Behavior based price personalization under vertical product differentiation

We study price personalization in a two period duopoly with vertically differentiated products. In the second period, a firm not only knows the purchase history of all customers, as in standard Behavior Based Price Discrimination models, but it also collects detailed information on its old customers, using it to engage in price personalization. The analysis reveals that there exists a natural market for each firm, defined as the set of customers that cannot be poached by the rival in the second period. The equilibrium is unique, except when firms are ex-ante almost identical. In equilibrium, only the firm with the largest natural market poaches customers from the rival. This firm has highest profits but not necessarily the largest market share. Aggregate profits are lower than under uniform pricing. All consumers gain but total welfare is only higher herein than under uniform pricing if firms' natural markets are sufficiently asymmetric. The low quality firm chooses the minimal quality level and a quality differential arises, though the exact choice for the high quality depends upon the cost specification.