Price dispersion and incomplete learning in the long run

Abstract

In each period a seller chooses a price, and the customer for that period buys either one unit or nothing. The relationship between price and purchase probability is one of two linear functions. It is shown that the seller, behaving optimally, does not necessarily learn which function is the actual relationship, since there can be a positive probability of sequences of prices converging to the price at which the two functions give the same purchase probability.