Learning about the arrival of sales

Abstract

We propose a simple model of optimal stopping where the economic environment changes as a result of learning. A primary application of our framework is an optimal sales problem when the demand for a seller's good is initially uncertain. We distinguish between two versions of the model. In the first version, a lower price is always more informative; in the second, an intermediate price conveys most information to the seller. For the first model, we show that learning leads to a higher posted price by the seller. In the second version, we give sufficient conditions so that learning leads to a higher posted price for an optimistic seller and a lower price for a pessimistic seller.