This paper reviews some government policy measures aimed at strengthening competition in the Russian university market and looks at the best international practices in this area. It analyzes the competitive behavior of universities under the current government policy on higher education and research and development and suggests an approach to assessing the efficiency of government stimulation of competition among universities and to predicting the outcomes of applying existing stimulation tools. This paper presents the results of assessing the current level of competition in the Russian university market using a nonstructural method, an adjusted Panzar-Rosse competition assessment model. We used the value of grants received by universities as part of government orders as one of the model factors and also analyzed the effects of other factors describing the size, entrance requirements, and research activities of universities. This article investigates how university income depends on the value of grants received (a ratio of total income to the size of grants) and on the number of students and teachers. The level of competition in this market is characterized by the elasticity of the total income of an average university based on the value of grants received. [This article was translated by Lucy Gunderson.]