Auctions with endogenous participation and an uncertain number of bidders: experimental evidence

Attracting bidders to an auction is a key factor in determining revenue. We experimentally investigate entry and bidding behavior in first-price and English clock auctions to determine the revenue implications of entry. Potential bidders observe their value and then decide whether or not to incur a cost to enter. We also vary whether or not bidders are informed regarding the number of entrants prior to placing their bids. Revenue equivalence is predicted in all four environments. We find that, regardless of whether or not bidders are informed, first-price auctions generate more revenue than English clock auctions. Within a given auction format, the effect of informing bidders differs. In first-price auctions, revenue is higher when bidders are informed, while the opposite is true in English clock auctions. The optimal choice for an auction designer who wishes to maximize revenue is a first-price auction with uninformed bidders.     

Revenue equivalence in asymmetric auctions

The Revenue Equivalence Theorem is generalized to the case of asymmetric auctions in which each player's valuation is drawn independently from a common support according to his/her distribution function.     

Asymptotic Revenue Equivalence in Auctions

We study the revenue in auctions of a single object when the number of bidders becomes large. We show that all sequences of auctions belonging to a class of mechanisms have limiting expected revenue equal to the expected best-use value of the object. An important special case that is covered is common value auctions, but more generally not even affiliation of values is assumed. This provides an asymptotic revenue equivalence result for settings beyond that of private values. Journal of Economic Literature Classification Numbers: D44, C72.     

Multidimensional private value auctions

We consider parametric examples of symmetric 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. We show that, in such environments, the revenue equivalence between the first and second price auctions (SPAs) breaks down and there is no definite revenue ranking; while the SPA is always efficient allocatively, the first price auction (FPA) may be inefficient; equilibria may fail to exist for the FPA. We also show that auction mechanisms provide different incentives for bidders to acquire costly information about opponents’ valuation.     

First-price equilibrium and revenue equivalence in a sequential procurement auction model

We analyze first-price equilibrium bidding behavior of capacity-constrained firms in a sequence of two procurement auctions. In the model, firms with a cost advantage in completing the project auctioned off at the end of the sequence may enter the unfavored first auction hoping to lose it. Equilibrium bidding in both auctions deviates from the standard Symmetric Independent Private Value auction model due to opportunity costs of bidding created by possibly employed capacity. For this sequential auction model with non-identical objects, we show that revenue equivalence applies.     

Bidding behavior in asymmetric auctions: An experimental study

We review an asymmetric auction experiment. Based on Plum (Int. J. Game Theory 20 (1992) 393) private valuations of the two bidders are independently drawn from distinct but commonly known distributions, one of which first-order stochastically dominates the other. We test the qualitative properties of that model of asymmetric auctions, in particular whether the weak bidder behaves more aggressively than the strong, and then test bidders’ preference for first- vs. second-price auctions.     

Pricing in position auctions and online advertising

Can search engines increase revenues by changing their position auctions? In this paper, I analyze position auctions with general pricing rules to answer this question. In these auctions, there are several items that are commonly ranked by bidders with unit demand. I show that revenues remain the same for position auctions with regular pricing rules where the price for an item depends on the bids of agents who win lower-ranked items. In addition, all of the bidders have the same ex post payoffs. I also show that regularity is a necessary condition to get ex post payoff equivalence.     

CHARITY AUCTIONS*

In a charity auction the public‐goods nature of auction revenue affects bidding incentives. We compare equilibrium bidding and revenue in first‐price, second‐price, and all‐pay charity auctions. Bidding revenue typically varies by selling format. First‐price auctions are less lucrative than second‐price and all‐pay auctions, and with sufficiently many bidders the all‐pay auction has the highest bidding revenue. However, revenue equivalence applies when the auctioneer can set a reserve price and fees plus threaten to cancel the auction. If the auctioneer cannot threaten cancellation, a reserve and bidding fee can augment revenue but again revenue varies by auction format     

A non-expected utility model and its application in practical auctions

ABSTRACT

This article presents a non-expected utility decision model which is nonlinear in the winning probabilities. The model not only explicitly expresses bidders’ attitudes to risk, but also addresses their preference over the bidding criteria. To demonstrate how to apply the model in the practical auction design, the first- and second-price auctions with both commission rate and reserve price are examined, respectively. For nonrisk-neutral bidders, the equilibrium bidding strategies are characterized, in which the commission rate has a significant influence on the bidding strategy through the critical valuation. However, the existence of the optimal commission rate is uncertain, but once it exists, it depends on the information rent of the highest or second highest order valuation in terms of the inverse hazard rate. With risk-aversion bidders, the only difference to the optimal reserve price is a constant between the first- and second-price auctions. The revenue comparisons show that the classical Revenue Equivalence Theorem fails in practical auctions with the commission rate. This article extends the application of the decision-making model in the auction design in theory and provides some guidance for the auction house and the seller to make their decisions in reality.     

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.     

Sequentially Optimal Auctions

In auctions where a seller can post a reserve price but if the object fails to sell cannot commit never to attempt to resell it, revenue equivalence between repeated first price and second price auctions without commitment results. When the time between auctions goes to zero, seller expected revenues converge to those of a static auction with no reserve price. With many bidders, the seller equilibrium reserve price approaches the reserve price in an optimal static auction. An auction in which the simple equilibrium reserve price policy of the seller mirrors a policy commonly used by many auctioneers is computed.Journal of Economic LiteratureClassification Numbers: C78, D44, D82.     

Equilibrium transformations and the Revenue Equivalence Theorem

I develop a method that transforms an equilibrium strategy profile from one auction to another. The method is constructive and does not require complicated computation. This provides a new approach to revenue equivalence and extends the theorem to domains where it had not previously been known, in particular to simultaneous multiple object auctions with complete information and to auction environments having correlated private values and common values.     

Treasury auctions in Spain: a linear approach

Abstract. The majority of Treasuries use discriminatory auctions to sell government debt. A few Treasuries use uniform auctions. The Spanish Treasury is the only one that uses a hybrid format of discriminatory and uniform auctions. All Treasury auctions are multiple-unit multiple-bid auctions, usually assumed to be common and unknown value auctions. Taking in account these features, we analyze the Spanish auction format, taking a linear approximation to bidders' multiple bids, and characterize a parameter set in which the Spanish format gives higher expected seller's revenue than discriminatory and uniform auctions. Policy implications are obtained by calibrating theoretical results with data. We thank S. Nu?ez, and seminar participants at GREQAM, CEFI, the 1999 CEF meeting in Boston and the 57th European Meeting of the Econcometric Society for suggestions. We are especially grateful to two anonymous referees for detailed comments that greatly improved the paper. Any error is our responsability. The authors express their thanks for financial support to Ministerio de Ciencia y Teconologia from Proyecto SEC2000-0723, n_o 9114.     

Mixed bundling auctions

We study multi-object auctions where agents have private and additive valuations for heterogeneous objects. We focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism. This class contains efficient auctions, pure bundling auctions, mixed bundling auctions, auctions with reserve prices and auctions with pre-packaged bundles. For any number of objects and bidders, both the pure bundling auction and separate, efficient auctions for the single objects are revenue-inferior to an auction that involves mixed bundling.     

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     

An experiment on auctions with endogenous budget constraints

We perform laboratory experiments comparing auctions with endogenous budget constraints. A principal imposes a budget limit on a bidder (an agent) in response to a principal-agent problem. In contrast to the existing literature where budget constraints are exogenous, this theory predicts that tighter constraints will be imposed in first-price auctions than in second-price auctions, tending to offset any advantages attributable to the lower bidding strategy of the first-price auction. Our experimental findings support this theory: principals are found to set significantly lower budgets in first-price auctions. The result holds robustly, whether the principal chooses a budget for human bidders or computerized bidders. We further show that the empirical revenue difference between first- and second-price formats persists with and without budget constraints.     

Bidder collusion

We analyze bidder collusion at first-price and second-price auctions. Our focus is on less than all-inclusive cartels and collusive mechanisms that do not rely on auction outcomes. We show that cartels that cannot control the bids of their members can eliminate all ring competition at second-price auctions, but not at first-price auctions. At first-price auctions, when the cartel cannot control members’ bids, cartel behavior involves multiple cartel bids. Cartels that can control bids of their members can suppress all ring competition at both second-price and first-price auctions; however, shill bidding reduces the profitability of collusion at first-price auctions.     

Expected revenue of all-pay auctions and first-price sealed-bid auctions with budget constraints

We show that all-pay auctions dominate first-price sealed-bid auctions when bidders face budget constraints. This ranking is explained by the fact that budget constraints bind less frequently in the all-pay auctions, which leads to more aggressive bidding in that format.     

Outside options: Another reason to choose the first-price auction

In this paper we study equilibrium and experimental bidding behaviour in first-price and second-price auctions with outside options.We find that bidders do respond to outside options and to variations of common knowledge about competitors’ outside options. However, overbidding in first-price auctions is significantly higher with outside options than without. First-price auctions yield more revenue than second-price auctions. This revenue-premium is significantly higher with outside options. In second-price auctions the introduction of outside options has only a small effect.     

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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