Within the heterogeneous IPV model, we analyze bidder collusion at first-price and second-price auctions, allowing for within-cartel transfers. Our focus is on cartels that contain a strict subset of all bidders and collusive mechanisms that do not rely on information from the auctioneer, such as the identity of the winner or the amount paid. We show that when a cartel cannot control the bids of its members, it can eliminate all competition among its members at a second-price auction, but not at a first-price auction. At a first-price auction, when the cartel cannot control its members’ bids, cartel behavior is characterized by multiple cartel bids that are different but very close to one another. This finding has important empirical implications. If a cartel can control the bids of its members, it can suppress all ring competition at both a second-price and a first-price auction; however, if shill bidding is feasible, then a cartel at a first-price auction does no better than one that cannot control its members’ bids.

We study a duopoly model of investment, in which each player learns about the quality of a common value project by observing some public background information, and possibly the experience of his rival. Investment costs are private information, and the background signal takes the form of a Poisson process conditional on the quality of the project being low. The resulting attrition game has a unique, symmetric equilibrium, which depends on initial public beliefs. We determine the impact of changes in the cost and signal distributions on investment timing, and how equilibrium is affected when a first-mover advantage is introduced. JEL classification: C73; D82; D83

The existence of collusion and heterogeneity across firms is known to introduce some asymmetry in bidding games. A major difficulty when considering asymmetric auctions is that the equilibrium strategies are solutions of an intractable system of differential equations. This paper proposes a simple method for estimating asymmetric first-price auctions within the affiliated private values (APV) paradigm. Specifically, we consider two types of bidders and derive the differential equations characterizing the Bayesian Nash equilibrium strategies. We show that these differential equations can be rewritten using the distribution of observed bids.

Abstract. We study entry and bidding patterns in sealed bid and open auctions. Using data from U.S. Forest Service timber auctions, we document a set of systematic e¤ects: sealed bid auctions attract more small bidders, shift the allocation towards these bidders, and can also generate higher revenue. A private value auction model with endogenous participation can account for these qualitative e¤ects of auction format. We estimate the model’s parameters and show that it can explain the quantitative e¤ects as well. We then use the model to assess bidder competitiveness, which has important consequences for auction design. We thank the editor Larry Katz and the referees for very helpful suggestions, and also Phil Haile, Jerry

We consider an augmented version of the symmetric private value auction model with independent types. The augmentation, intended to illustrate reality, concerns information bidders have about their opponents. To the standard assumption that every bidder knows his type and the distribution of types is common knowledge we add the assumption that the ranking of bidders' valuations is common knowledge. This set{up induces a particular asymmetric auction model that raises serious technical difficulties. We prove existence and uniqueness of equilibrium in pure strategies in the two bidder case. We also show that the model generally has no analytic solution. If the distribution of valuations is uniform, both bidders bid pointwise more aggressively relative to the standard symmetric case. However, this property does not apply to all distributions of valuations. Finally, we also provide a numerical solution of equilibrium bid functions for the uniform distribution case.

early stage with this research. Paul Milgrom, Steve Tadelis and Steve Brenner also provided very useful comments on various parts of this work. Pueo Keffer provided outstanding research assistance. All remaining errors are our own. * * Stanford University Collusion is an agreement among a group of firms, called a cartel, designed to limit competition among the participants. If all firms in the cartel follow the agreement, buyers will face higher prices, giving the cartel members profits above the normal competitive level. State and Federal Statutes have proscribed such agreements to protect consumers from collusive behavior, and

Economic theory is often abused in practical policy-making. There is frequently excessive focus on sophisticated theory at the expense of elementary theory; too much economic knowledge can sometimes be a dangerous thing. Too little attention is paid to the wider economic context, and to the dangers posed by political pressures. Superficially trivial distinctions between policy proposals may be economically significant, while economically irrelevant distinctions may be politically important. I illustrate with some disastrous government auctions, but also show the value of economic theory.

We consider discriminatory auctions for multiple identical units of a good. Players have private values, possibly for multiple units. None of the usual assumptions about symmetry of players ' distributions over values or symmetry of equilibrium play are made. Because of this, equilibria will typically involve inefficient allocations. Equilibria also become very difficult to solve for. Using an approach which does not depend on explicit equilibrium calculations we show that such auctions become arbitrarily close to efficient as the number of players, and possibly the number of objects, grows large, and provide a simple characterization of limit equilibria. 1.

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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.