Privacy and antitrust are on a collision course. Increasingly, privacy practices of large digital platforms are coming under antitrust scrutiny. It has become almost an article of faith that zero-price platforms exercise market power by offering lower levels of privacy. Yet, a rigorous examination of the assumptions underlying this data-price analogy is seriously lacking. Even more important, there is almost no empirical work that has been done in this area. This Article contributes to the debate by providing empirical evidence on the relationship between market power and privacy. First, we examine the privacy grade for each app in the Android App marketplace (covering the 2014-15 period)—as well as metrics that measure the number of users and app quality. These data suggest no relationship between privacy grades and measures of market concentration, that is, the Herfindahl-Hirschman Index (HHI) and market shares based on Google Play store categories. Second, we collected website traffic data from SimilarWeb and matched it to DuckDuckGo’s privacy ratings for sites in thirty-seven website categories. Again, the data suggest a lack of a reliable relationship between privacy ratings and market concentration. The theoretical analysis and empirical results cast doubt on the notion that firms exercise market power by reducing privacy levels.