Auction theory has recently investigated the demand-reduction incentives and potential inefficient allocations of multi-unit uniform-price auctions, such as those used by the U.S. Treasury for debt sales. Recent experimental results show that bidders do indeed strategically reduce their bids in uniform-price auctions. The present paper extends this area of research, both theoretically and experimentally, to consider the effects of varying the number of bidders. We derive several theoretical predictions, including: i) demand reduction should decrease with an increase in the number of bidders and ii) considerable demand reduction remains even in the asymptotic limit, although truthful bidding yields profits very close to those of equilibrium play. We empirically test our theory by examining bidding behavior of subjects in an actual marketplace, where we auction dozens of sportscards using both uniform-price and Vickrey auction formats. The field data are broadly consistent with the theoretical predictions of our model: most notably, demand reduction becomes much smaller and harder to detect as the number of bidders increases. JEL Classification: D44 (auctions), C93 (Field Experiments)

From July 1994 to July 1996, the Federal Communications Commission (FCC) conducted nine spectrum auctions, raising about $20 billion for the U.S. Treasury. The auctions assigned thousands of licenses to hundreds of firms. Were the auctions efficient? Did they award the licenses to the firms best able to turn the spectrum into valuable services for consumers? There is substantial evidence that the FCC 's simultaneous ascending auction worked well. It raised large revenues. It revealed critical information in the process of bidding and gave bidders the flexibility to adjust strategies in response to new information. As a result, similar licenses sold for similar prices, and bidders were able to piece together sensible sets of licenses. JEL No.: D44 (Auctions), L96 (Telecommunications) Keywords: Auctions, Multiple-Item Auctions, Spectrum Auctions Send comments to: Professor Peter Cramton Department of Economics University of Maryland College Park, MD 20742-7211 peter@cramton.umd.edu (301...

Whether rationality of economic behavior increases with expected payoffs and decreases with the cognitive cost it takes to formulate an optimal strategy remains an open question. We explore these issues with field data, using individual bids from sealed-bid auctions in which we sold nearly $10,000 worth of sportscards. Our results indicate that stakes do indeed matter, as high-priced ($70) cards produced more of the theoretically predicted strategic behavior than did lower-priced ($3) cards. We find additional evidence consistent with the importance of cognitive costs, as subjects more experienced with sportscard auctions exhibited a greater tendency to behave strategically than did less experienced bidders.

Uniform-price auctions of a divisible good in fixed supply admit underpricing equilibria, where bidders submit high inframarginal bids to prevent competition on prices. The seller can obstruct this behavior by tilting her supply schedule and making the amount of divisible good on offer change endogenously with its (uniform) price. Precommitting to an increasing supply curve is a strategic instrument to reward aggressive bidding and enhance expected revenue. A fixed supply may not be optimal even when accounting for the cost to the seller of issuing a quantity different from her target supply.

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Invited Paper for Production and Operations Management Customer behavior modeling has been gaining increasing attention in the operations man-agement community. In this paper we review current models of customer behavior in the revenue management and auction literatures and suggest several interesting research directions in this area. 1

We compare, experimentally, the Vickrey auction and an ascending-price auction recently introduced by Ausubel (1997). We evaluate the relative performance of both auctions in terms of efficiency and revenue in multi-unit environments where valuations either have a common-value component or are private information. We find that the Ausubel auction is less prone to overbidding and may yield higher revenue than the Vickrey auction. The gain in revenue seems to be coupled with a loss of efficiency.

When supply is fixed in advance, the uniform-price share auction is vulnerable to “collusive-seeming equilibria ” in which the realized price is less than a common knowledge lower bound on all bidder’s per share value vi. Our main result is that no collusive-seeming equilibria exist in a variation of the uniform-price auction in which the auctioneer sets supply so as to maximize profits after receiving bidders’announced demand schedules. Lack of precommitment to quantity levels, especially the ability to increase supply as a function of the bidding, is key. For example, consider the special case in which there is a common knowledge common value v (with n bidders): when the auctioneer precommits to a supply [ curve S (p) =a + bp,Nash nbv−a equilibria exist in which any price p ∈ b(n+1),v can be realized; when the auctioneer is only able to increase supply from a prespecified minimum ̂S, no collusive-seeming equilibria exist if bidders are restricted to submit differentiable demand schedules and to bid at prices no lower than c ′ ̂S, the auctioneer’s marginal cost; but when the auctioneer is only able to decrease supply from a prespecified maximum ̂ [ S, Nash equilibria exist in n−1 linear strategies in which any price p ∈ n v + c ′ ( ̂ S) n,v can be realized.

We present laboratory experiments of different multi-unit auction mechanisms. Two units of a homogeneous object were auctioned off among two bidders with flat demand for two units. We test whether expected demand reduction occurs in open and sealed–bid uniform–price auctions. Revenue equivalence is tested for these auctions as well as for the Ausubel, the Vickrey and the discriminatory sealed–bid auction. Furthermore, we compare the five mechanisms with respect to the efficient allocation of the units. We also provide some theoretical insights concerning the equilibria of uniform–price auctions with incomplete information.

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