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.     

Information acquisition and/or bid preparation: A structural analysis of entry and bidding in timber sale auctions

Recently, several auction models with entry have been proposed: in one model ( and ), bidders are assumed to draw their private values after they decide to enter. In another model ( and ), bidders are assumed to learn their values before their entry decisions are made. The entry cost in the latter model can be interpreted as bid preparation cost, while the entry cost in the former model consists of both costs from information acquisition and bid preparation. Moreover, these two models have different implications for important policies, e.g., the optimal reserve price. In this paper we provide a unified structural framework where the two models can be estimated and distinguished using the Bayesian method. We apply our method to analyze Michigan timber sale auctions.     

Revenue equivalence and income taxation

This paper considers the classical independent private values model of auction theory in the presence of income taxation. We show that revenue equivalence remains valid if income taxes are proportional. Progressive and regressive taxes lead, in general, to asymmetries between bidders with the well-known consequence that revenue equivalence no longer holds. However, if symmetry of the bidders is maintained, progressive (regressive) income tax implies a higher (lower) expected revenue in first-price than in second-price auctions. Financial support by theDeutsche Forschungsgemeinschaft is gratefully acknowledge.     

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.     

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.     

Optimal auctions and information disclosure

We characterise properties of optimal auctions if the seller may disclose information about the quality of the object for sale. We show that the seller maximizes his expected revenue by revelation of all information to all bidders and implementing a second price auction with appropriate reservation price.     

Learning through Simultaneous Play: Evidence from Penny Auctions

This paper contributes to the emerging empirical literature on penny auctions, a particular type of all‐pay auctions. We focus on the potential learning effects that bidders may experience over time but also (and particularly) across auctions as a result of their auction participation. Using detailed bid‐level information, we find that, similarly to earlier literature, bidders suffer from a sunk cost fallacy, whereby their probability of dropping out of an auction is decreasing in the number of bids they have already placed in that auction. Although we do find that learning through repeated participation alleviates the sunk cost fallacy, participation in simultaneous penny auctions emerges as a much more effective learning mechanism, ultimately contributing toward bidders earning higher individual surpluses.     

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.     

Revenue comparison of discrete private-value auctions via weak dominance

We employ weak dominance to analyze both first-price and second-price auctions under the discrete private-value setting. We provide a condition under which the expected revenue from second-price auction is higher than that of first-price auction. We also provide implications for large auctions, including the “virtual” revenue equivalence.     

He who must not be named

Landsberger et al. have studied a sealed bid first price auction with two players in which the ranking of the valuations is known. They argue that such a situation can arise in a sequential auction where only the name of the winner is revealed. In this paper we consider sequential auctions where two identical goods are sold sequentially to N players who are interested in both objects. In sealed bid auctions, no information is a priori revealed by the mechanism, but the seller can in principle reveal whatever he wants. We restrict our attention to the case where only the name of the winner is revealed to be in the context of Landsberger et al. for the second auction. The aim of the paper is to compare such a sequential auction with a simultaneous auction where both goods are sold as a bundle or equivalently with a sequential auction where no information is revealed. We first show that there exists an equilibrium of the sequential game in pure and monotone strategies. Then, the comparison of the seller's expected revenue in the two cases allows us to conclude that contrary to Landsberger et al.'s predictions, the seller can not use the information to increase his revenue. This result is obtained using simulations for a large class of distribution functions. The seller must not reveal the name of the winner between the two auctions and instead sell both goods using a simultaneous auction.Received: 31 July 2001, Accepted: 5 February 2003, JEL Classification: B44I wish to thank Laurent Linnemer, Thomas Ricke, Michael Visser and Shmuel Zamir for helpful comments and suggestions. I am very grateful to the referees and the associated editors in charge of my paper.     

On the Sub-optimality of Entry Fees in Auctions With Entry

We study a variation of Myerson’s (1981) model in which we allow for uncertainty about the number of bidders. In our set-up, an appropriate reserve price in a standard auction maximizes the auctioneer’s expected revenue. However, entry fees can be optimal only under some special conditions. Basically, there must be some homogeneity in bidders’ beliefs about the number of bidders and the auctioneer must know, to some extent, these beliefs.     

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.     

Common value auctions with independent types

In this paper I consider a common value model, with independent types, where the ex-post value of the good is influenced by the bidders' information at the auction stage. The seller cannot fully extract the surplus. In a symmetric model the optimal mechanism can be implemented through first price, second price, or English auctions; but not through a Dutch auction. Other properties of the optimal auctions are that the seller's reservation price is endogenous, and that in sealed bid auctions the price may exceed the value of the object (winner's curse).     

The Buyer's Option in Multi-Unit Ascending Auctions: The Case of Wine Auctions at Drouot

This paper studies multi-unit ascending (English) auctions with a buyer's option. The buyer's option gives the winner of an auction the right to purchase any number of units at the winning price. We develop a theoretical model and derive the optimal strategies for the bidders. The model predicts various behavioral implications (e.g., the winner never exercises the option, the price declines…) that are tested using a unique data set on wine auctions held at the Paris-based auction house Drouot. We also analyze why the buyer's option is used. Estimating the model in a structural econometric way, and using counterfactual comparisons, we find that the buyer's option does not affect the seller's revenue (relative to a system where the units are auctioned sequentially without the option). Drouot, however, saves a lot of time with the option and this effect represents a considerable amount of money. The time-saving effect seems thus to be the primary purpose of the buyer's option.     

On the lowest-winning-bid and the highest-losing-bid auctions

Theoretical models of multi-unit, uniform-price auctions assume that the price is given by the highest losing bid. In practice, however, the price is usually given by the lowest winning bid. We derive the equilibrium bidding function of the lowest-winning-bid auction when there are k objects for sale and n bidders with unit demand, and prove that it converges to the bidding function of the highest-losing-bid auction if and only if the number of losers n−k gets large. When the number of losers grows large, the bidding functions converge at a linear rate and the prices in the two auctions converge in probability to the expected value of an object to the marginal winner.     

Synergies and price trends in sequential auctions

In this paper we consider sequential second-price auctions where an individual's value for a bundle of objects is either greater than the sum of the values for the objects separately (positive synergy) or less than the sum (negative synergy). We show that the existence of positive synergies implies declining expected prices. When synergies are negative, expected prices are increasing. There are several corollaries. First, the seller is indifferent between selling the objects simultaneously as a bundle or sequentially when synergies are positive. Second, when synergies are negative, the expected revenue generated by the simultaneous auction can be larger or smaller than the expected revenue generated by the sequential auction. In addition, in the presence of positive synergies, an option to buy the additional object at the price of the first object is never exercised in the symmetric equilibrium and the seller's revenue is unchanged. Under negative synergies, in contrast, if there is an equilibrium where the option is never exercised, then equilibrium prices may either increase or decrease and, therefore, the net effect on the seller's revenue of the introduction of an option is ambiguous. Finally, we examine a special case with asymmetric players who have distinct synergies. In this example, even if one player has positive synergies and the other has negative synergies, it is still possible for expected prices to decline.Received: 12 December 2000, Accepted: 1 May 2002, JEL Classification: D44Flavio Menezes acknowledges the financial support from ARC (Grant A000000055) and CNPq. Monteiro acknowledges the financial support from CNPq and the hospitality of CERSEM where part of this paper has been written. We thank Richard Engelbrecht-Wiggans, Peter Sørensen and two anonymous referees for useful comments.     

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 fees in internet auctions

An auction house runs a second-price auction with a possibility of resale through re-auctions. It collects listing and closing fees from the seller. We find the fees which maximize the revenue of the auction house. In particular, we show that the optimal listing fee is zero. Our findings are consistent with the policies of eBay, Amazon, Yahoo, and other Internet auctions.      

Reputation in Auctions: Theory, and Evidence from eBay

Employing a procedure suggested by a simple theoretical model of auctions in which bidders and sellers have observable and heterogenous reputations for default, we examine the effect of reputation on price in a data set drawn from the online auction site eBay. Our main empirical result is that seller's, but not bidder's, reputation has an economically and statistically significant effect on price.     

Auctions with asymmetric common-values: The first-price format

We study the performance of the first-price format in auctions with asymmetric common-values. We show that, contrary to the result for second-price auctions, a small advantage for one player translates only to small changes in bidders’ strategies, and the equilibrium remains close to the first-price equilibrium of the original game. We characterize the equilibrium bidding strategies and their behavior as the degree of asymmetry increases. Finally, we compare the revenues at the optimal auction, the first-price auction and the second-price auction.