Growing marketization is one of the main tendencies of the modern sphere of education. Therefore the role of markets, competition, private initiative and cooperation in case of achieving economic and social goals is becoming more and more important. The paper focuses on game theory modeling of interaction between universities for researching the trends and peculiarities of higher education development. As a result the cooperative model of university reform is developed. The characteristic function is based on estimation of conventional units of university admission determined with consideration of the demand and supply structure of qualified labour market. The latter suggests an approach to the characteristic function construction in monetary terms based on modeling and forecasting the regional demand for professionals with higher education. The cooperative model is analyzed with the range of solution concepts including the Shapley value, the Core and the Nucleolus. The obtained results can be used to develop solutions within the general framework of the state policy on supporting higher education institutions at the regional level.