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.

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...

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Abstract. This paper presents some of the key techniques for reaching agreements in multi-agent environments. It discusses game-theory and economics based techniques: strategic negotiation, auctions, coalition formation, market-oriented programming and contracting. It also presents logical based mechanisms for argumentations. The focus of the survey is on negotiation of self-interested agents, but several mechanisms for cooperative agents who need to resolve conflicts that arise from conflicting beliefs about different aspects of their environment are also mentioned. For space reasons, we couldn’t cover all the relevant works, and the papers that are mentioned only demonstrate the possible approaches. We present some of the properties of the approaches using our own previous work. 1

Auctions are a basic tool for resource allocation in non-cooperative environments. Much work in computer science, and in artificial intelligence in particular, has been concerned with algorithms for winner determination in auctions in order to maximize a designer's revenue.

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

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,

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.

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.

Agents may contract some of their tasks to other agent even when they do not share a common goal. An agent may try to contract some of the tasks that it cannot perform by itself, or that may be performed more efficiently by other agents. One selfmotivated agent may convince another self-motivated agent to help it with its task, by promises of rewards, even if the agents are not assumed to be benevolent. We propose techniques that provide efficient ways to reach contracting in varied situations: the agents have full information about the environment and each other or subcontracting when the agents do not know the exact state of the world. We consider situations of repeated encounters, cases of asymmetric information, situations where the agents lack information about each other, and cases where an agent subcontracts a task to a group of agents. Situations where there is competition among possible contracted agents or possible contracting agents are also considered. In all situations we ...