In a dynamic model with overlapping generations of consumers, we study duopolistic competition when firms can price discriminate, at each period, between their previous customers and the consumers that they have never served. Long-term contracts are not enforceable. In (Markov-perfect) equilibrium, one firm charges higher prices to its past customers than to its new customers, as past customers have revealed their strong preferences for the firm; the other firm, however, rewards its previous customers by charging lower prices to them than to its new customers. This loyalty reward strategy comes from the interplay between the firms’ usual incentive to extract surplus from consumers with revealed strong preferences and their incentives to acquire information and to recognize their young loyal customers. The result also relies on the firms’ inability a priori to tell different generations apart. It is the outcome of the unique equilibrium of a simplified two-period (or T-period) version of the game and holds with forward-looking consumers who are impatient enough.