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.

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We analyze a market where (i) trade proceeds by random and anonymous pairwise meetings with bargaining; (ii) agents are asymmetrically informed about the value of the traded good; and (iii) no new entrants are allowed once the market is open. We show that information revelation and e±ciency never obtain in equilibrium, even as discounting is removed. This holds whether the asymmetry is two-sided or one-sided. In some cases there exist equilibria where a substantial amount goes untraded. This contrasts with the earlier literature, which was based on the steady-state equilibria of a model where agents enter the market every period.

We study the rates at which transaction prices aggregate information in common value auctions under the different information structures in Wilson (Rev. Econ. Stud. 44 (1977) 511) and Pesendorfer and Swinkels (Econometrica 65 (1997) 1247). We consider uniform-price auctions in which k identical objects of unknown value are auctioned to n bidders, where both n and k are allowed to diverge to infinity, and k=n converges to a number in 0; 1Þ: The Wilson assumptions lead to information aggregation at a rate proportional to n= ffiffiffi p k; but the price pffiffiffi aggregates information at a rate proportional to k in the PS setting. We also consider English auctions, and investigate whether the extra information revealed in equilibrium improves convergence rates in these auctions.

We estimate structural models of competitive bidding in symmetric low-price procurement auctions in order to address two empirical questions. First, we investigate the importance of common and private values using a general model which allows bidders' preferences to exhibit both components. Second, we see whether participants bid more aggressively (as measured by the markups of bids over expected costs) as the number of competitors in an auction increases. In common value auctions, the effect of increased competition on equilibrium markups is ambiguous since the increased competitive pressure which tends to lower markups is counteracted by the winner's curse, which counsels greater caution and more conservative bidding. This ambiguity is not present in private value models. We find evidence of common value components in a subset of the auctions we study. Furthermore, we estimate that bidders' markups averaged 20% in 3bidder auctions, but rose to 50% with 5 bidders and over...

ABSTRACT. This paper proves that the monotonicity of bidding strategies together with the rationality of bidders implies that the winning bid in a first price auction converges to the competitive equilibrium price as the number of bidders increases (Wilson (1977)). Instead of analyzing the symmetric Nash equilibrium, we examine rationalizable strategies (Bernheim (1984) and Pearce (1984)) among the set of monotonic bidding strategies to prove that any monotonic rationalizable bidding strategy must be within a small neighborhood of the “true ” valuation of the object, conditioned on the signal received by the bidder. We obtain an information aggregation result similar to Wilson (1977), while dispensing with almost all symmetric assumptions and using a milder solution concept than the Nash equilibrium. In particular, if every bidder is ex ante identical, then any rationalizable bidding strategy must be within a small neighborhood of the symmetric Nash equilibrium. In a symmetric first price auction, the symmetry of outcomes is implied rather than assumed.

We derive the limit distributions of equilibrium bids in common value auctions as the number of bidders grows large. We view the common value auction as a statistical experiment in which the winning bids are estimators of the unknown common value, whereby the question of information aggregation is equivalent to whether the winning bids in a sequence of auctions is a consistent estimator of the true common value. Our results are directly analogous to the econometric task of characterizing the asymptotic properties of a consistent sequence of estimators. While the previous literature has demonstrated that information aggregation obtains across all the common auction forms, our analysis uncovers important dierences. We nd that rstprice, second-price, and English auctions aggregate information much faster than uniform-price multi-object auctions. However, this ranking is very sensitive to assumptions about the information structure, with the information aggregation properties of the Eng...

We analyze competitive pressures in a sequence of auctions with a growing number of bidders, in a model that includes private and common valuations as special cases. We show that the key determinant of bidders' surplus (and implicitly auction revenue) is how the goods are distributed. In any setting and sequence of auctions where the allocation of good(s) is concentrated among a shrinking proportion of the population, the winning bidders enjoy no surplus in the limit. If instead the good(s) are allocated in a dispersed manner so that a non-vanishing proportion of the bidders obtain objects, then in any of a wide class of auctions bidders enjoy a surplus that is bounded away from zero. Moreover, under dispersed allocations, the format of the auction matters. If bidders have constant marginal utilities for objects up to some limit, then uniform price auctions lead to higher revenue than discriminatory auctions. If agents have decreasing marginal utilities for objects, then uniform price auctions are asymptotically efficient, while discriminatory auctions are asymptotically inefficient. Finally, we show that in some cases where dispersed allocations are efficient, revenue may increase by bundling goods at the expense of efficiency.