The two level dynamic model is presented, representing the process of innovation implementation. The main task of this paper is conducting an analytical research of the model and different information regulations, designing solutions based on information regulations to find the best possible management of the subjects of the system. The system consists of several management entities (center, agents), the system is hierarchical. The Center manages the innovation process, agents promote innovations. But at the same time, agents have third-party income from activity that is not related to the promotion of innovations. The Pontryagin maximum principle is used for analytical research, the information regulations of the Hermeyer games G1, G2 are used. Numerical solutions are constructed, experiments are carried out, and the results are analyzed during the research.

Keywords: analytical research, Pontryagin's maximum principle, motivation, compulsion, Hermeyer games G1, G2, optimal management

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 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

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