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 have emerged as the primary means of assigning spectrum licenses to companies wishing to provide wireless communication services. Since July 1994, the Federal Communications Commission (FCC) has conducted 33 spectrum auctions, assigning thousands of licenses to hundreds of firms. Countries throughout the world are conducting similar auctions. I review the current state of spectrum auctions. Both the design and performance of these auctions are addressed.

This paper is an economist's guide to the recent phenomenon of auctions taking place on the Internet. I present a brief history of the development of Internet auctions as a type of electronic commerce, and give the results of an extensive survey of 142 different auction sites operating during autumn 1998. I estimate the size distribution of the sites, and find that revenues at the largest sites have been growing at more than 10% per month in 199899. Other issues addressed here include the business models the auction sites use, what goods they offer for sale, and what kinds of auction mechanisms they use. These new Internet auction institutions pose questions for economic theory, and give opportunities where auction theory might be used to improve Internet auctions in practice. I also present detailed data on the 1999 competition between the large incumbent eBay and the recent well-funded entrants Yahoo! and Amazon, and demonstrate that the different types of fees charged by auctioneers...

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.

This paper analyzes six spectrum auctions conducted by the Federal Communications Commission (FCC) from July 1994 to May 1996. These auctions were simultaneous multipleround auctions in which collections of licenses were auctioned simultaneousl y. This auction form proved remarkably successful. Similar items sold for similar prices and bidders successfully formed efficient aggregations of licenses. Bidding behavior differed substantially in the auctions. The extent of bidder competition and price uncertainty played an important role in determining behavior. Bidding credits and installment payments also played a major role in several of the auctions. JEL No.: D44 (Auctions), L96 ( Telecommunications) Keywords: Auctions, Multi-Object Auctions, Spectrum Auctions Send comments to: Professor Peter C. Cramton Department of Economics University of Maryland College Park, MD 20742-7211 email: peter@cramton.umd.edu phone: (301) 405-6987 *I am grateful to the National Science Foun...

In this paper we present a new improved design for multi-object auctions and report on the results of experimental tests of that design. We merge the better features of two extant but very di#erent auction processes, the Simultaneous Multiple Round (SMR) design used by the FCC to auction spectrum and the Adaptive User Selection Mechanism (AUSM) of Banks, Ledyard, and Porter (1989). Then, by adding one crucial new feature, we are able to create a new design, the Resource Allocation Design (RAD) auction process, which performs better than both. Our experiments demonstrate, in both simple and complex environments, that the RAD auction achieves higher e#ciencies, lower bidder losses, and faster times to completion without increasing the complexity of a bidder's problem.

This paper proposes a new dynamic design for auctioning multiple heterogeneous commodities, generalizing earlier work that treated identical objects. An auctioneer wishes to allocate one or more units of each of K heterogeneous commodities to n bidders. The auctioneer announces a vector of current prices, bidders report back quantities demanded at these prices, and the auctioneer adjusts the prices. Units are credited to bidders at the current prices as their opponents ’ demands decline, and the process continues until every commodity market clears. Bidders, rather than being required to behave as price-takers, are permitted to strategically exercise their market power. Nevertheless, with pure private values, the proposed auction yields Walrasian equilibrium prices. An efficient outcome results, as from a Vickrey-Clarke-Groves mechanism, but bidders are only required to evaluate their demands along a one-dimensional path of prices, rather than reporting their utilities over the entire (K-dimensional) consumption set. The auction is also more transparent and potentially simpler for bidders to understand, and has the advantage of assuring the privacy of the upper portions of bidders ’ demands. Theoretically, the new auction provides a new foundation for convergence to Walrasian

Recent auction theory suggests that multi-unit uniform-price auctions, as used by the U.S. Treasury for debt sales, produce incentives that may cause bidders to bid less than their true valuations, resulting in inefficient allocations and reduced revenue. In this paper, we present the results of a field experiment in which we auction nearly $10,000 worth of sportscards in two-unit, two-person sealed-bid auctions. We randomize participants into uniform-price and Vickrey auction treatments, and find underbidding in the uniform-price auctions' second-unit bids, as predicted. In contrast with theoretical predictions, however, we find that individual's first-unit bids are significantly higher in the uniform-price than in the Vickrey treatment. The bid differences are large enough to affect the allocation of goods, as split allocations result significantly more often in the uniform-price treatment. We find no significant difference in revenues across auction formats.

We experimentally investigate the sensitivity of bidders demanding multiple units of a homogeneous commodity to the demand reduction incentives inherent in uniform price auctions. There is substantial demand reduction in both sealed bid and ascending price clock auctions with feedback regarding rivals’ drop-out prices. Although both auctions have the same normal form representation, bidding is much closer to equilibrium in the ascending price auctions. We explore the behavioral process underlying these differences along with dynamic Vickrey auctions designed to eliminate the inefficiencies resulting from demand reduction in the uniform price auctions. Key words: multi-unit demand auctions, uniform price auction, dynamic Vickrey auction, demand reduction, experiment.

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