The Shill Bidding Effect versus the Linkage Principle

The analysis of second price auctions with externalities is utterly modified if the seller is unable to commit not to participate in the mechanism. For the General Symmetric Model introduced by Milgrom and Weber [P. Milgrom, R. Weber, A theory of auctions and competitive bidding, Econometrica 50 (1982) 1089-1122] we characterize the full set of separating equilibria that are symmetric among buyers and with a strategic seller being able to bid in the same way as any buyer through a so-called shill bidding activity. The revenue ranking between first and second price auctions is different from the one arising in Milgrom and Weber: the benefits from the highlighted ‘Linkage Principle’ are counterbalanced by the ‘Shill Bidding Effect.’     

Market behavior in bid,offer, and double auctions: A Reexmination

This study examines the robustness of the previously observed [Smith (1964)] differences in market behavior between double auctions (both buyers and sellers may enter price quotes), bid auctions (only buyers may enter price quotes), and offer auctions (only sellers may enter price quotes). Based on the results of twenty-one market experiments, we find little support for the a priori hypothesis that bid auction prices tend to be greater than double auction prices which tend to be greater than offer auction prices.     

A comparison of first price multi-object auctions

We compare simultaneous multi-object English-type ascending price auctions with first price sealed bid auctions in private values environments with multi-object demands. Special attention is paid to the effect of closing rules on ascending auctions’ outcomes. We find that simultaneous ascending auctions with the soft closing rule are the most efficient, while the sealed bid auctions generate the highest revenue. Ascending auctions with the hard closing rule display a significant amount of late bidding, resulting in the lowest among the three institutions revenue and efficiency.

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Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.      

Equilibrium reserve prices in sequential ascending auctions

We study a model where bidders have perfectly correlated valuations for two goods sold sequentially in two ascending-price auctions. The seller sets a reserve price before the beginning of each auction. Despite the lack of commitment by the seller, we characterize an equilibrium and study its properties. Strategic non-disclosure of information takes the form of non-participation in the early auction by low-valuation bidders, while high-valuation bidders bid up to their true valuations. Some buyers who would profitably buy at the reserve price refrain from participating in order to decrease the second-auction reserve price.     

Sealed bid auctions with ambiguity: Theory and experiments

This study presents a laboratory experiment of the first and second price sealed bid auctions with independent private values, where the distribution of bidder valuations may be unknown. In our experimental setting, in first price auctions, bids are lower with the presence of ambiguity. This result is consistent with ambiguity loving in a model that allows for different ambiguity attitudes. We also find that the first price auction generates significantly higher revenue than the second price auction with and without ambiguity.     

Trading mechanism selection with directed search when buyers are risk averse

We endogenize the trading mechanism selection in a model of directed search with risk averse buyers and show that the unique symmetric equilibrium entails all sellers using fixed price trading. Mechanisms that prescribe the sale price as a function of the realized demand (auctions, bargaining, discount pricing, etc.) expose buyers to the “price risk”, the uncertainty of not knowing how much to pay in advance. Fixed price trading eliminates the price risk, which is why risk averse customers accept paying more to shop at such stores.     

Internet auctions with many traders

We study a multi-unit auction environment similar to eBay. Sellers, each with a single unit of a homogeneous good, set reserve prices at their own second-price auctions. Each buyer has private value for the good and wishes to acquire a single unit. Buyers can bid as often as they like and move between auctions. We characterize a perfect Bayesian equilibrium for this decentralized dynamic mechanism in which, conditional on reserve prices, an efficient set of trades occurs at a uniform price. In a large but finite market, the sellers set reserve prices equal to their true costs under a very mild distributional assumption, so ex post efficiency is achieved. Buyers’ strategies in this equilibrium are simple and do not depend on their beliefs about other buyers’ valuations, or the number of buyers and sellers.     

The high/low divide: Self-selection by values in auction choice

Most prior theoretical and experimental work involving auction choice has assumed bidders find out their value after making a choice of which auction to enter. We examine whether or not bidders knowing their value prior to making a choice of which among multiple alternative auction formats to enter impacts their choice decision and/or the outcome of the auctions. The results show a strong impact on auction choice. Subjects with low values choose the first price sealed bid auction more often while subjects with high values choose the ascending auction more often. The number of bidders in each auction, revenue, efficiency and average bidder surplus all end up equalized.     

An experimental investigation of entry cost effects in sealed-bid dollar auctions

We experimentally study the effect of entry costs on bidding and entry behavior in common value auctions. We find, with entry costs, players bid lower in first price and higher in second price auctions, compared to no entry fee auctions.     

Imperfect Competition in Auction Designs

We study the competition between two owners of identical goods who wish to sell them to a pool of potential buyers. The sellers compete simultaneously setting reserve prices for their second price sealed bid auctions. Upon observing the set reserve prices, the buyers decide simultaneously in which auction to bid. We show that this game has (at least) one equilibrium and that all equilibria are inefficient: reserve prices are not driven to zero (cost). We also discuss where and why the parallel between optimal auction design and optimal pricing in the case of monopoly breaks down for oligopoly.     

WHO SEARCHES?*

We consider a directed search model with buyers and sellers and determine whether buyers look for sellers or vice versa. The buyers and sellers can choose to search or wait; what they do in equilibrium depends on the relative size of the two populations and the price formation mechanism. We study bargaining and auctions and find that when one population is much larger than the other the former searches and the latter waits. Under auction with roughly equal populations some buyers and sellers search and some wait. Our results challenge the practice of postulating who searches and who waits.     

Multiple unit auctions with strategic price-quantity decisions

Summary. I study a multiple unit auction where symmetric risk-neutral bidders choose prices and quantities endogenously. In the model, bidders (a) may place non-linear valuations on the auctioned units, and (b) bid for several units at the same price (“lumpy” bids). I characterize quantity-symmetric and strictly monotone-increasing price equilibria for discriminatory and competitive auctions, and show that (i) if quantity strategy profiles are equal across auctions revenue- equivalence holds, (ii) expected revenue is higher if bidders bid for the entire supply rather than for shares of it, and (iii) equilibrium allocations may fail to be Pareto-optimal. Received: April 14, 1995; revised version: September 3, 1997     

Competitive auctions

We study a class of single-round, sealed-bid auctions for an item in unlimited supply, such as a digital good. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e. encourages bidders to bid their true valuations) and on all inputs yields profit that is within a constant factor of the profit of the optimal single sale price. We justify the use of optimal single price profit as a benchmark for evaluating a competitive auctions profit. We exhibit several randomized competitive auctions and show that there is no symmetric deterministic competitive auction. Our results extend to bounded supply markets, for which we also give competitive auctions.     

Bid Functions in Auctions and Fair Division Games: Experimental Evidence

In auctions a seller offers a commodity for sale and collects the revenue. In fair division games the object is collectively owned by the group of bidders who equally share the revenue. We run an experiment in which the participants face four types of allocation games (auctions and fair division game under two price rules, first– versus second–price rule). We collect entire bid functions rather than bids for single values and investigate price and efficiency of the different trading institutions. We find that the first–price auction is more efficient than the second–price auction, whereas economic rationality assuming heterogeneous bidders suggests the opposite. Furthermore, we study the structure of individual bid functions.     

Asymmetric first price auctions

A new approach to asymmetric first price auctions is proposed which circumvents the need to examine bidding strategies directly. Specifically, the ratio of bidders' (endogenous) payoffs is analyzed and compared to the ratio of the (exogenous) distribution functions that describe beliefs. Most of the results are inferred from this comparison. In the existing theoretical literature, assumptions of first order stochastic dominance or stronger imply that the latter ratio has very specific properties, but no such assumptions are imposed here. It is proven that first order stochastic dominance is necessary for bidding strategies not to cross. When this assumption is relaxed in the numerical literature it is done in a manner that leads to exactly one crossing. However, it is straightforward to construct examples with several crossings. Finally, bid distributions will cross in auctions with two bidders whenever second order (but not first order) stochastic dominance applies.     

COMPARING PUBLIC PROCUREMENT AUCTIONS

This article contrasts two auction formats often used in public procurement: first price auctions with ex post screening of bid responsiveness and average bid auctions (ABAs), in which the bidder closest to the average bid wins. The equilibrium analysis reveals that their ranking is ambiguous in terms of revenues, but the ABA is typically less efficient. Using a data set of Italian public procurement auctions run alternately under the two formats, a structural model of bidding is estimated for the subsample of first price auctions and used to quantify the efficiency loss under counterfactual ABAs.     

Sequential selling mechanisms

Summary In this paper we attempt to formalize the idea that a mechanism that involves multilateral communication between buyers and sellers may be dominated by one that involves simple bilateral communication. To do this we consider the well known problem in which a seller tries to sell a single unit of output to a group ofN buyers who have independently distributed private valuations. Our arguments hinge on two considerations. First, buyers communicate their willingness to negotiate with the seller sequentially, and second, buyers have the option of purchasing the good from some alternative supplier. It is shown that the seller cannot improve upon a procedure in which she offers the good to each buyer in turn at a fixed price. The seller reverts to multilateral communication if possible, only when no buyer is willing to pay the fixed price. In reasonable environments buyers will be too impatient to wait for the outcome of a multilateral negotiation and all communications will be bilateral.In many problems in mechanism design, informed traders have no alternative to participation in the mechanism that is offered by its designer. The best mechanism from the designer's point of view is then the one that is most efficient at extracting informational rents, that is, a simple auction. In a competitive environment it is likely to be costly for buyers to participate in an auction or any other multilateral selling scheme in which the seller must process information from many different buyers because alternative trading opportunities will be disappearing during the time that the seller is collecting this information. Buyers might be willing to participate in an auction, but only if they could be guaranteed that the competition that they face will not eliminate too much of their surplus.At the other extreme to the auction is a simple fixed price selling scheme 1. The seller simply waits until he meets a buyer whose valuation is high enough, given the opportunities that exist in the rest of the market, for him to be willing to pay this price. The seller extracts the minimum of the buyer's informational rents since the price that a buyer pays is independent of his valuation. Yet the seller might like this scheme if adding a second bidder to the process makes it very difficult for him to find a buyer with a valuation high enough to want to participate.In the presence of opportunity costs, the seller faces a trade-off between his ability to extract buyers informational rents and his ability to find buyers who are willing to participate in any competitive process. In practice this trade-off will impose structure on the method that is used to determine a price. In markets where there are auctions, limits are put on buyer participation. In tobacco auctions bids are submitted at a distinct point in time from buyers who are present at that time. In real estate auctions time limits are put on the amount of time the seller will wait before making a decision. These restrictions on participation are presumably endogenously selected by the seller (possibly in competition with other mechanism designers) with this trade-off in mind.On the other hand, markets in which objects appear to trade at a fixed price are rarely so simple. A baker with a fixed supply of fresh bagels is unlikely to collect bids from buyers and award the bagels to the high bidder at the end of the day. Buyers are unlikely to be willing to participate in such a scheme since they can buy fresh bagels from a competitor down the street. Yet despite the fact that bagels sell at a fixed price throughout the day, most bakers are more than willing to let it be known that they will discount price at the end of the day on any bagels that they have not yet sold. Selling used cars presents a similar problem. Each potential buyer for the used car is likely to have inspected a number of alternatives, and is likely to know the prices at which these alternative can be obtained. A seller who suggests that buyers submit a bid, then wait until the seller is sure that no higher offer will be submitted is asking buyers to forgo these alternative opportunities with no gain to themselves. To avoid the rigidity of the pure fixed price scheme most used cars are sold for a fixed price or best offer. These examples suggest that the best selling mechanism may involve a complex interplay between participation and surplus extraction considerations.The purpose of this paper is to provide a simple formalism within which the factors that determine the best contract can be evaluated. We consider the best known environment from the point of view of auction design in which there are a large number of buyers with independent private valuations for a unit of an indivisible commodity that is being sold by a single supplier who acts as the mechanism designer. We modify this standard problem in two critical ways. First, we assume that the seller meets the potential buyers sequentially rather than all at once. Secondly we assume that buyers have a valuable alternative that yields them a sure surplus. This creates a simple bidding cost that is effectively the expected loss in surplus (created by the disappearance of outside alternatives) that the buyer faces during the time that he spends negotiating with the seller.These simple assumptions allow us to calculate the impact of competition and communication costs using completely standard arguments from the mechanism design literature. We are able to show that with these assumptions the seller's expected surplus will be highest if the object is sold according to the following modified fixed price scheme: the seller contacts each of the potential buyers in turn and either offers to negotiate or announces that he no longer wishes to trade. If he offers to negotiate and the buyer agrees, the buyer immediately has the option of trading for sure with the seller at a fixed price set ex ante. If the buyer does not wish to pay this fixed price, he may submit an alternative bid. The seller will then continue to contact new buyers, returning to trade with the buyer only if no buyer wishes to pay the fixed price and no higher bid is submitted.It will be clear that in our environment, both the simple fixed price scheme and the simple auction are feasible. The simple auction prevails when the fixed price is set equal to the maximum possible valuation, while the simple fixed price scheme occurs when the fixed price is set so that buyers are willing to participate if and only if they are willing to pay the fixed price. Our results will show that a simple auction in never optimal for the seller. The seller can always strictly improve his payoff by moving to a scheme in which there is some strictly positive probability that trade will occur at the fixed price. On the other hand, there are reasonable circumstances in which the seller cannot achieve a higher payoff than the one she gets by selling at a fixed price. It is shown that for any positive participation cost, there is a large, but finite, number of potential buyers so that the seller cannot achieve a higher payoff than what she gets by selling at a fixed price. Two simple, but important continuity results are also illustrated. As the cost of participation in the mechanism increases (decreases), the probability with which the seller's unit of output is sold at a fixed price goes to one (zero) in the best modified fixed price mechanism for the seller.Our paper is not the first to generate such a modified fixed price scheme. Both McAfee and McMillan (1988) and Riley and Zeckhauser (1983) come up with similar schemes for the case in which the seller must bear a fixed cost for each new buyer that she contacts. There are two essential differences between our model and theirs. First, as the cost is interpreted as the opportunity cost of participation in the mechanism, it is reasonable to imagine that the seller advertises the mechanism ex ante. Another way of putting this is that the seller pays a fixed rather than a variable cost to communicate the mechanism to buyers. This makes it possible to assume that the mechanism is common knowledge to the seller and all the buyers at the beginning of the communication process. For this reason we can make our case using completely standard arguments. Secondly, the mechanism in the opportunity cost case plays a different allocative role than it does in the case when the seller bears a cost. The mechanism must decide whether buyers should communicate with the seller or pursue their alternative activities, as well as who should trade and at what price. It is this allocative role that makes bilateral communication superior to multilateral communication in a competitive environment. These differences allow us to show, for example, that a simple fixed price scheme is undominated for the seller when the number of buyers is finite. As shown by McAfee and McMillan, this is only possible when the number of potential buyers is infinite when the seller bears the cost of communication.Remarkably, the existence of opportunity costs to buyer participation is not, by itself, sufficient to explain why sellers might prefer bilateral communications mechanisms. Samuelson (1983) and McAfee and McMillan (1987) show that when buyers must pay a fixed cost to submit a bid, which is equivalent to giving up a valuable alternative, a seller cannot expect to earn more than she does in a second price auction (though Samuelson shows that the reserve price may depend on the number of potential buyers). One of the contributions of this paper is to show that the assumption that buyers make their participation decisions simultaneously is critical to this result. Simultaneous entry decisions means that whether or not any particular buyer is assigned to the alternative activity is independent of any other buyer's valuation. With sequential communication the seller is able to relax this constraint. It is precisely the enlargement of the class of feasible mechanism that breaks down the optimality of the simple auction.The second author acknowledges the support of the Social Sciences and Humanities Research Council of Canada and the CRDE at the Université de Montreal.     

Convergence of outcomes and evolution of strategic behavior in double auctions

We study the emergence of strategic behavior in double auctions with an equal number of buyers and sellers, under the distinct assumptions that orders are cleared simultaneously or asynchronously. The evolution of strategic behavior is modeled as a learning process driven by a genetic algorithm. We find that, as the size of the market grows, allocative inefficiency tends to zero and performance converges to the competitive outcome, regardless of the order-clearing rule. The main result concerns the evolution of strategic behavior as the size of the market gets larger. Under simultaneous order-clearing, only marginal traders learn to be price takers and make offers equal to their valuations/costs. Under asynchronous order-clearing, all intramarginal traders learn to be price makers and make offers equal to the competitive equilibrium price. The nature of the order-clearing rule affects in a fundamental way what kind of strategic behavior we should expect to emerge.     

Sorting versus screening: Search frictions and competing mechanisms

In a market where sellers compete by posting trading mechanisms, we allow for a general search technology and show that its features crucially affect the equilibrium mechanism. Price posting prevails when meetings are rival, i.e., when a meeting by one buyer reduces another buyer's meeting probability. Under price posting buyers reveal their type by sorting ex-ante. Only if the meeting technology is sufficiently non-rival, price posting is not an equilibrium. Multiple buyer types then visit the same sellers who screen ex-post through auctions.     

Sealed bid auctions with uncertainty averse bidders

Summary. Traditional analysis of auctions assumes that each bidder's beliefs about opponents' valuations are represented by a probability measure. Motivated by experimental findings such as the Ellsberg Paradox, this paper examines the consequences of relaxing this assumption in the first and second price sealed bid auctions with independent private values. The multiple priors model of Gilboa and Schmeidler [Journal of Mathematical Economics, 18 (1989), 141–153] is adopted specifically to represent the bidders' (and the auctioneer's) preferences. The unique equilibrium bidding strategy in the first price auction is derived. Moreover, under an interesting parametric specialization of the model, it is shown that the first price auction Pareto dominates the second price auction. Received: December 15, 1995; revised version: February 19, 1997