Does the seller of a house facing a large number of buyers always decrease its price when its first offer is rejected?

This paper identifies the optimal two-period price sequence in the attempt for selling a good, with take-it-or-leave-it offers, when the seller faces ambiguity about the buyers' willingness to pay. If the first round fails, the seller updates its beliefs on the state of the market in accordance with Bayes rule and quotes a second and final price. We show that the optimal sequence of prices can be increasing. Furthermore, we describe the optimal sequence of prices with a myopic seller who does not update his beliefs in the second period. In this case, the optimal price sequence is always decreasing.