Personalized pricing with imperfect customer recognition

We consider a duopoly model where firms charge personalized prices to the consumers they can recognize and a uniform price to the rest of consumers. We assume that each firm can identify only a fraction of consumers at each point of the Hotelling line. This fraction is determined by two factors, denoted as intensive and extensive margin, that define the degree of accuracy and the extension of the information respectively. We show that profits are non-monotonic in the size of the two margins and we characterize under which information conditions the firms’ profits are maximized. Finally, we provide some policy implications concerning the protection of consumers. In particular we show that when firms face restrictions in collecting information so that their competition is prevented, consumers surplus is maximized when personalized and uniform prices coexist.