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.

We develop general recursive methods to solve for optimal contracts in dynamic principal-agent environments with hidden states and hidden actions. Starting from a general mechanism with arbitrary communication, randomization, full history dependence, and without restrictions on preferences or technology, we show that the optimal contract can be implemented as a recursive direct mechanism. A curse of dimensionality which arises from the interaction of hidden income and hidden actions can be overcome by introducing utility bounds for behavior off the equilibrium path. Environments with multiple actions are implemented using multiple layers of such off-path utility bounds.

Firm-commitment offer prices are conditioned on information in the indications of interest solicited from prospective investors. When such information can be used to persuade some investors to purchase shares at a price in excess of their initial estimate of the fair value, underwriters have an incentive to overstate investor interest. Our analysis shows that this incentive is eliminated when the underwriter makes a commitment to secondary market price stabilization. Destroying the underwriter's incentive to overstate interest reduces the total surplus captured by initial investors in IPOs. Further efficiency gains are associated with penalty bid systems that permit the underwriter to make the stabilization commitment selectively. Price stabilization can thus be viewed as a bonding mechanism that improves the efficiency of the primary equity market. 2 Price Stabilization as a Bonding Mechanism in New Equity Issues 1. Introduction Why do investment banks routinely support the seconda...

you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at

The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. Auctions have been around for more than 2,000 years. The Babylonians arranged marriages by auction. The Roman legions sold booty at auction, and on one notable occasion, the Praetorian Guard killed the emperor and put up the whole empire for auction. Today, members of the general public sell at auction such diverse things as tobacco, fish, cut flowers, works of art, thoroughbred horses, and used cars. The U.S. government sells natural resources by auction and may soon take bids on radio airwaves and pollution rights. And in the largest auctions in recorded human history, the U.S. Treasury each year sells roughly $2.5 trillion worth of debt. With such large amounts at stake, even small improvements in the Treasury’s auction procedure can lead to large gains for taxpayers. In this paper,

We incorporate multiagent, principal-agent theory into general equilibrium analysis. The traded commodities are multiagent contracts that include a description of the individual’s job, effort level, and state-contingent consumption. These contracts are club goods. The competitive equilibrium and the Pareto program are formulated. The contracts are identified with firms, so the market determines which firms exist and who is assigned to which firm in what capacity. An example is provided in which the internal organization of firms and the distribution of firm classes vary with the aggregate capital endowment and its distribution across agents. A simplex-based algorithm for solving the Pareto program is developed. We would like to thank the referees, the editors, Bryan Ellickson, Lionel McKenzie, Suzanne Scotchmer, William Zame, and seminar participants from Alicante, Chicago,

Two auctions are held in sequence with the possibility of learning between the second and the first. The buyer optimally chooses to discriminate against the winner of the first auction in the second. The optimal mechanism has a discontinuity in the winner’s second bid; this strictly dominates a sequence of independent sealed bid auctions. 1.

Abstract: We present amodel of price discrimination where a monopolist faces a consumer who is privately informed about the distribution of his valuation for an indivisible unit of good but has yet to learn privately the actual valuation. The monopolist sequentially screens theconsumer with a menu ofcontracts: the consumer self-selects once by choosing a contract and then self-selects again when he learns the actual valuation. A deterministic sequential mechanism is a menu of refund contracts, eachconsisting ofanadvance payment and a refund amount incase of no consumption, but sequential mechanisms mayinvolve randomization. We characterize the optimal sequential mechanism when some consumer types are more eager in the sense of rst-order stochastic dominance, and when some types face greater valuation uncertainty inthesense of mean-preserving-spread. Weshow that it can be optimal to subsidize consumer types with smaller valuation uncertainty (through low refund, as in airplane ticket pricing) in order to reduce the rent tothose with greater uncertainty. The size of distortion depends both on the type distribution and on how informative theconsumer's initial private knowledge is about his valuation, but not on how much he initially knows about thevaluation per se. Acknowledgements: We would like tothank Mark Armstrong, Michael Chwe, Jim Peck, Sherwin Rosen, Lars Stole, Wing Suen, the Associate Editor and the referees for helpful comments. The Associate Editor and the referees also suggested that we investigate situations where rst-order stochastic dominance does not hold. {i

The literature on procurement auctions (reverse auctions) typically assumes that the suppli-ers are uncapacitated (see, e.g. Dasgupta and Spulber, 1990; Ankolekar et al., 2005; Chen, 2004; Che, 1993). Consequently, these auction mechanisms award the contract to a single supplier. We consider a model where suppliers have limited production capacity, and both marginal costs and the production capacities are private information. We construct the optimal direct mecha-nism that maximizes the retailer’s expected profit. We provide a closed-form solution when the distribution of the cost and production capacities satisfies a modified regularity condition (My-erson, 1981). We also present a sealed low bid implementation of the optimal direct mechanism for the special case of identical suppliers, i.e. symmetric environment. This implementation requires each supplier to submit a bid consisting of the desired marginal payment and total available production capacity. These bids serve as the input to a simple optimization problem that computes the quantity allocation for each firm. We extend the model to multi-product procurement with complementarities. The results in this paper are applicable to a number of principle-agent mechanism design problems where the agents have privately known upper bound on the allocations. Examples of such problems include monopoly pricing with adverse selection and forward auctions.

The literature on procurement auctions typically assumes that the suppliers are uncapacitated (see, e.g. Dasgupta and Spulber, 1990; Che, 1993). Consequently, these auction mechanisms award the contract to a single supplier. We study mechanism design in a model where suppliers have limited production capacity, and both the marginal costs and the production capacities are private information. We provide a closed form solution for the revenue maximizing direct mechanism when the distribution of the cost and production capacities satisfies a modified regularity condition (Myerson, 1981). We also present a sealed low bid implementation of the optimal direct mechanism for the special case of identical suppliers, i.e. symmetric environment. The results in this paper extend to other principle-agent mechanism design problems where the agents have a privately known upper bound on allocation. Examples of such problems include monopoly pricing with adverse selection and forward auctions.