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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Abstract. Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a difficult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard for combinatorial auctions, the Generalized Vickrey Auction (GVA). Traditional analysis of these mechanisms—in particular, their truth revelation properties—assumes that the optimization problems are solved precisely. In reality, these optimization problems can usually be solved only in an approximate fashion. We investigate the impact on such mechanisms of replacing exact solutions by approximate ones. Specifically, we look at a particular greedy optimization method. We show that the GVA payment scheme does not provide for a truth revealing mechanism. We introduce another scheme that does guarantee truthfulness for a restricted class of players. We demonstrate the latter property by identifying natural properties for combinatorial auctions and showing that, for our restricted class of players, they imply that truthful strategies are dominant. Those properties have applicability beyond the specific auction studied.

The US government recently sold spectrum rights using an innovative auction design, the simultaneous ascending auction, invented by economic theorists. The auction outcomes were broadly consistent with the expectations of the theorists. The auction form should have many other applications. March 21, 1998 Just as the Nobel committee was recognizing game theory's role in economics by awarding the 1994 prize to John Nash, John Harsanyi, and Reinhard Selten, game theory was being put to its biggest use ever. Billions of dollars worth of spectrum licenses were being sold by the US government, using a novel auction form designed by economic theorists. Suddenly, game theory became news. William Safire in the New York Times called it "the greatest auction in history." The Economist remarked, "When government auctioneers need worldly advice, where can they turn? To mathematical economists, of course . . . As for the firms that want to get their hands on a sliver of the airwaves, their best bet is to go out first and hire themselves a good game theorist." Fortune said it was the "most dramatic example of game theory's new power . . . It was a triumph, not only for the FCC and the taxpayers, but also for game theory (and game theorists)." Forbes said, "Game theory, long an intellectual pastime, came into its own as a business tool." The Wall Street Journal said, "Game theory is hot." The government auctioned licenses to use the electromagnetic spectrum for personal communications services (PCS): mobile telephones, two-way paging, portable fax machines, and wireless computer networks. Thousands of licenses were offered, varying in both geographic coverage and the amount of spectrum covered. The bidders were the local, long-distance, and cellular telephone companies, as well as...

Online auctions have recently gained widespread popularity and are one of the most successful forms of electronic commerce. We examine a dataset of eBay coin auctions to explore features of online bidding and selling behavior. We address three main issues. First, we measure the extent of the winner’s curse. We find that for a representative auction in our sample, a bidder’s expected profits fall by 3.2 percent when the expected number of bidders increases by one. Second, we document that costly entry is a key component in understanding observed bidding behavior. For a representative auction in our sample, a bidder requires $3.20 of expected profit to enter the auction. Third, we study the seller’s choice of reserve prices. We find that items with higher book value tend to be sold using a secret as opposed to posted reserve price with a low minimum bid. We find that this is, to a first approximation, consistent with maximizing behavior. We also develop new techniques for structurally estimating common value auction models. 1

Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes and furniture. Because of complementarities (or substitution effects) between the different assets, bidders have preferences not just for particular items but for sets or bundles of items. For this reason, economic efficiency is enhanced if bidders are allowed to bid on bundles or combinations of different assets. This paper surveys the state of knowledge about the design of combinatorial auctions. Second, it uses this subject as a vehicle to convey the aspects of integer programming that are relevant for the

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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.

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...