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