We study the evolution of prices set by duopolists who are uncertain about the perceived degree of product differentiation. Customers sometimes view the products as close substitutes, sometimes as highly differentiated. As the informativeness of the quantities sold increases with the price differential, there is scope for active learning by firms. When information has low value to the firms, they charge the same price as would be set by myopic players, and there is no price dispersion. When firms value information more highly, on the other hand, they actively learn by creating price dispersion. Such price dispersion arises in a cyclical fashion, and is most likely to be observed when the firms' environment changes sufficiently often, but not too frequently. Firms' payoffs are higher when they use correlated pricing strategies. Contrary to what one might expect, such coordination need not hurt consumers, provided they are sufficiently impatient.