Dynamic price discrimination with customer recognition

This paper studies a general two-period model of product line pricing with customer recognition. Specifically, we consider a monopolist who can sell vertically differentiated products over two periods to heterogeneous consumers. Each consumer demands one unit of the product in each period. In the second period, the monopolist can condition the price-quality offers on the observed purchasing behavior in the first period. In this setup, the monopolist can price discriminate consumers in two dimensions: by quality as well as by purchase history. We fully characterize the monopolist's optimal pricing strategy when there are two types of consumers. When the type space is a continuum, we show that there is no fully separating equilibrium, and some properties of the optimal contracts (price-quality pairs) are characterized within the class of partitional perfect Bayesian equilibria.