Ascending price Vickrey auctions

We show that an ascending price auction for multiple units of a homogeneous object proposed by Ausubel (i) raises prices for packages until they reach those nonlinear and non-anonymous market clearing prices at which bidders get their marginal products and (ii) the auction is a primal–dual algorithm applied to an appropriate linear programming formulation in which the dual solution yields those same market clearing prices. We emphasize the similarities with efficient incentive compatible ascending price auctions to implement Vickrey payments when there is a single object or when objects are heterogeneous but each buyer does not desire more than one unit. A potential benefit of these common threads is that it helps to establish the principles upon which Vickrey payments may be implemented through decentralized, incentive compatible procedures.     

The Effect of Bidder Heterogeneity on Combinatorial Conservation Auction Designs

In an iterative combinatorial auction, bidders can submit bids on individual and/or on combinations of projects in a series of intermediate rounds, where bid prices are revised before a final allocation is made. The iterative format is useful for conservation service procurement as landholders can rely on market information revealed through the rounds to evaluate their choices of projects and bid prices. However, there is no single way of providing the market information. Different designs for generating price information have been proposed. Little is known about the performance of iterative combinatorial auction designs when heterogeneous bidders, with different cost structures, participate in an auction. Using an agent based model, we evaluate a selected set of designs under different bidder heterogeneity scenarios. We observe that higher degrees of heterogeneity lead to lower auction efficiency and that auction outcomes are highly sensitive to price feedback design choices.     

EXPERIMENTAL EVIDENCE ON ENGLISH AUCTIONS: ORAL OUTCRY VERSUS CLOCK

This paper tests experimentally, in a common value setting, the equivalence between the Japanese English auction (or clock auction) and an oral outcry auction where bidders are allowed to call their own bids. We find that (i) bidding behaviour is different in each type of auction, but also that (ii) this difference in bidding behaviour does not affect significantly the auction prices. This lends some support to the equivalence between these two types of auction. The winner's curse is present: overbidding led to higher than expected prices (under Nash bidding strategies) in both types of auction. Although interesting and encouraging, the results clearly indicate that further research is necessary, particularly with a modified experimental design.     

Explaining Overbidding in First Price Auctions Using Controlled Lotteries

In this paper, we study the behavior of individuals when facing two different, but incentive-wise identical, institutions. We pair the first price auction with an equivalent lottery. Once a subject is assigned a value for the auctioned object, the first price auction can be modeled as a lottery in which the individual faces a given probability of winning a certain payoff. This set up allows us to explore to what extent the misperception of the probability of winning in the auction is responsible for bidders in a first price auction to bidding above the risk neutral Nash equilibrium prediction. The first result we obtain is that individuals, even though facing the same choice over probability/payoff pairs, behave differently depending on the type of choice they are called to make. When facing an auction, subjects with high values tend to bid significantly above the bid they choose in the corresponding lottery environment. We further find that in both the lottery and the auction environments, subjects tend to bid in excess of the bid predicted by the risk neutral model, at least for intermediate range values. Finally, we find that the difference between the lottery behavior and the auction behavior is substantially, but not totally, eliminated by showing the subjects the probability of winning the auction.     

Optimal auctions with asymmetrically informed bidders

Summary. The paper analyzes a problem of optimal auction design when the seller faces asymmetrically informed bidders. Specifically, we consider a continuum of risk-neutral uninformed bidders taking part into the auction along with n risk-averse informed bidders. The contribution of the paper is threefold. First, we fully characterize the optimal auction in this non standard environment and in a very general set-up. We find that when informed bidders reveal “bad news” about the value of the good, the seller optimally awards the object to the uninformed bidders. Secondly, we show that the seller is better off in presence of uninformed bidders because this allows to lower the informational rents paid to the informed bidders. Last, we find that, with bi-lateral risk neutrality, the seller always awards the good to the uninformed bidders thereby keeping all the surplus.Received: 22 October 2004, Revised: 21 April 2005, JEL Classification Numbers: D44, D82.We are very grateful to two anonymous referees, Jacques Crémer, Patrick François, Angel Hernando-Veciana and seminar participants at the 2004 SCSE conference (Quebec, Canada) for their valuable comments. Moez Bennouri acknowledges the financial support by the Initiative of the New Economy (INE) program of SSHRC (Canada).     

Auction theory adaptations for real life applications

We develop extensions to auction theory results that are useful in real life scenarios.1. Since valuations are generally positive we first develop approximations using the log-normal distribution. This would be useful for many finance related auction settings since asset prices are usually non-negative.2. We formulate a positive symmetric discrete distribution, which is likely to be followed by the total number of auction participants, and incorporate this into auction theory results.3. We develop extensions when the valuations of the bidders are interdependent and incorporate all the results developed into a final combined realistic setting.4. Our methods can be a practical tool for bidders and auction sellers to maximize their profits. The models developed here could be potentially useful for inventory estimation and for wholesale procurement of financial instruments and also non-financial commodities.All the propositions are new results and they refer to existing results which are stated as Lemmas.     

Demand reduction and preemptive bidding in multi-unit license auctions

Multi-unit ascending auctions allow for equilibria in which bidders strategically reduce their demand and split the market at low prices. At the same time, they allow for preemptive bidding by incumbent bidders in a coordinated attempt to exclude entrants from the market. We consider an environment where both demand reduction and preemptive bidding are supported as equilibrium phenomena of the ascending auction. In a series of experiments, we compare its performance to that of the discriminatory auction. Strategic demand reduction is quite prevalent in the ascending auction even when entry imposes a (large) negative externality on incumbents. As a result, the ascending auction performs worse than the discriminatory auction both in terms of revenue and efficiency, while entrants’ chances are similar across the two formats.     

Multiple-unit English auctions

This paper examines the outcome of an ascending-price multiple-unit auction. Two bidders, facing continuous, downward-sloping demand functions, participate in the auction of some divisible objects. The auctioneer starts the process by announcing an initial price and asking both bidders to submit sealed-bids of desired quantities. The auctioneer increases the price until the total amount bid for is less than the total supply. We compute the outcome of this auction game under full information and suggest that this mechanism may not maximize expected revenue.     

Late and multiple bidding in second price Internet auctions: Theory and evidence concerning different rules for ending an auction

In second price Internet auctions with a fixed end time, such as those on eBay, many bidders submit their bids in the closing minutes or seconds of an auction. We propose an internet auction model, in which very late bids have a positive probability of not being successfully submitted, and show that late bidding in a fixed deadline auction can occur at equilibrium in auctions both with private values and with uncertain, dependent values. Late bidding may also arise out of equilibrium, as a best reply to incremental bidding. However, the strategic advantages of late bidding are severely attenuated in auctions that apply an automatic extension rule such as auctions conducted on Amazon. Field data show that there is more late bidding on eBay than on Amazon, and this difference grows with experience. We also study the incidence of multiple bidding, and its relation to late bidding.     

Budget-constrained sequential auctions with incomplete information

I study a budget-constrained, private-valuation, sealed-bid sequential auction with two incompletely-informed, risk-neutral bidders in which the valuations and income may be non-monotonic functions of a bidder's type. Multiple equilibrium symmetric bidding functions may exist that differ in allocation, efficiency and revenue. The sequence of sale affects the competition for a good and therefore also affects revenue and the prices of each good in a systematic way that depends on the relationship among the valuations and incomes of bidders. The sequence of sale may affect prices and revenue even when the number of bidders is large relative to the number of goods. If a particular good, say α, is allocated to a strong bidder independent of the sequence of sale, then auction revenue and the price of good α are higher when good α is sold first.     

Auctioning divisible goods

Summary. We derive equilibrium bidding strategies in divisible good auctions for asymmetrically informed risk neutral and risk averse bidders when there is random noncompetitive demand. The equilibrium bid schedules contain both strategic considerations and explicit allowances for the winner's curse. When the bidders' information is symmetric, the strategic aspects of bidding imply that there always exist equilibria of a uniform-price auction with lower expected revenue than provided by a discriminatory auction. When bidders are risk averse, there may exist equilibria of the uniform-price auction that provide higher expected revenue than a discriminatory auction. Received: November 4, 1999; revised version: March 9, 2001     

License prices for financially constrained firms

It is often alleged that high auction prices inhibit service deployment. We investigate this claim under the extreme case of financially constrained bidders. If demand is just slightly elastic, auctions maximize consumer surplus if consumer surplus is a convex function of quantity (a common assumption), or if consumer surplus is concave and the proportion of expenditure spent on deployment is greater than one over the elasticity of demand. The latter condition appears to be true for most of the large telecom auctions in the US and Europe. Thus, even if high auction prices inhibit service deployment, auctions appear to be optimal from the consumers’ point of view.      

Auctions with variable supply: Uniform price versus discriminatory

We examine an auction in which the seller determines the supply after observing the bids. We compare the uniform price and the discriminatory auction in a setting of supply uncertainty, where uncertainty is caused by the interplay of two factors: the seller's private information about marginal cost and the seller's incentive to sell the profit-maximizing quantity, given the received bids. In every symmetric mixed strategy equilibrium, bidders submit higher bids in the uniform price auction than in the discriminatory auction. In the two-bidder case, this result extends to the set of rationalizable strategies. As a consequence, we find that the uniform price auction generates a higher expected revenue for the seller and a higher trade volume.     

Robustness of the Incentive Compatible Combinatorial Auction

Goods are said to be combinatorial when the value of a bundle of goods is not equal to the sum of the values of the same goods unbundled. Investigations of combinatorial allocation problems should recognize that there are two separate aspects of such problems: anenvironmental distinction between multiple-unit allocation problems which involve combinatorial goods and those which do not do so, and aninstitutional distinction between auctions in which combinatorial values can be expressed as part of the bidding rules and those in which they cannot. Forsythe and Isaac (Research in Experimental Economics, Vol. 2 (1982). Greenwich, Conn.: JAI Press, Inc.) reports the extension of the Vickrey auction into a demand-revealing, multiple unit, private goods auction that can incorporate combinatorial values. This current paper places that theoretically demand-revealing institution in a series of experimental environments in order to generate results (e.g. efficiencies) which may serve as a benchmark for other auctions (combinatorial or otherwise) whose implementation characteristics may be more favorable. To aid in interpretation of our Vickrey experimental results, we also provide results of alternatives to Vickrey allocations from both institutional and heuristic sources, as well as a discussion of the source of the Vickrey auctions high efficiencies even in the presence of misrevelation.     

The (in) effectiveness of procurement auctions in the public sector

This article studies procurement auctions in the public sector using game theoretical tools. The article shows that when participants in an auction are agents with low abilities (low type), as is common in the public sector, they place the same contract request. As a result, the auction mechanism will rarely produce real competition, thus making this mechanism, which limits bidders to those already within the system, ineffective for use in the public sector job market.     

Laboratory Behavior in Spot and Forward Auction Markets

Auctions that require advance production increase seller costs because inventories must be held. This cost does not exist in production-to-demand markets for which production follows trading, and sales exactly match quantities produced. Data from laboratory computerized double auction markets show that advance-production prices are significantly higher and quantities traded are significantly lower than they are in production-to-demand auctions. Price convergence patterns show advance-production sellers moving toward 9% higher prices and 22% greater earnings.     

Asymmetric information about rivals'' types in standard auctions

We study auctions in which bidders may know the types of some rival bidders but not others. This asymmetry in bidders' knowledge about rivals' types has different effects on the two standard auction formats. In a second-price auction, it is weakly dominant to bid one's valuation, so the knowledge of rivals' types has no effect, and the good is allocated efficiently. In a first-price auction, bidders refine their bidding strategies based on their knowledge of rivals' types, which yields an inefficient allocation. We show that the inefficient allocation in the first-price auction translates into a poor revenue performance. Given a standard regularity condition, the seller earns higher expected revenue from the second-price auction than from the first-price auction, whereas the bidders are better off from the latter.     

Multi-unit auctions with private information: an indivisible unit continuous price model

We construct a model of multi-unit auctions in which I bidders bid for two indivisible units of a common value good. Using a first-order approach, we find that there are equilibria in which bidders bid the same price for both units in the discriminatory auction, but not in the uniform auction. When there are only two bidders, under certain conditions, there are linear equilibria for both the discriminatory and the uniform auction formats. In all equilibria, bidders equalize the expected marginal benefit of bidding to the marginal costs of bidding. We show that comparison of the seller??s expected revenue across auction formats depends only on the ratio of the precision of private information to the precision of public information.     

Reserve price signaling

In a general auction model in which bidders’ signals are affiliated, we characterize the unique separating equilibrium in which the seller can use reserve prices to credibly signal her private information. When the buyers’ signals are independent, the optimal reserve price is shown to be increasing in the number of bidders under certain conditions. We also demonstrate that the probability that the item is sold at the reserve price can increase as the number of bidders increases, which indicates a more central role for reserve prices than perceived in the standard auction models.     

Efficiency and competition in the long run: The survival of the unfit

In a dynamic contest the current incumbent competes against a randomly assigned entrant in a private value all pay auction each period. We focus on equilibria where the beliefs about the incumbent's type and the employed strategies are stationary. We show that inefficient types survive, even if the entrants arrive very frequently, because the entrant plays more aggressively than the incumbent, allowing a low type entrant to win against a high type incumbent. In an example we show that if the incumbent is challenged more often, then the equilibrium type of the incumbent is higher on average. When the value of the prize is the same for all players (the case studied in the public choice literature), the equilibrium rent of the bidders is fully dissipated as the incumbent is challenged infinitely often. The technical contribution lies in showing the existence of stationary equilibrium in an incomplete information game.