This paper provides an elementary, non-technical, survey of auction theory, by introducing and describing some of the critical papers in the subject. (The most important of these are reproduced in a companion book, The Economic Theory of Auctions, Paul Klemperer (ed.), Edward Elgar (pub.), forthcoming.) We begin with the most fundamental concepts, and then introduce the basic analysis of optimal auctions, the revenue equivalence theorem, and marginal revenues. Subsequent sections address risk-aversion, affiliation, asymmetries, entry, collusion, multi-unit auctions, double auctions, royalties, incentive contracts, and other topics. Appendices contain technical details, some simple worked examples, and a bibliography for each section.

Auctions typically involve the sale of many related goods. The FCC spectrum auctions and the Treasury debt auctions are examples. With conventional auction designs, large bidders have an incentive to reduce demand in order to pay less for their winnings. This incentive creates an inefficiency in multi-unit auctions. Large bidders reduce demand for additional units and so sometimes lose to smaller bidders with lower values. We demonstrate this inefficiency in several auction settings: flat demand and downwardsloping demand, independent private values and correlated values, and uniform pricing and pay-your-bid pricing. We also establish that the ranking of the uniform-price and pay-your-bid auctions is ambiguous. We show how a Vickrey auction avoids this inefficiency and how the Vickrey auction can be implemented with a simultaneous, ascending-bid design (Ausubel 1997). Bidding behavior in the FCC spectrum auctions illustrates the incentives for demand reduction and the associated inefficiency.

We consider auction design in a setting with costly preference elicitation. We motivate the role of proxy agents, that are situated between bidders and the auction, and maintain partial information about agent preferences and compute equilibrium bidding strategies based on the available information. The proxy agents can also elicit additional preference information incrementally during an auction. We show that indirect mechanisms, such as proxied ascending-price auctions, can achieve better allocative efficiency with less preference elicitation than direct mechanisms, such as sealed-bid auctions.

Measuring software security is difficult and inexact; as a result, the market for secure software has been compared to a ‘market of lemons.’ Schechter has proposed a vulnerability market in which software producers offer a time-variable reward to free-market testers who identify vulnerabilities. This vulnerability market can be used to improve testing and to create a relative metric of product security. This paper argues that such a market can best be considered as an auction; auction theory is then used to tune the structure of this ‘bug auction ’ for efficiency and to better defend against attacks. The incentives for the software producer are also considered, and some fundamental problems with the concept are articulated.

We test specific implications of existing models of reputation using eBay data on auction prices, sale rates, and seller reputation. Our basic model combines elements from Diamond’s (1989) and Levin and Smith’s (1994) models and features both adverse selection and moral hazard. The empirical evidence provides strong support for two implications of this basic model: that once a seller receives the first negative buyer feedback, both the sales rate drops and the frequency of negative feedback increases. We consider a variety of alternative theories of seller Electronic commerce presents the theoretical and the empirical economist with a number of interesting research questions. Traditional markets rely significantly on the trust created by repeated interaction and personal relationships. Electronic markets, by contrast, tend to be rather more anonymous. Can the

Wedeveloptestsforcommonvaluesatfirst-price sealed-bid auctions. Our tests are nonparametric, require observation only of the bids submitted at each auction, and are based on the fact that the “winner’s curse ” arises only in common values auctions. The tests build on recently developed methods for using observed bids to estimate each bidder’s conditional expectation of the value of winning the auction. Equilibrium behavior implies that in a private values auction these expectations are invariant to the number of opponents each bidder faces, while with common values they are decreasing in the number of opponents. This distinction forms the basis of our tests. We consider both exogenous and endogenous variation in the number of bidders. Monte Carlo experiments show that our tests can perform well in samples of moderate sizes. We apply our tests to two different types of U.S. Forest Service timber auctions. For unit-price (“scaled”) sales often argued to fit a private values model, our tests consistently fail to find evidence of common values. For “lumpsum ” sales, where aprioriarguments for common values appear stronger, our tests yield mixed evidence against the private values hypothesis.

Firms need to spend time and money to figure out how much assets for sale are worth to them. Which selling procedure is likely to generate better incentives for information acquisition? We show that multi-stage and in particular ascending price auctions with breaks (that allow for information acquisition) perform better than their static counterpart. This is because dynamic formats allow bidders to observe the number of competitors left throughout the selling procedure, hence to get a much better estimate of their chance of winning. Since information acquisition tends to generate higher revenues, our analysis provides a new rationale for using dynamic formats rather than sealed-bid ones. Our conclusion is reinforced when multiple objects are sold, because dynamic formats may not only provide bidders with estimates on whether competition is soft or not, but also on which object competition is softer.

Abstract: In a general auction model with affiliated signals, common components to valuations and endogenous entry, we compute the equilibrium bidding strategies and outcomes, and derive a lower bound on the optimal reserve price. This lower bound can be computed using data on past auction combined with information about the subsequent sales prices of unsold goods. We compute the lower bound using data from FDIC real estate auctions. We find the point estimate for an upper bound on the optimal reserve for real estate to be 75 % of appraised value. Using data from private real estate auctions, we show that when reserve prices are around 50 % of appraised value, seller revenues are increasing in the reserve price.

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In an optimal auction, a revenue-optimizing seller often awards goods inefficiently, either by placing them in the wrong hands or by withholding goods from the market. This conclusion rests on two assumptions: (1) the seller can prevent resale among bidders after the auction; and (2) the seller can commit to not sell the withheld goods after the auction. We examine how the optimal auction problem changes when these assumptions are relaxed. In sharp contrast to the no resale assumption, we assume perfect resale: all gains from trade are exhausted in resale. In a multiple object model with independent signals, we characterize optimal auctions with resale. We prove generally that with perfect resale, the seller's incentive to misassign goods is destroyed. Moreover, with discrete types, any misassignment of goods strictly lowers the seller's revenue from the optimum. In auction markets followed by perfect resale, it is optimal to assign goods to those with the highest values.