This article studies the effects of consumer information on the intensity of competition. In a two dimensional duopoly model of horizontal product differentiation, firms use consumer information to price discriminate. I contrast a full privacy and a no privacy benchmark with intermediate regimes in which the firms target consumers only partially. No privacy is traditionally detrimental to industry profits. Instead, I show that with partial privacy firms are always better-off with price discrimination: the relationship between information and profits is hump-shaped. Consumers prefer either no or full privacy in aggregate. However, even though this implies that privacy protection in digital markets should be either very hard or very easy, the effects of information on individual surplus are ambiguous: there are always winners and losers. When an upstream data seller holds partially informative data, an exclusive allocation arises. Instead, when data is fully informative, each competitor acquires consumer data but on a different dimension
