In many markets firms have same information about their customers resulting
from the consumers' past choice behavior. Given this information, firms ca
n better target their market practices with respect to their customers. Thi
s article considers such a situation in a duopoly with infinitely lived fir
ms and overlapping generations of consumers. Firms can set different prices
for their previous customers and their new customers. A new customer may e
ither have bought the competing product in the previous period or be new to
the market. I identify three effects: (i) Firms lower prices to attract th
e competitor's previous customers. (ii) Greater consumer patience intensifi
es competition. (iii) Greater firm patience softens the competitive interac
tion. With patient firms and consumers, prices are lower than when there is
no customer recognition.