A mathematical model for managing a commercial organization that specializes in the production and sale of asphalt and asphalt concrete is presented and analyzed in this paper. The study is based on mathematical modeling principles and management theory. An organized two-tier management system has been proposed, consisting of an asphalt manufacturer and its clients. The problem was considered numerically using various types of input data, and the company "FIRM PROFILE LLC" provided necessary information for calculations. The paper analyzes the results obtained and offers practical recommendations for improving the management of this enterprise.

Keywords: optimal management, mathematical modeling, simulation modeling, enterprise model, hierarchical system

The dynamic model of personnel management in a real estate agency is investigated. The structure of the management system includes a real estate company as a Leader and a realtor as a Slave. The relations between them are built on the basis of a hierarchy corresponding to the information regulations of the Stackelberg games. Motivation is used as a method of hierarchical management. Algorithms for achieving equilibrium in different information regulations are presented. The numerical implementation of these algorithms is based on simulation modeling, the results are analyzed.

Keywords: real estate company, hierarchy, simulation, stackelberg's game, stackelberg's game with feedback, motivation, leader, slave, dynamic system

In a competitive environment, the definition of an effective strategy for the development of a company acquires great importance and is impossible without the use of mathematical modeling methods. The article proposes a hierarchically organized model of an IT enterprise. The consideration was carried out on the example of Electronic Medicine LLC. The Cobb-Douglas production function is used to describe the firm's activities. Numerical calculations are made by simulation for real input data. The Stackelberg equilibrium is constructed, and the results obtained are analyzed.

Keywords: hierarchical modeling, Stackelberg equilibrium, Cobb-Douglas production function, simulation

One of the most important problems of our time is the excessive emission of carbon dioxide into the atmosphere. The article proposes a mathematical model of the system for monitoring the emission of carbon dioxide into the atmosphere. The model is two-level hierarchically organized. Industrial enterprises act as a lower-level subject of management, and the state or its authorized body acts as a top-level subject. All subjects of management of the lower level seek only to maximize their gain. The main goal of the upper level entity is to maintain the quality of atmospheric air within the specified range. The problem is considered in a game setting. The Stackelberg equilibrium is constructed. The construction algorithm is specified, and it is programmatically implemented. An analysis of the obtained results is given, a number of conclusions are made about the optimal strategies of all participants in the system, based on the results obtained in the course of applying the Stackelberg algorithm.

Keywords: Stackelberg equilibrium, two-level hierarchical model, leading, trailing, carbon dioxide, Rosprirodnadzor, Federal Service for Supervision of Natural Resources

The mathematical model of coordination of private and public interests in the implementation of innovations in the case of multiple agents is studied. It is taken into account the presence of two management levels, that are several agents and the supervisor.The relationship between the supervisor and the agents is designed hierarchically in accordance with the information regulations of the Stackelberg games. Two mehods, simulation modeling and the method of qualitatively representative scenarios (QRS), are used to construct Stackelberg equilibria. Numerical experiments have been carried out using these two methods. The analysis of the obtained results is given.

Keywords: Stackelberg game, simulation modeling, method of qualitatively representative scenarios (QRS), supervisor, agents

The banking system occupies a dominant position in the modern market economy. The banking system is directly related to risks, one way or another, affecting the entire asset distribution system. The specificity of resource management in a bank requires the synthesis of methods of financial and economic analysis, the use of accounting methods, strategic planning, budgeting. This article describes a two-level mathematical model of interaction between the Central Bank of the Russian Federation and a commercial bank. For the research, the method of simulation was chosen, the algorithm for constructing the Stackelberg equilibrium was implemented in software.

Keywords: two-level hierarchical model, Stackelberg equilibrium, Central Bank of the Russian Federation, commercial bank, refinancing rate, management parameters, subjects of management

The continually increasing rate of human economic activity leads to changes in many natural systems. Their restoration is one of the most important tasks today. For this purpose, protected areas have been created, such as natural reserves, national parks, and wildlife sanctuaries. National parks are of particular interest, as they are the only protected areas listed above where tourism is allowed and organized. However, their activities cannot exist without sufficient financial support. This article describes a two-level optimal control model of the national park activity. For the purpose of exploring and analysing the proposed model, an algorithm that can be used to find the Stackelberg equilibrium guaranteeing the sustainable development of the national park is proposed and implemented in software.

Keywords: two-level hierarchical model, Stackelberg equilibrium, national park, leader, follower,subjects of management ,control parameters

The development of the construction industry leads to an increase in small businesses both in construction and in the sale of building materials. Besides, small business fills the market with various goods, solves various social and economic issues such as unemployment, industry monopoly. However, its activity can't exist without sufficient financial support. A two-level mathematical model of interaction between a retail enterprise and a commercial bank as a funding structure is considered. To research the proposed model, the method of simulation modeling based on numerical search was used. A computer program was created to build a Stackelberg equilibrium algorithm with hierarchical control as an impulsion. The algorithm can be used to find the optimal values of the control parameters of an individual entrepreneur and a commercial bank. These values maximize the objective functions and profit of the system participants. The identification of the proposed model was carried out on the basis of data obtained from the Internet. Finally, the results were obtained using numerical examples.A number of conclusions could be made about the functioning of the entire system.

Keywords: hierarchy,two-level system, credit, Stackelberg, small business, bank

The mathematical model of coordination of private and public interests in the implementation of innovations in the case of multiple agents is studied. It takes into account the presence of two management levels, which are a supervisor and several agents. The relationship between the supervisor and the agents is based on a hierarchy in accordance with the information regulations of Stackelberg games. The incentive method is used as a method of hierarchical management. Algorithms for constructing equilibria for different information regulations are specified. The numerical implementation of the proposed algorithms is based on simulation. The analysis of the obtained results is given.

Keywords: Stackelberg game, Stackelberg game with feedback, hierarchy, simulation, innovation, motivation, supervisor, agents

The article considers the task of combating the opportunistic behavior of a supervisor and agents in a river water quality control system. A three-level hierarchical model is being built, including the principal, supervisor and agent. Each of the entities seeks to maximize its objective function. The motivation method is used as a control method at both levels. The behavior of the system in the case of information regulations of the Stackelberg game is investigated. The substantiation of the derivation of functions used in the model is given. The results of model simulation under various initial conditions are demonstrated. An analysis of the results is given.

Keywords: Stackelberg balance, three-level system, motivation, imitation, opportunistic behavior, river water quality, hierarchy

The paper contains information about a stationary model of coordination of private and public interests in the allocation of resources. The study is conducted in a game setting, taking into account the hierarchy in the relations between the subjects. Take into account the subjects of management on two levels: the supervisor and the agents. Between agents occurs non-antagonistic game in which the Nash equilibrium.When modeling the interaction between the supervisor and agents, the Stackelberg equilibrium is constructed. Algorithms for solving the problem are specified, simulation experiments for a number of characteristic input data are carried out. The analysis of the obtained results is given.

Keywords: supervisor, agent, Nash equilibrium, hierarchical system, Stackelberg equilibrium, subject of management, private interests, public interests

This article examines the structure of the mathematical model, which is based on the agreement of private and public interests of agents. The main task of modeling is to review the possible options and determine the appropriate strategy to maximize revenue for those promoting innovations. The first option is the public interest (interest of the enterprise). In this version, agent promotes innovation, for which he receives encouragement from the supervisor. The second option is a private interest (personal interest of agent). Here agent is engaged in third-party activity, which also brings him income. The model is hierarchical, two-level. The algorithms for constructing equilibria for different game strategies are given. The numerical implementation of the proposed algorithms is based on simulation modeling. Numerical calculations are carried out. A comparative analysis of the effectiveness of various management mechanisms for the model of innovative development of the enterprise is given.

Keywords: Stackelberg game, Stackelberg game with feedback, hierarchy, simulation, innovation process, motivation

The article deals with the task of dealing with the opportunistic behavior of the supervisor and agents in the river water quality control system. A two-level hierarchical model is built, including a supervisor (master) and agents (slaves). Each of the subjects seeks to maximize their objective function. In the model, the principal is implicitly present, fighting against the opportunistic behavior of the supervisor and agents. As the method of control used the method of inducement. The behavior of the system is investigated in the case of Shtakelberg’s information regulations. The algorithm for finding the Stackelberg equilibrium is indicated. The results of model simulation under various initial conditions are demonstrated. An analysis of the results is provided.

Keywords: Shtakelberg equilibrium, two-level system, prompting, imitation, opportunistic behavior, river water quality, hierarchy

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