Price discrimination in a double horizontal differentiated duopoly market

Using a model of double horizontal differentiation, in which a variety dimension is added to a "linear city" duopoly model, I show that even when costs and demand are symmetric, price discrimination may be an equilibrium phenomenon. In the model, each customer has a preferred variety and a preferred firm. Customers have perfect information about all prices and may be induced to switch varieties and firms given a sufficient price difference. The price discrimination equilibrium exists when a sufficient subset of consumers are particularly price sensitive with respect both to variety and firm.