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The goal of this article is to study the effects of legal protection of personal data (privacy) on competition, and to investigate to which extent privacy is complementary or opposed to antitrust policy. First, we highlight the role of the costs faced by consumers due to privacy regulation, including the consent costs occuring when consumers want to use an online service. Second, we extend Campbell, Goldfarb et Tucker [2015]’s model on the advertising-supported Internet by introducing different consent costs. We show that, in some cases, firms may prefer to exclude high-consent consumers from the market, so as to target the remaining consumers.