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 studies bidder collusion with communication in repeated auctions when no side transfer is possible. It presents a simple dynamic bid rotation scheme with co-ordinates bids based on communication history and enables intertemporal transfer of bidders’ payoffs. The paper derives a sufficient condition for such a dynamic scheme to be an equilibrium and characterises the equilibrium payoffs in a general environment with affiliated signals and private or interdependent values. With IPV, it is shown that this dynamic scheme yields a strictly higher payoff to the bidders than any static collusion scheme which co-ordinates bids based only on the current reported signals.

This paper describes the signaling that occurred in many of the FCC spectrum auctions. The FCC's simultaneous ascending auctions allowed bidders to bid on numerous communication licenses simultaneously, with bidding remaining open on all licenses until no bidder was willing to raise the bid on any license. Simultaneous open bidding allowed bidders to send messages to their rivals, telling them on which licenses to bid and which to avoid. This "code bidding" occurs when one bidder tags the last few digits of its bid with the market number of a related license. Such bids can help bidders coordinate a division of the licenses, and enforce the proposed division through targeted punishments. Often the meaning of a bid is clear without attaching a market number in the trailing digits. Such a "retaliating bid" need not end in a market number to warn off a rival from a contested market. We examine how extensively bidders signaled each other with retaliating bids and code bids in the DEF-block ...

In reviewing the theoretical and empirical literature on collusion, this paper distills methods for detecting cartels and distinguishing collusion from competition.

We propose a semi-cooperative game theoretic approach to check whether a given coalition is stable in a Bayesian game with independent private values. The ex ante expected utilities of coalitions, which are achieved at an incentive compatible (noncooperative) coalitional equilibrium, describe a (cooperative) partition form game. A coalition is core-stable if the core of a specific characteristic function, derived from the partition form game, is not empty. As an application, we study collusion in auctions in which the bidders’ final utility possibly depends on the winner’s identity. We show that such direct externalities offer a possible explanation for cartels’ structures (not) observed in practice.

Abstract: We study the formation of supplier coalitions in the context of a buyer-centric procurement market. Considered under a second-price descending seal-bid auction, we propose a two-stage auction mechanism that allows suppliers to form coalitions with one another. Building on the foundations of core games and bidding-rings, we explore the idea of “managed collusion ” which provides a means to enhancing bidder profitability. We identify six basic requirements for a valid coalition mechanism including characteristics such as individual rationality, welfare compatibility, maintaining competition, and financial balancedness. We show that such mechanism could be constructed so that the buyer does not loose the advantage from supplier competition, and that a stable coalition structure could be formed. We propose a profit distribution scheme among members in the supplier coalition and show that the proposed scheme provides proper incentive such that (1) the best strategy for a coalition member is to comply with the coalition agreement, and (2) bidding the true cost is the best strategy so long as the bids are uniformly distributed and the bidder’s cost is above a certain threshold. We also investigate the stable coalition structure under the proposed mechanism and show that under symmetric information there exists one unique strongly stable coalition structure.

We study an optimal collusion-proof auction in an environment where subsets of bidders may collude not just on their bids but also on their participation. Despite their ability to collude on participation, informational asymmetry facing the potential colluders can be exploited significantly to weaken their collusive power. The second-best auction — i.e., the optimal auction in a collusion-free environment — can be made collusion-proof, if at least one bidder is not collusive, or there are multiple bidding cartels, or the second-best outcome involves a nontrivial probability of the object not being sold. In case the secondbest outcome is not weak collusion-proof implementable, we characterize an optimal collusion-proof auction. This auction involves nontrivial exclusion of collusive bidders — i.e., the object is not sold to any collusive bidder with positive probability.

comments. Eddie Dekel and three anonymous referees from Econometrica provided insightful comments that greatly enhanced the paper. We analyze bidder collusion at first-price and second-price auctions. Our focus is on less than all-inclusive cartels and collusive mechanisms that do not rely on auction outcomes. We show that cartels that cannot control the bids of their members can eliminate all ring competition at second-price auctions, but not at first-price auctions. At first-price auctions, when the cartel cannot control members ’ bids, cartel behavior involves multiple cartel bids. Cartels that can control bids of their members can suppress all ring competition at both second-price and first-price auctions; however, shill bidding reduces the profitability of collusion at first-price auctions.

In this paper, we study mergers in oral or second-price auctions and compare them to mergers in sealed-bid or rst-price auctions. We use an adaptation of the logit qualitative choice model to characterize the underlying bidder value distributions. In second-price auctions, this model has a closed-form relationship between winning bids (prices) and the probabilities of winning (shares), and this relationship gives rise to a Her ndahl-like formula that predicts merger e ects. We compare mergers in second-price auctions to mergers in rst-price auctions. Despite their di erences, sealed-bid merger e ects are predicted by the oral Her ndahl-like formula. The source of this curious similarity is not apparent.

This paper provides an explanation for why cartels are not observed frequently in mineral-rights auctions even though it was not illegal for them to form. We use the techniques of mechanism design to characterize the e±cient, incentive compatible cartel and show that it can be implemented by a ¯rstprice knockout tournament with information sharing. We show, however, that bidders with the highest signals typically prefer to bid alone rather than join the cartel. We examine bid data from federal o®shore oil and gas auctions for evidence that cartels used bid coordination schemes. We also examine the determinants of joint bidding. 1