We study the impact of personalized pricing (or perfect price discrimination) in a general oligopoly model. Existing research based on the Hotelling model suggests that competitive personalized pricing intensifies competition, harms firms and benefits consumers. This result extends to our general model if the market is fully covered (i.e., all consumers buy). However, if the market is not fully covered, this result can be completely reversed---competitive personalized pricing can benefit firms and harm consumers. Nevertheless, in the long run with free entry, personalized pricing leads to the socially optimal market structure and so favors consumers.