalition. In this case there is a game in normal form in which Nash-equilibrium is found. The second is when both elements are equal and form the coalition. In this case Pareto-optimal set is found. The third is when one element subordinates to the other element without their union into the coalition. In this situation there is a hierarchical Г1 or Г2 game in which Stackelberg equilibrium is found or the Germeyer’s theorem is applied. The forth is when one element subordinates to the other element with their union into the coalition. The aim of investigation was to compare the influence of hierarchy, possible cooperation and different types of public and private activity functions of elements on the performance of purpose commitments. The research has shown that equality of elements is the better than hierarchy. Besides, elements assign more resources to the public purposes if they form the coalition.

Keywords: purpose using, non-purpose using, hierarchical system, equal players, player cooperation, private activity function, public activity function, Stackelberg equilibrium, Nash eqilibrium, Pareto-optimal set