Best foot forward or best for last in a sequential auction?

Should a seller with private information sell the best or worst goods first? Considering the sequential auction of two stochastically equivalent goods, we find that the seller has an incentive to impress buyers by selling the better good first because the seller's sequencing strategy endogenously generates correlation in the values of the goods across periods. When this impression effect is strong enough, selling the better good first is the unique pure-strategy equilibrium. By credibly revealing to all buyers the seller's ranking of the goods, an equilibrium strategy of sequencing the goods reduces buyer information rents and increases expected revenues in accordance with the linkage principle.

1. Introduction

* Is it better to make a strong first impression or build up to a strong finish? For instance, should a government privatize its best firms first to impress buyers, or should it warm up the market by starting with less valuable firms? And should a firm divesting multiple units start with the most profitable units, or should it wait until buyers have learned more from earlier sales? Related choices arise in a wide variety of situations, such as whether to schedule the best papers in a conference first to raise expectations, or schedule them last after the audience is better informed. The traditional counsel to "put one's best foot forward" might seem appropriate, but so does the admonition to "save the best for last."

To investigate this conflicting advice we consider the issue of strategic sequencing from two perspectives. First, if a strategy can be committed to, which sequencing strategy offers the highest payoffs? For instance, will revenues be highest if a government commits to privatizing the best or worst firms first? Second, from an equilibrium perspective, which sequencing strategies are credible even without commitment? For instance, if buyers believe that a firm is selling the best (or worst) units first, will the firm actually benefit from doing so, or will it prefer to fool buyers by reversing the order?

To analyze these questions, we consider an auction model where the seller wants to maximize revenues from the sale of two goods. This model allows us to consider the particular issue of strategic sequencing in auction environments, such as privatization auctions, and also to use the tools of auction theory to gain insight into the problem more generally. For the auction of each good we follow a standard Milgrom and Weber (1982) model in which all auction participants, including the seller, have some private information about the value of the good. The values of the two goods are identically and independently distributed based on public information. We investigate whether the seller, based on her own private information about the values of the goods, should sell the better or worse good first.

We start by considering the simpler case where the goods are auctioned simultaneously so that no information is released between auctions. In a simultaneous auction, the equivalent of a sequencing strategy is for the seller to rank the two goods. Such information raises the expected price for one good and lowers it for the other good, but we find that on average it generates higher expected revenues than selling the goods in random order. This follows from the "linkage principle" that a policy of publicly revealing information equalizes the knowledge of buyers and thereby leads to more competitive bidding (Milgrom and Weber, 1982). A problem with implementing the linkage principle is that the seller has an incentive to exaggerate, so committing to a policy of truthful revelation can be difficult. Looking at this issue from an equilibrium perspective, we show that ranking the goods can be credible because the ranking provides both favorable and unfavorable information at the same time. The ranking does not fully reveal the seller's information, but it does reveal some information and therefore increases seller revenues.

Using the results from the simultaneous auction, we then consider the sequential auction where one of the two goods is sold first. The difference is that buyers of the second-period good now observe the first-period price or other information about the first-period good. For instance, in a privatization auction, buyers of a firm sold later see the price of a firm sold first and, if the interval between auctions is sufficient, may also observe the post-privatization performance of the first firm. Because the values of the two goods are independently distributed, information from the first period may seem irrelevant for the second-period good. However, we show that the seller's sequencing strategy endogenously generates correlation across the two auction periods by truncating the distribution of the second-period good. Because of this endogenous correlation, the first-period information is itself a public signal that, on average, increases the second-period price in accordance with the linkage principle. (1) Therefore, if the seller can commit to a sequencing strategy, revenues are increased by both the rank information and the first-period information.