A model of sales with differentiated and homogeneous goods

This paper extends the classical model of sales (Varian, 1980; Rosenthal, 1980) by adding product differentiation. Instead of uninformed (i.e. loyal) customers, our setting features “variety seekers”. These consumers regard the products as imperfect substitutes. As in the original model, the firms also serve “bargain seekers” who buy the cheapest product. The discontinuous demand structure precludes any pure-strategy equilibria. We characterize the symmetric mixed-strategy equilibrium of the modified game. In contrast to the original model, the upper bound on prices and the equilibrium expected profits are decreasing in the mass of bargain seekers. •Product differentiation has substantive consequences for price dispersion.•The bounds on prices depend on the equilibrium expected price.•Expected profits and the bounds on prices decrease with the mass of bargain seekers.•The setting nests the classical model of sales as a special case.