Bidder collusion at first-price auctions

We show that in simple environments, a bidding ring operating at a first-price sealed-bid auction cannot achieve any gains relative to non-cooperative bidding if the ring is unable to control the bids that its members submit at the auction. This contrasts with results for the case in which the ring can control its members’ bids or prevent all but one of the ring members from participating in the auction. Numerical examples suggest that this result extends to some more complex environments. The analytic results use linear programming techniques that have potential applications to a number of other economic problems.     

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.     

Bayesian estimation approaches to first-price auctions

This paper considers Bayesian estimation strategies for first-price auctions within the independent private value paradigm. We develop an ‘optimization’ error approach that allows for estimation of values assuming that observed bids differ from optimal bids. We further augment this approach by allowing systematic over or underbidding by bidders using ideas from the stochastic frontier literature. We perform a simulation study to showcase the appeal of the method and apply the techniques to timber auction data collected in British Columbia. Our results suggest that significant underbidding is present in the timber auctions.     

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.     

The public release of information in first-price sealed-bid auctions

We determine the conditions under which the seller in a first-price sealed-bid auction has an incentive to reveal his private information about the mean of bidders’ valuations in order to increase his expected revenue. With risk-neutral bidders, we show that the seller’s expected revenue is higher when information is revealed. However, when bidders are risk-averse, this result does not necessarily hold; it depends on the bidders’ risk-aversion level and on the number of bidders.     

Quantile-based nonparametric inference for first-price auctions

We propose a quantile-based nonparametric approach to inference on the probability density function (PDF) of the private values in first-price sealed-bid auctions with independent private values. Our method of inference is based on a fully nonparametric kernel-based estimator of the quantiles and PDF of observable bids. Our estimator attains the optimal rate of Guerre et al. (2000), and is also asymptotically normal with an appropriate choice of the bandwidth.     

The econometrics of auctions with asymmetric anonymous bidders

We consider standard auction models when bidders’ identities are not-or are only partially-observed by the econometrician. We first adapt the definition of identifiability to a framework with anonymous bids and explore the extent to which anonymity reduces the possibility of identifying private value auction models. Second, in the asymmetric independent private value model which is nonparametrically identified, we generalize Guerre, Perrigne and Vuong’s estimation procedure [Optimal nonparametric estimation of first-price auctions, Econometrica 68 (2000) 525-574] and consider the asymptotic properties of our multi-step kernel-based estimator. Monte Carlo simulations illustrate the practical relevance of our estimation procedure in small data sets.     

Competitive bidding and proprietary information

We consider the sale of an object by sealed-bid auction, when one bidder has private information and the others have access only to public information. The equilibria of the bidding game are determined, and it is shown that at equilibrium the informed bidder's distribution of bids is the same as the distribution of the maximum of the others' bids. The expected profit of the informed bidder is generally positive, while the other bidders have zero expected profits. The equilibrium bid distributions and the bidders' expected profits are shown to vary continuously in the parameters of the bidding game.     

Systemic risk mitigation in financial networks

We propose a multi-period clearing framework, where the level of systemic risk is mitigated through the provision of liquidity assistance. The interbank liability network evolves stochastically over time, and assets of defaulted banks are sold to qualified banks within the network through a first-price sealed-bid auction. We find that policies targeting systemically important banks are more effective in core-periphery network structures, whereas those maximizing the total liquidity in the system are preferred in random network configurations. We assess sensitivity of systemic risk to variations in interbank liabilities as well as to their correlation structure.     

Auctions with endogenous participation

We study endogenous-participation auctions where bidders only know the number of potential participants. After seeing their values for the object, potential participants decide whether or not to enter the auction. They may not want to enter the auction since they have to pay participation costs. We characterize equilibrium bidding strategies and entry decisions for both first- and second-price sealed-bid auctions when participation is endogenous. We show that there is a pure strategy entry equilibrium where only bidders with values greater than a certain cut-off point actually bid. In this context, both types of auctions generate the same expected revenue. We also show that, contrary to the predictions of the fixed number of bidders literature, the seller's expected revenue may decrease when the number of potential participants increases. In addition, we show that it is optimal for the seller to charge an entry fee, which contrasts with results from the existing literature on auctions with entry. As in the fixed-n literature, we show that first-price auctions generate more expected revenue than second-price auctions when buyers are risk-averse. Finally, we characterize the optimal auction – the auction that maximizes the seller's expected revenue – by using a direct revelation mechanism. The optimal auction involves a reserve price larger than the optimal reserve price in the fixed-n literature. The winner's payment is the second highest bid less the participation cost and losers receive a subsidy equal to the participation cost. Received: 17 August 1998 / 21 September 1999     

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.     

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.     

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.     

Semi-nonparametric estimation of independently and identically repeated first-price auctions via an integrated simulated moments method

In this paper we propose to estimate the value distribution of independently and identically repeated first-price auctions directly via a semi-nonparametric integrated simulated moments sieve approach. Given a candidate value distribution function in a sieve space, we simulate bids according to the equilibrium bid function involved. We take the difference of the empirical characteristic functions of the actual and simulated bids as the moment function. The objective function is then the integral of the squared moment function over an interval. Minimizing this integral to the distribution functions in the sieve space involved and letting the sieve order increase to infinity with the sample size then yields a uniformly consistent semi-nonparametric estimator of the actual value distribution. Also, we propose an integrated moment test for the validity of the first-price auction model, and an data-driven method for the choice of the sieve order. Finally, we conduct a few numerical experiments to check the performance of our approach.     

排污权拍卖的最优机制设计

采用拍卖的方式分配排污权既是环境污染外部性的内部化,又是市场价格扭曲的纠正。本文基于一级密封价格拍卖方式,分析了排污权拍卖中厂商的最优策略和政府对排污权拍卖的机制设计问题。     

Econometrics of first-price auctions with entry and binding reservation prices

This paper considers the structural analysis of first-price auctions with entry and binding reservation prices. The presence of entry decisions and binding reservation prices complicates the structural analysis. Building on the recent theoretical work on entry in auctions, this paper assumes that each potential bidder first decides whether or not to incur an entry cost and become an active bidder using a symmetric mixed strategy. Then each active bidder bids optimally following the increasing Nash–Bayesian equilibrium strategy. Using the observed bids and the number of actual bidders, we propose an MSM estimator to estimate the parameters in the distribution of private values and the distribution of the number of active bidders. Our approach can be used to validate the theoretical auction model, to test whether the reservation prices are binding, and to test the mixed-strategy of entry.     

Common-value auction versus posted-price selling: an agent-based model approach

Previous theoretical work has compared a private-value auction and posted-price market, and an affiliated-value auction and a posted-price market to determine the selling method preferred by sellers. Much less, however, is known about the seller’s preferred selling method when the buyers have a common value of the item. Our objective is to determine if a first-price auction or a posted-price market provides a seller with the larger expected revenue when buyers have a common value of the item being sold. An agent-based posted-price market and an agent-based first-price common-value auction with a reserve price are developed to compare these selling methods. Holding the buyers’ uncertainty about the value of the item constant, the seller prefers the posted-price market when the seller has no uncertainty about the item’s value. When the seller has an equal level of uncertainty as the buyers, the seller’s expected revenue for each market is similar. As the seller’s uncertainty increases beyond the level of the buyers’ uncertainty, the auction with a reserve price eventually becomes the preferred choice.     

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.     

Optimal decisions in foreign exchange bidding markets

I characterize optimal bidding decisions in bidding markets where each agent does not perceive she can significantly affect the market outcome. Using a foreign exchange bidding framework to provide a micro-foundation for the shape of a bidder's payoff function, I show that (1) in a discriminatory auction a bidder bids for a price that equals the value of the marginal product of her bid quantity, and (2) in a competitive auction a bidder bids for a price that equals the value of the average product of her bid quantity. An example illustrates the comparative properties of these solutions.     

Revenue and efficiency effects of resale in first-price auctions

We study first-price auctions in a model with asymmetric, independent private values. Asymmetries lead to inefficient allocations, thereby creating a motive for resale after the auction is over. In our model, resale takes place via monopoly pricing—the winner of the auction makes a take-it-or-leave-it offer to the loser. Our goal is to compare equilibria of the first-price auction without resale (FPA) with those of the first-price auction with resale (FPAR). For the three major families of distributions for which equilibria of the FPA are available in closed form, we show that resale possibilities increase the revenue of the original seller. We also show by example that, somewhat paradoxically, resale may actually decrease efficiency.