Almost Common Value Auctions: An Experiment

In almost common value auctions one bidder has a higher (private) value for the item than the other bidders. Theory predicts that even a small private value advantage can have an explosive effect in English auctions, with advantaged bidders always winning and sharp decreases in revenue. These predictions fail to materialize for experienced bidders who have learned to avoid the worst effects of the winner's curse. Bidding is better characterized as proportional, with advantaged bidders tending to bid as in a pure common value auction after adding their private value advantage to their estimated value of the item.     

Optimal auctions for asymmetrically budget constrained bidders

We consider an environment with a single divisible good and two bidders. The valuations of the bidders are private information but one bidder has a commonly known budget constraint. For this environment we derive the revenue maximizing subsidy free dominant strategy incentive compatible auction.      

Keyword auctions with budget-constrained bidders

We study a keyword auction model where bidders have constrained budgets. In the absence of budget constraints, Edelman et al. (Am Econ Rev 97(1):242–259, 2007) and Varian (Int J Ind Organ 25(6):1163–1178, 2007) analyze “locally envy-free equilibrium” or “symmetric Nash equilibrium” bidding strategies in generalized second-price auctions. However, bidders often have to set their daily budgets when they participate in an auction; once a bidder’s payment reaches his budget, he drops out of the auction. This raises an important strategic issue that has been overlooked in the previous literature: Bidders may change their bids to inflict higher prices on their competitors because under generalized second-price, the per-click price paid by a bidder is the next highest bid. We provide budget thresholds under which equilibria analyzed in Edelman et al. (Am Econ Rev 97(1):242–259, 2007) and Varian (Int J Ind Organ 25(6):1163–1178, 2007) are sustained as “equilibria with budget constraints” in our setting. We then consider a simple environment with one position and two bidders and show that a search engine’s revenue with budget constraints may be larger than its revenue without budget constraints.     

Bundling and the Reduction of the Winner's Curse

The paper studies the effects of bundling on the bidding strategies and seller revenues in auctions when the bidders have common values for the objects. Bundling of objects before the auction reduces the problem of the winner's curse, and the bidders bid more aggressively. This does not mean that a bundled auction is always better for the seller's revenue. Indeed, there is another effect that makes the bundled auction preferable (from the seller's standpoint) if and only if the number of bidders is small. While this is the only effect present in an independent-private-values model, it does not vanish when bidders have pure common values for the objects. The paper concludes that a bundled auction is unambiguously better for the seller than separate auctions when the number of bidders is small.     

Competitive bidding and proprietary information

We consider the sale of an object by sealed-bid auction, when one bidder has private information and the others have access only to public information. The equilibria of the bidding game are determined, and it is shown that at equilibrium the informed bidder's distribution of bids is the same as the distribution of the maximum of the others' bids. The expected profit of the informed bidder is generally positive, while the other bidders have zero expected profits. The equilibrium bid distributions and the bidders' expected profits are shown to vary continuously in the parameters of the bidding game.     

Anticipation of Auction Fever: Entry Decision,Reserve Price and the Choice of Auction Design

This paper analyzes the entry decision of rational bidders who expect to experience auction fever in English auctions. It shows that nonparticipation decision reduces seller's expected profit and this effect may outweigh the positive effect of the auction fever. We analyze the choice between English and second‐price sealed‐bid auctions and the optimal reserve price in English auctions. We show that it might be optimal for the seller to set a reserve price below her own valuation of the object. Finally, we show that the order in which bidders place their bids matters and the first bidder always has an advantage. Copyright © 2011 John Wiley & Sons, Ltd.     

First-price auctions where one of the bidders’ valuations is common knowledge

We analyze a private and independent valuation first-price auction under the assumption that one of the bidders’ valuations is common knowledge. We show that no pure strategy equilibrium exists and we characterize a mixed strategy equilibrium in which the bidder whose valuation is common knowledge randomizes her bid while the other bidders play pure strategies. In an example with the uniform distribution, we compare the expected profits of seller and buyers in this auction with those in a standard symmetric private valuation model.     

Optimal disclosure of costly information packages in auctions

In an independent, private values, second-price auction with entry fees we discuss the way in which a seller should optimally spread costly information among the bidders. We find that marginal gross revenues do not generally behave monotonically in total information release. In the two bidder case, essentially, any asymmetric allocation of information dominates the symmetric information allocation. Even the bidder who gets less information is willing to pay a higher entry fee for asymmetric information allocations than for the symmetric one. His entry fee coincides with that of the better informed bidder. Losses from allocating an amount of information non-optimally can be substantial.     

Econometric models of asymmetric ascending auctions

We develop econometric models of ascending (English) auctions which allow for both bidder asymmetries as well as common and/or private value components in bidders’ underlying valuations. We show that the equilibrium inverse bid functions in each round of the auction are implicitly defined (pointwise) by a system of nonlinear equations, so that conditions for the existence and uniqueness of an increasing-strategy equilibrium are essentially identical to those which ensure a unique and increasing solution to the system of equations. We exploit the computational tractability of this characterization in order to develop an econometric model, thus extending the literature on structural estimation of auction models. Finally, an empirical example illustrates how equilibrium learning affects bidding during the course of the auction.     

The public release of information in first-price sealed-bid auctions

We determine the conditions under which the seller in a first-price sealed-bid auction has an incentive to reveal his private information about the mean of bidders’ valuations in order to increase his expected revenue. With risk-neutral bidders, we show that the seller’s expected revenue is higher when information is revealed. However, when bidders are risk-averse, this result does not necessarily hold; it depends on the bidders’ risk-aversion level and on the number of bidders.     

Dominance solvability of second-price auctions with differential information

We study a class of common-value second-price auctions with differential and finite information. This class is characterized by the property that each bidder’s information set is connected with respect to the common value. We show that the entire class is dominance solvable, and that there is a natural single-valued selection from the resulting set of sophisticated equilibria. Additionally, it is shown that bidder’s information advantage over other bidders is rewarded in sophisticated equilibria.     

Synergies in Wireless Telephony: Evidence from the Broadband PCS Auctions

We examine bid data from the first two broadband PCS spectrum auctions for evidence of value synergies. First, we estimate a benchmark regression for the determinants of final auction prices. Then, we include variables reflecting the extent to which bidders ultimately won or already owned the adjacent wireless properties. Consistent with geographic synergies in an ascending-bid auction, prices were higher when the highest losing bidder had adjacent licenses. The footprints of winning bidders suggest that they were often successful in realizing these synergies.     

Econometrics of first-price auctions with entry and binding reservation prices

This paper considers the structural analysis of first-price auctions with entry and binding reservation prices. The presence of entry decisions and binding reservation prices complicates the structural analysis. Building on the recent theoretical work on entry in auctions, this paper assumes that each potential bidder first decides whether or not to incur an entry cost and become an active bidder using a symmetric mixed strategy. Then each active bidder bids optimally following the increasing Nash–Bayesian equilibrium strategy. Using the observed bids and the number of actual bidders, we propose an MSM estimator to estimate the parameters in the distribution of private values and the distribution of the number of active bidders. Our approach can be used to validate the theoretical auction model, to test whether the reservation prices are binding, and to test the mixed-strategy of entry.     

Second-Price Auctions with Asymmetric Payoffs: An Experimental Investigation

A series of two-player, second-price common-value auctions are reported. In symmetric auctions, bidders suffer from a winner's curse. In asymmetric auctions in which one bidder has a private value advantage, the effect on bids and prices is proportional rather than explosive (the prediction of Nash equilibrium bidding theory). Although advantaged bidders are close to making best responses to disadvantaged bidders, the latter bid much more aggressively than in equilibrium, thereby earning negative average profits. Experienced bidders consistently bid closer to the Nash equilibrium than inexperienced bidders, although these adjustments towards equilibrium are small and at times uneven.     

Core-stable rings in second price auctions with common values

In a common value auction in which the information partitions of the bidders are connected, all rings are core-stable. More precisely, the ex ante expected utilities of rings, at the (noncooperative) sophisticated equilibrium proposed by Einy et al. [Einy, E., Haimanko, O., Orzach, R., Sela, A., 2002. Dominance solvability of second-prices auctions with differential information. Journal of Mathematical Economics 37, 247–258], describe a cooperative games in characteristic function form, in spite of the underlying strategic externalities. A ring is core-stable if the core of this characteristic function is not empty. Furthermore, every ring can implement its sophisticated equilibrium strategy by means of an incentive compatible mechanism. An example shows that, if the bidders’ information partitions are not connected, rings may no longer be core-stable.     

Advertising a second-price auction

This study examines a symmetric private-value second-price auction model in which the seller solicits bidders at a cost, sets a reserve price, and receives a payoff which is a convex combination of revenue and welfare. The bidder’s valuations are drawn from a distribution with a decreasing hazard rate and non-decreasing virtual valuations. We find that at equilibrium the seller adopts an advertising policy which minimizes the uncertainty over the number of participants, and sets a reserve price which only depends on the distribution of valuations and the weight on revenue in the objective function. A welfare-maximizing seller is shown to advertise more than a revenue-maximizing seller, and a ceteris paribus increase in the advertising level is proved to increase the expected winner’s rent.     

Who else is bidding? The Pareto optimality of disclosing bidder identities

This paper examines whether the seller of an object should reveal the identities of the participating bidders before bids become due. It is shown that when bidders experience identity dependent externalities and auction participation is exogenous, then for a large class of standard auction mechanisms, a policy of revelation serves to realize a higher surplus because it improves the accuracy of each bidder's estimate of her ex-post willingness-to-pay, and therefore changes the auction allocation in a more ex-post efficient manner. Furthermore, it is shown that the policy of revelation increases both the expected seller revenues as well as ex-ante expected bidder payoffs. Received: 4 February 2000 / Accepted: 15 November 2000 An earlier version of this paper had the title 'Disclosure of Bidder Identities'. I thank an anonymous referee and an Associate Editor for suggestions that improved the paper. I also acknowledge comments made by participants of the Auctions session during the North American Winter Meetings of the Econometric Society 2001 held in New Orleans. I remain solely responsible for any errors.     

Ranking reversals in asymmetric auctions

This paper compares the first-price auction and the second-price auction with several asymmetric bidders who are either weak or strong. The ranking of these auctions in terms of profit may flip as the exogenous reserve price or the number of weak or strong bidders change. Similarly, with endogenous reserve prices the ranking may depend on the seller’s own-use valuation. In other words, the ranking may be fragile to changes along these dimensions. Existing models rule out such ranking reversals by imposing substantial structure on type distributions. The current paper relies on simple mechanism design arguments that require less structure.     

Creating a winner’s curse via jump bids

We show that jump bids can be used by a bidder to create a winner’s curse and preserve an informational advantage that would otherwise disappear in the course of an open ascending auction. The effect of the winner’s curse is to create allocative distortions and reduce the seller’s expected revenue. Two novel features of equilibrium jump bids are derived. First, the jump bid may fail to hide completely the value of the common value component. Second, a bidder with a higher type might jump bid less frequently than a bidder with a lower type.     

Efficiency and information aggregation in auctions with costly information

Consider an auction in which k identical objects are sold to n > k bidders who each have a value for one object which can have both private and common components to it. Private information concerning the common component of the object is not exogenously given, but rather endogenous and bidders face a cost to becoming informed. If the cost of information is not prohibitively high, then the equilibrium price in a uniform price auction will not aggregate private information, in contrast to the costless information case. Moreover, for a wide class of auctions if the cost of information is not prohibitively high then the objects can only be allocated in a weakly efficient sense, and then only if the equilibrium proportion of endogenously informed agents is vanishing as the economy grows. In spite of these results, it is shown that there is a mechanism for which there exist equilibria and for which (weak) efficiency is achieved as the economy grows in the face of endogenous information acquisition.Received: 6 August 2001, Accepted: 27 July 2002, JEL Classification: C72, D44, D82Financial support under NSF grant SBR-9507912 is gratefully acknowledged. I thank Valentina Bali for conversations out of which this project grew, and Larry Ausubel for a very helpful discussion of an early version of this paper at the 1998 summer meetings of the Econometric Society from which I have borrowed in structuring the exposition of the paper. I also thank Andy Postlewaite, Jeroen Swinkels, and an associate editor and anonymous referee for helpful comments and suggestions on earlier drafts.