Globalization and the development of the knowledge economy increase competition in the higher education market. Improving the competitiveness of higher education in the world market in the second decade of the 21st century has officially become a project to be implemented by the state. In this regard, it is extremely important to study the competition among and competitiveness of universities. The purpose of this study is to substantiate the existence of quasi-competition among Russian universities and assess its impact on improving the efficiency of Russian higher education. The research hypothesis is that despite the inequality in the system of higher education, there is quasi-competition, not only within the groups of leading universities at the federal level and among regional universities, but also against everyone, and this competition increases the efficiency of the system as a whole. Particular attention is paid to such specific feature of university competition as competition for public funding, competition in a regulated market with high concentration and even monopoly. As a practical case for studying the competition of universities, the fight for applicants is considered as a vivid manifestation of competition. The information base of the study is the results of annual surveys of applicants of Ural Federal University. The main method of research is the economic and mathematical analysis of the results of surveys of graduates. It is concluded that the quasi-competition model best describes the established higher education markets. The Russian system of higher education operates under the dominance of state funding and quasi-market competition. An important aspect of the study is to identify the relationship between competition in the field of higher education and university funding. Competition between universities increases financial inequality in the higher education system. At the same time, in a number of areas, especially in terms of preparing bachelors, regional universities can compete with leading universities. The influence of competition on the higher education system contributes to the increase in the efficiency of universities through their struggle for a limited set of resources. An interesting practical finding of the study, which can be useful when planning admission campaigns, is that price competition for undergraduate applicants is inferior to competition for the quality of education in the campaign to attract students to master’s programs.