Price dispersion in duopolies with heterogeneous consumers

In this paper, I modify Varian's [Varian, H.R. (1980). A model of sales, American Economic Review, 70(4), 651-659] model of sales to allow for heterogeneity in consumer preferences. I show that in mixed strategy equilibria each firm charges a finite number of prices. Using this characterization, I examine the effect of consumer heterogeneity on firms' optimal pricing strategies.