Dynamic Game-theoretical Models of Innovation Management in Universities Taking into Account Opportunistic behavior

The article studies the issues of innovation implementation in universities. A three-level hierarchically organized model is proposed to describe the process of innovation implementation in universities. The model includes agents (followers, in whose role teachers act), supervisors (subjects of middle-level management, universities) and a principal (leader, the state). The principal (the state) is the first to announce its behavior strategy. Supervisors choose their management strategies when the principal’s choice is already known, but the agents’ choice is not yet known. Agents (teachers) make their choice when the management strategies of the other subjects are already known. Supervisors, like agents, make their choice independently of each other. The principal subsidizes the innovative development of higher education institutions by allocating funds for the development of new electronic courses. The new electronic courses being developed are considered as innovative products that contribute to the innovative development of higher education institutions. Supervisors receive subsidies from the principal for the development and implementation of innovative products. They determine the required volume of new courses issued by agents. Agents develop new electronic training courses for subsequent sale and implementation in the educational process. Supervisors keep part of the subsidies received from the principal for themselves, and transfer part to agents. Agents receive subsidies, the amount of which depends on the demand for the courses they develop, and manage the quality of the courses they develop, improving their qualifications. The possibility of corruption in the system is provided for and methods for combating it are defined. Lower and middle management entities may be subject to corruption. Agents may offer bribes to supervisors, in exchange for which they inflate the portion of subsidies transferred to agents. An analysis is conducted of how the presence of corruption affects the innovative development of universities. Thus, a dynamic three-level model is constructed, in which the dynamics are described by a difference equation reflecting the change in the general innovative level of the education system depending on the agents’ controls. Algorithms for constructing a solution for different combinations of Stackelberg games with and without feedback on control between the state and universities and between universities and teachers are indicated. In a non-antagonistic game of universities among themselves, as in a game of teachers, a Nash equilibrium is built. The results of numerical experiments are presented, their analysis is given. A number of meaningful conclusions and recommendations are made.