We design an asymmetric duopoly model with inherited market dominance such that the dominant firm and the smaller firm can price discriminate based on consumers’ purchase history. We show that uniform pricing softens competition leading to higher industry profits than under history-based pricing. Consumers benefit from history-based price discrimination unless the switching cost is sufficiently high and the inherited degree of dominance is sufficiently weak. A ban on history-based pricing would typically introduce a distributional conflict between consumers and producers. Finally, we establish that the gains to industry profits associated with uniform pricing exceed the associated losses to consumers.