The article analyzes the change in approaches to determining the dominant position in digital markets. The authors indicate the main directions of improving the antimonopoly legislation in these directions. The paper also considers the problems of the quantitative criterion, which in turn leads to the conclusion about the increased role of qualitative criteria for determining the dominant position of the subject. The development of the digital economy forces us to develop other, alternative criteria. These alternative criteria include network effects and the mode of access to big data. In this regard, the authors consider the concept of a network effect, its features. In turn, the possession of big data is seen as a source of abuse in the digital economy.