The Optimal Sequence of Costly Mechanisms

An impatient, risk-neutral monopolist must sell one unit of an indivisible good within a fixed number of periods while one-period-lived buyers with independent private values arrive over time. In each period, the seller can either run a reserve price auction while incurring a cost or post a price without the cost. We characterize the optimal sequence of mechanisms that maximizes the seller’s expected profits. When there is an infinite number of periods, repeatedly running auctions with the same reserve price or posting a constant price is optimal. When there is a finite number of periods, the optimal sequence is a sequence of declining prices, a sequence of auctions with declining reserve prices converging to the static optimal monopoly reserve price, or a sequence of prices followed by a sequence of auctions. Most interestingly, a sequence of auctions before a sequence of posted prices is never optimal. The mechanism sequence of posted prices followed by auctions remains the general optimal sequence under various extensions of the basic setting and resembles a Buy-It-Now option.