Data privacy is usually regarded as a part of product quality, the protection of which can be improved by the implementation of the antitrust law. For firms, however, the nature of the two-sided market requires access to the user data for providing services. The aggravation of competition will increase the firms' demand for more data to gain competitive advantage. For users, due to the concealment strategy of data acquisition, cognitive limitations and over-sensitivity to product prices, it is also difficult to choose the firms with higher level of privacy protection in the competitive market. Because of these limitations of competition, improving data privacy protection through antitrust law is impossible.