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.     

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).     

Theoretical approaches to lowest unique bid auctions

In this paper, we analyze a game called the lowest unique bid auction (LUBA). It is known that there is no closed form solution for the symmetric mixed strategy equilibria in LUBA. We propose two alternative approaches. We use weak dominance to identify upper bounds for players’ bids. Under symmetry, we provide a method to compute a mixed strategy equilibrium by utilizing the recursive structure of the winning chances of the bids under one assumption.     

The effect of bid withdrawal in a multi-object auction

The Federal Communications Commission currently utilizes a simultaneous multi-round ascending bid auction to allocate Personal Communication Services licenses. In the auction, participants are allowed to withdraw standing bids at a penalty. The penalty is equal to the maximum of zero or the difference between the value of the withdrawn bid on a license and the highest bid after the withdrawal on that license. The withdrawal rule is designed to assist bidders wishing to assemble combinations of licenses who find themselves stranded with an assortment of licenses for which their bids sum to more than their value. This paper reports results of experiments that examine the effect of the withdrawal rule in environments in which losses can occur if packages of licenses must be assembled piecemeal. The experiments demonstrate that there is a tradeoff with using the rule: efficiency and revenue increase, but individual losses are larger. Furthermore, the increased efficiency does not outweigh the higher prices paid so that bidder surplus falls in the presence of the withdrawal rule. Received: 10 October 1997 / Accepted: 10 September 1998     

Corruption and auctions

We investigate how corruption affects the outcome of a first-price auction (bidding behavior, efficiency and the seller’s expected revenue). The auctioneer approaches the winner to offer the possibility of a reduction in his bid in exchange for a bribe. The bribe can be a percentage of the difference between the winning and the second-highest bid or a fixed amount. We show that there exists a symmetric bidding strategy equilibrium that is monotone, i.e., higher valuation buyers bid higher. Corruption does not affect efficiency but both the auctioneer’s expected bribe and the seller’s expected revenue depend on the format of the bribe payments. We also find the optimal bribe scheme.     

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.     

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.     

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.     

Inverse S-shaped probability weighting functions in first-price sealed-bid auctions

It is often observed in first-price sealed-bid auction experiments that subjects tend to bid above the risk neutral Nash equilibrium predictions. One possible explanation for this overbidding phenomenon is that bidders subjectively weight their winning probabilities. In the relevant literature, the probability weighting functions (PWFs) suggested to explain overbidding imply the underweighting of all probabilities. However, such functions are not in accordance with the PWFs commonly used in the literature (i.e., inverse S-shaped functions). In this paper we introduce inverse S-shaped PWFs into first-price sealed-bid auctions and investigate the extent to which such weighting functions explain overbidding. Our results indicate that bidders with low valuations underbid, whereas those with high valuations overbid. We accordingly conclude that inverse S-shaped PWFs provide a partial explanation for overbidding.     

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.     

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.     

Descending price multi-item auctions

We propose a simultaneous descending price auction mechanism to sell multiple heterogeneous items, each owned by a distinct seller, to a number of buyers. Each buyer has known private valuations on items, and wants at most one item. We show that if the sellers follow a descending price offer procedure and the buyers follow a greedy strategy for accepting the offers, the auction results in a nearly efficient allocation, and terminates close to a competitive equilibrium price vector. The descending price offer strategy of the sellers is close to a Nash equilibrium. However, we show that the buyers are better off waiting in our auction. There is a maximum limit (corresponding to the minimum competitive equilibrium price vector) till which they can wait without running into the risk of not winning any item. If the buyers wait within this limit, the prices can be brought arbitrarily close to a uniquely defined competitive equilibrium price vector.     

A model for sealed-bid auctions with independent private value and common value components

This paper shows how a decision-making model can be applied to a sealed-bid auction with both independent private value (IPV) and common value (CV) components. The model yields estimates for the winning bid and for the actual value and error components of the winning bid as functions of the number of bidders and the underlying value and error distributions, assuming that these distributions are normal. The winner's curse and the special cases of IPV and CV auctions are examined using the model.     

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.     

Defensive sniping and efficiency in simultaneous hard-close proxy auctions

A well-known myopic bidding strategy fails to support an equilibrium of simultaneous ascending proxy auctions for heterogeneous items when a hard-close rule is in place. This is because, in common with the single-auction case, last minute bidding (sniping) is a best response to naive behaviour. However, a modification to the myopic strategy in which all bidders submit an additional bid in the closing stages of the auction–a practice I call ‘defensive sniping’–is shown to yield an efficient, belief-free equilibrium of such environments. This equilibrium is essentially unique within the class of belief-free, efficient equilibria.     

Detection of collusion in government procurement auctions

Research on bidder collusion in procurement auctions is reasonably successful in unveiling the mechanisms of collusion among the bidders. But it is relatively weak in forwarding effective practical methods of collusion detection before the winner is declared, because they presuppose the knowledge of collusion in specific auctions. Past studies, however, point out the need for working with bid price-to-reserve price ratios rather than bid prices or winning bid prices, to be free from the problem of heteroscedasticity. They also draw an important inference that the set of collusive data are significantly different from the set of competitive data. On the basis of these basic facts, the current paper outlines a seven-step approach to collusion detection. The approach makes rudimentary statistical analysis of bid price-to-reserve price ratios for all the bidders. The analysis comprises tests of equality of means, medians and variance and tests of skewness, autocorrelation and normality of the ratios. It divides the ratios into two significantly different clusters. The cluster with the higher mean and variance values of the ratios corresponds to collusive bidding with the other cluster corresponding to competitive bidding. The paper proposes the construction of a process control chart to detect occurrence of collusion in an auction immediately after the price bids are opened. The approach is illustrated by applying it to data from procurement auctions for construction projects in a State Department of the Republic of India.     

The condominium problem; auctions for substitutes

This paper considers the problem of designing selling procedures for substitutes (like condominium units). Oral, ascending auctions for the right to choose are efficient. This is a common type of auction used for the sale of real estate. Efficiency is not optimal from the seller’s viewpoint. An optimal procedure distorts the right-to-choose auction to favor in late rounds bidders whose preferred object has already been sold. This optimal auction is complex. A revenue improving departure from efficiency can be achieved by simply auctioning all the rights to choose before any of them is exerted.Received: 5 February 2003, Accepted: 15 February 2005, JEL Classification: D44I acknowledge very helpful comments by Joe Harrington, Ken Hendricks, and anonymous referees. Financial aid from the European Commission through the TMR Program (contract FMRX-CT98-0203) and the Spanish MCyT (Grants SEC 2002-02506 and SEC 2003-08080) is also gratefully acknowledged.     

Money Out of Thin Air: The nationwide Narrowband pcs Auction

The Federal Communications Commission held its first auction of radio spectrum at the Nationwide Narrowband PCS Auction in July 1994. The simultaneous multiple-round auction, which lasted five days, was an ascending bid auction in which all licenses were offered simultaneously. This paper describes the auction rules and how bidders prepared for the auction. The full history of bidding is presented. Several questions for auction theory are discussed. In the end, the government collected $617 million for ten licenses. The auction was viewed by all as a huge success an excellent example of bringing economic theory to bear on practical problems of allocating scarce resources.     

Using announcement options in the bid construction phase for disaster relief procurement

This paper presents an analysis of the bid construction phase of procurement auctions in disaster relief and humanitarian logistics. Substitution and partial fulfillment options are presented in formulations to allow bidders with fewer inventories to offer substitute item types and partial bids in auctions. During the auction announcement phase, a coordinating platform for disaster locations (i.e., auctioneer) allows substitution and partial fulfillment options to the relief suppliers (i.e., bidders) when acceptable. Thus, suppliers with fewer inventories can offer substitute item types and participate in more auctions by partially bidding. A genetic algorithm, a simulated annealing algorithm and an integer program are used for the analysis of the bid construction phase with different announcement options. Heuristic solution techniques and an IP formulation help understand the dynamics of the bid construction problem. It is shown that the addition of substitution and partial fulfillment options is essential to diversify and increase the usable capacity of the supplier base. Additionally, the partial fulfillment option enables better usage of supplier inventories in an environment with scarce supplies.