We consider the problem of a monopolist with an object to sell before some deadline, facing n buyers with independent private values. The monopolist posts prices but has no commitment power. We show that the monopolist can always secure at least the larger of the static monopoly proﬁt and the revenue from a Dutch auction with a zero reserve price. When there are only a few buyers, her proﬁts are higher than this bound, and she essentially posts unacceptable prices up to the very end, at which point prices collapse to a “reservation price” that exceeds marginal cost. When there are many buyers, the seller abandons this reservation price in order to more eﬀectively screen buyers. Her optimal policy then replicates a Dutch auction, with prices decreasing continuously over time. With more units to sell, prices jump up after each sale.
Hörner, Johannes and Samuelson, Larry, "Managing Strategic Buyers" (2008). Cowles Foundation Discussion Papers. 2000.