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.

Economists have lately been called upon not only to analyze markets, but to design them. Market design involves a responsibility for detail, a need to deal with all of a market’s complications, not just its principle features. Designers therefore cannot work only with the simple conceptual models used for theoretical insights into the general working of markets. Instead, market design calls for an engineering approach. Drawing primarily on the design of the entry level labor market for American doctors (the National Resident Matching Program), and of the auctions of radio spectrum conducted by the Federal Communications Commission, this paper makes the case that experimental and computational economics are natural complements to game theory in the work of design. The paper also argues that some of the challenges facing both markets involve dealing with related kinds of complementarities, and that this suggests an agenda for future theoretical research.

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...

William Vickrey's predicted equivalences between first-price sealed-bid and Dutch auctions, and between second-price sealed-bid and English auctions, are tested using field experiments that auctioned off collectible trading cards over the Internet. The results indicate that the Dutch auction produces 30 percent higher revenues than the first-price auction format, a violation of the theoretical prediction and a reversal of previous laboratory results, and that the English and second -price formats produce roughly equivalent revenues. (JEL C93, D44) Forthcoming, American Economic Review Department of Economics, 415 Calhoun Hall, Vanderbilt University., Nashville, TN 37235 (Email: reiley@vanderbilt.edu) Although I financed the actual experiments myself while a graduate student, I very gratefully acknowledge the financial support of the National Science Foundation, grant SBR-9811273, for subsequent work on this paper. I wish to thank Marius Hauser and Mary Lucking-Reiley for their research assistance, and Skaff Elias for product information about Magic: the Gathering. I am grateful to an anonymous referee, Orley Ashenfelter, Ann Bell, Jim Cox, Rachel Croson, Ron Harstad, Elton Hinshaw, John List, Preston McAfee, Jennifer Reinganum, Bill Sethares, Vernon Smith, David Wildasin, participants at the Economic Science Association annual meetings, and especially Glenn Ellison, for their advice and constructive criticism.

The Vickrey auction has been widely advocated for multiagent systems. First we review its limitations so as to guide practitioners in their decision of when to use that protocol. These limitations include lower revenue than alternative protocols, lying in non-private-value auctions, bidder collusion, a lying auctioneer, and undesirable revelation of sensitive information. We discuss the special characteristics of Internet auctions: third party auction servers, cryptography, and how proxy agents relate to the revelation principle and fail to promote truth-telling.

The revenue-equivalence theorem 1 for auctions predicts that expected seller revenue is independent of the bidding rules, as long as equilibrium has the properties that the buyer with the highest reservation price wins and any buyer with the lowest possible reservation price has zero expected surplus. Thus, in particular, the two most common auction institutions- the open "English " auction and the sealed high-bid auction- are equivalent despite their rather different strategic properties. This strong prediction of equivalence seems at odds, however, with the empirical observation that rarely is any given kind of commodity sold through more than one sort of auction. Thus, for example, art is nearly always auctioned off according to the English rules, whereas job contracts are normally awarded through sealed bids. Admittedly, in the public sector, there have been a few attempts to use both methods (lumber contracts in the Pacific Northwest) or to switch from one to the other (Treasury Bills). But changes have typically met great resistance. This is also in conflict with theory, since a corollary of the revenue equivalence theorem is that the expected surplus for any buyer is the same in the two auctions.

If individuals care about their status, defined as their rank in the distribution of consumption of one “positional ” good, then the consumer’s problem is strategic as her utility depends on the consumption choices of others. In the symmetric Nash equilibrium, each individual spends an inefficientlyhighamountonthe status good. Using techniques from auction theory, we analyze the effects of exogenous changes in the distribution of income. In a richer society, almost all individuals spend more on conspicuous consumption, and individual utility is lower at each income level. In a more equal society, the poor are worse off. (JEL

This paper addresses several basic problems inspired by the adaptation of economic mechanisms, and auctions in particular, to the Internet.

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