This article is dedicated to the struggle between major socioeconomic universities (SEUs) of Russia for leading positions in the higher education market. It is shown that only in Russia are SEUs, along with classical universities and technological institutes, the strongest players in the market of higher education establishments. The ranking data of the country’s higher schools of economics for 2013–2016 are given, which demonstrate the escalating competition between the most successful SEUs of Russia, manifested in regular “castling” between the higher education institutions in the top list ranking. The authors emphasize the importance of factors of competitive growth, such as the publication of leading economics journals, the creation of a network of scientific divisions in the structure of universities, the formation of an all–Russia information agenda on their territories, and the development of regional analytics centers.