We consider parametric examples of two-bidder private value auctions in which each bidder observes her own private valuation as well as noisy signals about her opponent’s private valuation. In such multidimensional private value auction environments, we show that the revenue equivalence between the first and second price auctions breaks down and there is no definite revenue ranking; while the second price auction is always efficient allocatively, the first price auction may be inefficient and the inefficiency may increase as the signal becomes more informative; equilibria may fail to exist for the first price auction. We also show that auction mechanisms provide different incentives for bidders to acquire costly information about opponents ’ valuation.

Target firms are often faced with bidders that are not equally well informed. This reduces the competition between the bidders, since a less well informed bidder fears the winner’s curse more. We analyze how a target should optimally be sold in the presence of asymmetric bidders. We show that a sequential procedure can extract the highest possible transaction price. The target first offers an exclusive deal to a better informed bidder, without considering a less well informed bidder. If rejected, the target either offers an exclusive deal to the less well informed bidder (now ignoring the better informed bidder), or it encourages every bidder to participate in a modified first-price auction. We discuss the key factors that affect the optimal procedure, how deal protection devices can mitigate commitment problems, and also some empirical implications.

Differences in cost efficiency and productivity across firms may introduce asymmetries in procurement auctions. Relying on a structural approach, this article investigates potential asymmetry among firms bidding for snow removal contracts in Montreal. The empirical results show that firms located in close proximity have a cost advantage relative to other firms in the most urbanised part of Montreal because of prohibitive equipment storage costs. The extent of inefficiency due to asymmetry is empirically assessed. Various policy experiments are performed. A bidding preference policy shows that the city could expect to reduce its costs for allocating snow removal contracts. When biddersÕ willingness to pay depends in part on observable variables, the principal’s interest is not best served by creating a level auction playing field. This article studies procurement auctions for snow removal contracts in Montreal. It investigates the degree to which companies in disadvantageous locations should win even if they do not submit the lowest bid. From the submitted bids, a novel empirical methodology estimates the extent of cost variation across firms along with its variation within location. Although the dispersion is substantial, the gain from treating bidders unequally is limited.

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Auctions used to sell houses often attract a diverse group of bidders, with realtors and speculators out for a bargain competing against buyers with a real interest in the house. Value asymmetries such as these necessitate careful consideration of the auction format as revenue equivalence cannot be expected to hold. From a theoretical viewpoint, Myerson’s (1981) mechanism design approach has identified the seller’s optimal choice. The proposed mechanism entails assigning credits to weaker bidders to promote competition and setting bidder-specific reserve prices. In practice, however, sellers often lack the detailed information needed to choose credits and reserve prices optimally, nor can they always discriminate among bidders. A more practical solution to the seller’s problem is suggested by the "Amsterdam auction, " where a premium is offered to encourage weak bidders to compete aggressively. This auction format, which has been used to sell houses in Amsterdam for centuries, treats all bidders the same and does not rely on detailed information about their value-distributions. In this paper, we consider premium auctions like the one in Amsterdam and demonstrate their revenue-generating virtues in asymmetric situations. We report the

We study …first-price auctions in a model with asymmetric, independent private values. Asymmetries lead to inefficient allocations thereby creating a motive for resale after the auction is over. In our model, resale takes place via monopoly pricing the winner of the auction makes a take-it-or-leave-it offer to the loser. Our goal is to compare equilibria of the fi…rst-price auction without resale (FPA) with those of the fi…rst-price auction with resale (FPAR). For the three major families of distributions for which equilibria of the FPA are available in closed form, we show that resale possibilities increase the revenue of the original seller. We also show by example that, somewhat paradoxically, resale may actually decrease efficiency.

Collusion is a serious problem in many procurement auctions. In this research, I study a model of rst price sealed bid procurement auctions with asymmetric bidders. I demonstrate that the equilibrium to the model is unique and describe three algorithms that can be used to compute the inverse equilibrium bid functions. I then use the computational algorithms to compare competitive and collusive bidding. The algorithms are useful for structural estimation of auction models and for assessing the damages from bid-rigging. 1 This is a revision of Chapter 2 of my 1997 University of Minnesota Ph.D. dissertation. Thanks to Bob Marshall for a very helpful conversation at the start of this research. Also thanks to my advisors John Geweke and Andy McLennan for encouragement. Ken Judd, 3 anonymous referees and seminar participants at numerous universities provided very useful criticism. I alone, however, am responsible for any remaining errors and omissions. 1 1 Introduction. Bid-rigging is a serious problem in many procurement auctions. According to Pesendorfer (1995), bid-rigging ac-counts for 50 percent of the cases led by the Justice Department’s anti-trust division that result in a criminal convic-

We consider a model of preference in an asymmetric procurement auction with two suppliers. The buyer can award the contract to a preferred supplier at the bid of a competing supplier. As such, the preferred supplier has a right-of-first-refusal. The preferred supplier may be an independent firm who has paid for the preference or may be a subsidiary of the buyer. Preference creates an allocative distortion that is qualitatively different than the distortion that arises in an asymmetric first-price auction. For a family of power distributions on the costs, we examine the effects of preference on the expected price paid by the buyer. If the buyer is not compensated for the preference, the expected price in the preference auction will be higher than either an efficient auction or a first-price auction. However, if the buyer can sell preference in a pre-auction, the net expected price will always be lower than an efficient auction, or even the first-price auction. The stronger supplier with the more favorable cost distribution has a greater willingness to pay for preference, and will outbid the weaker supplier to acquire the preference in the pre-auction. Similarly, the buyer can lower the net expected price by acquiring the stronger supplier as a preferred subsidiary. Martin would like to acknowledge the financial support of the Instituto de Analisis Economico (IAE, Institute for

In this paper, we propose a new approach to analyzing asymmetric 6rst price auctions. Specifically, we examine winning probabilities, exploiting the connection between winning probabilities and payoffs known from mechanism design. This circumvents the need to look directly at bidding strategies, which are generally complex. We derive new results, and more easily prove almost all existing results. The approach also sheds light on hitherto unexamined types of asymmetry. Specifically, we consider auctions with predictable and unpredictable buyers. Moreover, the method also applies to asymmetric all-pay auctions, where all buyers pay their own bid, and about which little is currently known.

romanh at cs dot ubc dot ca The use of sampling is investigated for computing equilibrium bidding strategies in auctions. An algorithm is proposed that requires minimal assumptions on the agents. In this paper we concentrate on asymmetric auctions with independent bidder valuations, however the approach is extendable to other scenarios, for example having bidders with different risk attitudes. Results are presented and the performance of the algorithm is discussed.