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.

Many interesting propositions in the economics of information are built on the assumption that the log of the cumulative distribution function of a random variable is a concave function. This property is equivalent

We present new identification results for models of first-price, second-price, ascending (English), and descending (Dutch) auctions. We analyze a general specification of the latent demand and information structure, nesting as special cases the pure private values and pure common values models, and allowing both ex ante symmetric and asymmetric bidders. We address identification of a series of nested models and derive testable restrictions that enable discrimination between models on the basis of observed data. The simplest model–that of symmetric independent private values–is nonparametrically identified even if only the transaction price from each auction is observed. For more complex models, identification and testable restrictions are obtained when additional information of one or more of the following types is available: (i) the identity of the winning bidder or other bidders, (ii) one or more bids in addition to the transaction price; (iii) exogenous variation in the number of bidders; (iv) bidder-specific covariates; (v) auction-specific covariates. While many private values (PV) models are nonparametrically

In the context of pre-Bayesian games we analyze resource selection games with unknown number of players. We prove the existence and uniqueness of a symmetric safety-level equilibrium in such games and show that in a game with strictly increasing linear cost functions every player benefits from the common ignorance about the number of players. In order to perform the analysis we define safety-level equilibrium for pre-Bayesian games, and prove that it exists in a compact-continuous-concave setup; in particular it exists in a finite setup. 1

This paper proposes a semiparametric estimation procedure of the first-price auction model with risk averse bidders within the independent private values paradigm. We show that the model is nonidentified in general from observed bids. Moreover, any distribution of bids can be rationalized by an auction model with either constant relative risk aversion or constant absolute risk aversion. Thus identification of the model must be achieved through additional restrictions. We then establish semiparametric identification under a common but unknown support condition and parameterization of the bidders' utility function. Next we propose a semiparametric method for estimating the corresponding auction model using local polynomial estimators. This method involves several steps and allows to recover the parameters of the utility function as well as the bidders' private values and their distribution. An attractive computational advantage of our method is that it does not require solving the differential equation characterizing the equilibrium strategy. An illustration of the method on U.S. Forest Service timber sales is proposed. In particular, a test of bidders' risk neutrality is performed.

In this paper, we study an auction where bidders only know the number of potential applicants. After seeing their values for the object, bidders decide whether or not to enter the auction. Players may not want to enter the auction since they have to pay participation costs. We characterize the optimal bidding strategies for both first- and secondprice sealed-bid auction when participation is endogenous. We show that only bidders with values greater than a certain cut-off point will bid in these auctions. In this context, both auctions generate the same expected revenue. We also show that, contrarily to the predictions of the fixed-n literature, the seller’s expected revenue may decrease when the number of potential participants increases. In addition, we show that it is optimal for the seller to charge an entry fee, which contrasts greatly with results from the existing literature on auctions with entry.

Within the heterogeneous independent private values model, we analyze bidder collusion at …rst and second price single-object auctions, allowing for within-cartel transfers. Our primary focus is on coalitions that contain a strict subset of all bidders. To analyze collusion, a richer environment is required than that required to analyze non-cooperative behavior. We must account for the possibility of shill bidders as well as mechanism payment rules that may depend on the reports of cartel members, their bids at the main auction, and auction outcomes. We show there are environments in which a coalition at a …rst price auction can produce no gain for the coalition members beyond what is attainable from non-cooperative play. In contrast, a coalition at a second price auction achieves the maximal collusive gain in all but a few cases. In some cases involving shill bidders, no collusive gain is possible. For the environments for which we have contrasting results, a coalition does at least as well at a second price auction as at a …rst price auction. We are grateful to Vijay Krishna for helpful discussions. The authors can be reached at

This paper introduces general games with incomplete information in which the number, as well as the types or identities, of the participating players are determined by chance and might not be known to the players when they make their choices of actions. In these games, the selection of the number and types of players is modeled as a finite point process on a suitable type space. Definitions of pure-strategy, mixed-strategy, and correlated equilibria in random-player games are given, extending the corresponding ones for finite games, Bayesian games, and games with population uncertainty, which may all be considered as special cases

The economic literature on online auctions is rapidly growing, because the enormous amount of freely available field data and the emergence of numerous innovative auction design features on auction platforms such as eBay have created excellent research opportunities. In this article, we survey the theoretical, empirical and experimental research on bidding strategies (including the timing of bids and winner’s curse effects) and seller strategies (including reserve price policies and the use of buy-now options) in online auctions, as well as some of the literature dealing with online auction design (including the stopping rule and multi-object auction rules). Section 1: Why do information systems make auctions (even) more popular? Long before any electronic information systems were in place, people used auctions to trade all kinds of goods and services. In his comprehensive overview of the history of auctions, Cassady (1967) reports auctions of items of almost any size, from jewels and spices to ships and provinces. The range of services that have been auctioned is also enormous, including anything from a dance on a local church festivity to the lifetime work force of a slave. While being widespread, however, auctions were not the most common way of trading because the costs of conducting and participating in an auction were typically too high for the every-day trade of common goods. Evidently, the use of auctions is subject to the trade-off between the advantage of price discovery (i.e. discovering the highest valuation bidder) and the disadvantage of having high transaction costs (i.e. the costs of finding a buyer and negotiating a sale). Because of this, auctions are most valuable when the party running the auction (both in buy and sell auctions) is

This paper analyzes symmetric, single item auctions in the private values framework, with buyers whose preferences satisfy the axioms of Yaari’s (1987) dual theory of choice under risk. It is shown that when their valuations are independently distributed, risk averse buyers are indifferent among all the auctions contained in a big family of mechanisms that includes the standard auctions. It is also shown that in the linear equilibria of the sealed bid double auction, as the degree of players ’ risk aversion grows arbitrarily large, the ex post inefficiency of the mechanism tends to vanish. Journal of Economic Literature classification numbers: D44; D81.