Uniform vs. discriminatory auctions with variable supply - experimental evidence

In the variable supply auction considered here, the seller decides how many costumers with unit demand to serve after observing their bids. Bidders are uncertain about the seller’s cost. We experimentally investigate whether a uniform or a discriminatory price auction is better for the seller in this setting. Exactly as predicted by theory, it turns out that the uniform price auction produces substantially higher bids, and consequently yields higher revenues and pro…ts for the seller. Somewhat surprisingly but again predicted by theory, it also yields a higher number of transactions, which makes it the more e¢ cient auction format. JEL-classi…cation numbers: D44, C92. Key words: auctions, experiment, discriminatory, uniform. We thank Jordi Brandts, Jürgen Eichberger, and Kjell Nyborg as well as seminar participants at UCL, the WZB Berlin, and the universities of Cologne and Heidelberg for very helpful comments. Paul Stange and Pablo Cala…ore provided excellent research assistance. Financial support by the Deutsche Forschungsgemeinschaft through SFB 504 is gratefully acknowledged. yDepartment of Economics, University of Heidelberg, Grabengasse 14, 69117 Heidelberg, Germany, email: [email protected] 1 Introduction Suppose you want to sell several homogeneous items (concert tickets, photo prints, tie-dyed T–shirts, stocks in an IPO, etc.). You are uncertain about potential buyers’willingness to pay of for those objects. How should you go about selling the objects if each buyer demands only one item? Given the uncertainty about willingness to pay, an auction is an obvious choice. But should you use a uniform price auction or a discriminatory price auction? We assume that the seller’s production cost (or his reserve price) for each object is his private information.1 In this case it is of advantage to the seller to design the auction as one with variable supply, that is, an auction in which the number of items sold is not …xed in advance but may depend on the submitted bids. After observing the bids, the seller chooses the number of items to sell in a pro…t maximizing way. Of course, bidders take this into account when deciding on their bids. We also assume that all bidders attach the same value to items sold although this fact is not known to the seller.2 In the discriminatory auction each bidder has to pay his bid if being served by the seller. Obviously, the seller will do so if and only if the bid is at least as high as the seller’s marginal production cost. In the uniform auction all bidders served by the seller pay the same price, which equals the lowest bid served.3 Clearly, if all bids are below marginal cost, the seller will not sell any items. However, if several of the bids are above marginal cost, the seller must decide whether to serve a smaller number of buyers and receive a higher price, or serve a larger number of buyers at a lower price. Damianov and Becker (2007) analyze this situation for the general case with n bidders and general distributions of production cost. They show that As an example consider a “secret reserve price”on eBay. This is mainly for simplicity and can be considered a …rst step to a more general analysis. But it can also be justi…ed in some situations, e.g. when a resale market exists for the items. 3 In the literature one sometimes …nds an alternative version in which the price equals the highest bid not served. However, in practice the latter version does not seem to be in much use, e.g. most treasury auctions use our version. Furthermore, in the current setting with unit demand by bidders, the highest–bid–not–served rule would not make much sense as the seller could never sell all units.