Fixed revenue auctions: theory and behavior

Economic Inquiry, July, 2008 by Cary A. Deck, Bart J. Wilson

I. INTRODUCTION

There are numerous varieties of auction institutions used in practice and studied in the economics literature. The four standard mechanisms for selling a fixed quantity as in a single unit or lot are the English, Dutch, first-price sealed bid, and second-price sealed bid auctions. The widely known theoretical results are that the English and second-price auctions are equivalent as are the Dutch and first-price auctions. One of the most insightful theoretical results of private value auctions is that under certain assumptions the expected revenue is constant across the four mechanisms (see McAfee and McMillan 1987; Milgrom 1987; Myerson 1981). But behavioral examinations of private value auctions have consistently found that the relationships among the formats are not so straightforward. English clock auctions generate truthful revelation as predicted; however, second-price auctions, which should also generate truthful revelation, do not reliably do so in a laboratory setting (Harstad 2000; Kagel, Harstad, and Levine 1987). Further, revenue equivalence does not hold between first-price and second-price auctions (Coppinger, Smith, and Titus 1980). (1) In part, this is due to the fact that many bidders in first-price auctions act as if they are risk averse. Furthermore, Dutch auctions and first-price sealed bid auctions are not behaviorally isomorphic; observed prices are significantly lower in the Dutch clock auctions than in first-price auctions (Cox, Roberson, and Smith 1982).

Almost exclusively, the focus of previous work has been on auctions determining the selling price for a prespecified lot. (2) However, in some situations, a seller may be more concerned about raising a fixed amount of revenue. For example, a business may sell off just enough inventory to gain the needed liquidity to undertake a particular project. A person may pawn just enough items to secure money with which to pay the monthly bills. Alternatively, in a procurement setting, a buyer may desire to acquire as much as possible for some nonfungible fixed budget. For example, a researcher whose grant is expiring may buy as many supplies as possible with the remaining money or a firm may have a fixed advertising budget with which to buy the most effective campaign. Though not typically thought of in this way, auctions can be used to solve these types of problems as well. (3) We define a fixed revenue auction to be a bidding mechanism in which a prespecified total payment is exchanged for a variable quantity of a good. (4) Wessen and Porter (1997) developed a fixed revenue auction to cover the $326,000 cost of moving antennae for the Cassini mission to Saturn. The auction allowed competing research teams to place bids in terms of the mass they desired on the craft and the price per unit for the mass.

The goal of this paper is to understand the behavioral properties of fixed revenue auctions utilizing the four standard mechanisms. To enable comparisons with the extensive literature on auctions, the environment is designed to allow the maximum similarity between auctions in the two dimensions. This includes placing nontrivial restrictions on buyer values to yield a theoretical equivalence between auction dimensions. Given this, one might be inclined to suppose that the behavioral properties are a forgone conclusion. This need not be the case as evidenced by the aforementioned lack of isomorphism between first-price and Dutch auctions and between English and second-price auctions in the standard setting. Experiments have shown that even simple changes in framing can impact behavior. (5) For example, framing a lottery as a gain or a loss can change the value one places on the lottery and framing the ultimatum game as a buyer-seller interaction can lead to behavior more consistent with material self-interest. A change in auction dimension, however, is more than a simple framing effect; it is a change in the underlying decision problem. A priori, it is not known how a dimensional change will influence behavior. If behavior differs by dimension, the experiments could provide new insights into how people approach these institutions. (6) If behavior is consistent with previous results, then it provides greater confidence in the robustness of previous work.

The next section presents a theoretical treatment of each mechanism in a fixed revenue context. Separate sections discuss the design and results of laboratory experiments investigating behavior in these auctions. A final section contains concluding remarks. As a prelude to our results, we find that under a generalization of the typical assumption regarding values, the theoretical and behavioral properties of the four standard auctions translate to a fixed quantity dimension in a consistent and an intuitive way.

II. THEORETICAL MODEL

We begin by considering the standard, fixed quantity auction format and then identify where and how fixed revenue auctions differ from the familiar model. In the single (fixed)-unit, independent private value auction, there are n bidders who value the lot up for auction. In the English auction, the price starts low and increases until only one bidder remains willing to purchase. The sole remaining bidder buys the item at the final price. (7) The Dutch auction begins with a high price that falls until a bidder agrees to purchase at that price. In contrast, first- and second-price sealed bid auctions are both static in that potential buyers submit sealed bids. For the first-price sealed bid auction, the party submitting the highest bid wins the auction and pays a price equal to his winning bid, whereas in the second-price sealed bid auction, the party submitting the highest bid wins but pays a price equal to the second highest bid.