Learning buyers' valuation distribution in posted-price selling

A dynamic pricing model is studied where a seller of an asset faces a sequence of potential buyers whose valuation distribution is unknown to the seller. The seller learns more about the distribution in the selling process and becomes less optimistic as the object remains unsold. We characterize the optimal posted prices which incorporate updated beliefs every period, and derive a rather tight sufficient condition under which these prices decline over time. An example is provided where the optimal prices can actually increase over time if the condition is violated.