On second-price auctions and imperfect competition

Consider two sellers each of whom has one unit of an indivisible good and two buyers each of whom is interested in buying one unit. The sellers simultaneously set reserve prices and use second-price auctions as rationing device. An equilibrium in pure strategies where each seller has a regular customer is characterized. The result is applied in order to demonstrate that not allowing sellers to use second-price auctions may enhance total surplus.     

Semiparametric identification and estimation in multi-object,English auctions

Within the independent private-values paradigm, we derive the data-generating process of winning bids for two different objects sold sequentially at English auction, assuming the valuations across objects for a particular bidder are potentially dependent. We demonstrate that, within the Archimedean family of copulas, the model is identified using only observed winning bids, and then propose a semiparametric estimation strategy to recover the joint distribution of valuations. We implement our methods using data from fish auctions held in Denmark and estimate whether bundling is expected-revenue enhancing.     

On the existence of an increasing symmetric equilibrium in (k + 1)-st price common value auctions

In a classical result, Milgrom (1981a) established that the Monotone Likelihood Ratio Property (MLRP) is a sufficient condition for the existence of an increasing symmetric equilibrium in (k + 1)-st price common value auctions. We show: (1) If MLRP is violated, then for any number of bidders and objects there exists a distribution of the common value such that no increasing symmetric equilibrium exists; (2) If MLRP is violated, then for any distribution of the common value there exist infinitely many pairs of the number of bidders and the number of objects such that an increasing symmetric equilibrium does not exist; (3) There are examples where an increasing symmetric equilibrium exists even when the signal distribution violates MLRP.     

Synergies and price trends in sequential auctions

In this paper we consider sequential second-price auctions where an individual's value for a bundle of objects is either greater than the sum of the values for the objects separately (positive synergy) or less than the sum (negative synergy). We show that the existence of positive synergies implies declining expected prices. When synergies are negative, expected prices are increasing. There are several corollaries. First, the seller is indifferent between selling the objects simultaneously as a bundle or sequentially when synergies are positive. Second, when synergies are negative, the expected revenue generated by the simultaneous auction can be larger or smaller than the expected revenue generated by the sequential auction. In addition, in the presence of positive synergies, an option to buy the additional object at the price of the first object is never exercised in the symmetric equilibrium and the seller's revenue is unchanged. Under negative synergies, in contrast, if there is an equilibrium where the option is never exercised, then equilibrium prices may either increase or decrease and, therefore, the net effect on the seller's revenue of the introduction of an option is ambiguous. Finally, we examine a special case with asymmetric players who have distinct synergies. In this example, even if one player has positive synergies and the other has negative synergies, it is still possible for expected prices to decline.Received: 12 December 2000, Accepted: 1 May 2002, JEL Classification: D44Flavio Menezes acknowledges the financial support from ARC (Grant A000000055) and CNPq. Monteiro acknowledges the financial support from CNPq and the hospitality of CERSEM where part of this paper has been written. We thank Richard Engelbrecht-Wiggans, Peter Sørensen and two anonymous referees for useful comments.     

Semiparametric estimation in models of first-price,sealed-bid auctions with affiliation

Within the affiliated private-values paradigm, we develop a tractable empirical model of equilibrium behaviour at first-price, sealed-bid auctions. The model is non-parametrically identified, but the rate of convergence in estimation is slow when the number of bidders is even moderately large, so we develop a semiparametric estimation strategy, focusing on the Archimedean family of copulae and implementing this framework using particular members—the Clayton, Frank, and Gumbel copulae. We apply our framework to data from low-price, sealed-bid auctions used by the Michigan Department of Transportation to procure road-resurfacing services, rejecting the hypothesis of independence and finding significant (and high) affiliation in cost signals.     

Partial identification and testable restrictions in multi-unit auctions

Bidders’ values in discriminatory and uniform-price auctions are not necessarily point-identified under the assumptions of equilibrium bidding and independent private values, but meaningful policy analysis can proceed from bounds on bidder values. This paper provides upper and lower bounds on the set of values that can rationalize a given distribution of bids, under the additional (and standard) assumption of non-increasing marginal values. Novel testable implications of the best response hypothesis are also provided, again under the assumption of non-increasing marginal values.     

Multiple and last-minute bidding in competing internet auctions

The present paper proposes a theoretical model of the equilibrium bidding behavior in simultaneous competing private-value Internet auctions such as those on eBay. It shows that last-minute bidding and multiple bidding, two commonly observed bidding strategies, arise in equilibrium. It also suggests that last-minute bidding may lead to inefficient outcomes.     

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.     

Characterization of bidding behavior in multi-unit auctions

This paper considers a very general class of single or multi-unit auctions of indivisible objects. The model allows for interdependent values, multidiminensional types and any attitude towards risk. Assuming only optimal behavior, we prove that each bid is chosen in order to equalize the marginal benefit to the marginal cost of bidding. This generalizes many existing results in the literature. We use this characterization to obtain sufficient conditions for truthful bidding, monotonic best reply strategies and identification results for multi-unit auctions.     

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.     

Existence of optimal auctions in general environments

We provide a unified approach to the problem of existence of optimal auctions for a wide variety of auction environments. We accomplish this by first establishing a general existence result for a particular Stackelberg revelation game. By systematically specializing our revelation game to cover various types of auctions, we are able to deduce the existence of optimal Bayesian auction mechanisms for single and multiple unit auctions, as well as for contract auctions with moral hazard and adverse selection. In all cases, we allow for risk aversion and multidimensional, stochastically dependent types.     

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.     

Risk aversion and asymmetry in procurement auctions: Identification,estimation and application to construction procurements

This article studies a model of asymmetric risk averse bidding within the independent private value paradigm. The inherent asymmetry in cost and risk aversion imposes an original restriction on the observed bid data, an exact equality which leads to the model semiparametric identification and estimation. The unobserved arguments of this equality need to be simulated in order to estimate the bidders’ Constant Relative Risk Aversion or Constant Absolute Risk Aversion parameters and their heterogeneous cost distributions. In the Los Angeles City Hall construction contracts offered between 1994 and 2003, the model and methodology help reveal that financial asymmetries affect the firms’ cost distribution, while experience influences their degree of risk aversion.     

Optimal disclosure of costly information packages in auctions

In an independent, private values, second-price auction with entry fees we discuss the way in which a seller should optimally spread costly information among the bidders. We find that marginal gross revenues do not generally behave monotonically in total information release. In the two bidder case, essentially, any asymmetric allocation of information dominates the symmetric information allocation. Even the bidder who gets less information is willing to pay a higher entry fee for asymmetric information allocations than for the symmetric one. His entry fee coincides with that of the better informed bidder. Losses from allocating an amount of information non-optimally can be substantial.     

拆分招标的供应商数量研究

许多企业在采购时,常常将整笔业务拆分为两个合同:较大的第一合同和较小的第二合同,通过分批二级价格封闭式招标来选择不同的供应商供货。本文通过建立分批招标模型分析了供应商的投标策略和买方的采购策略,得出了当参加第一合同竞标的供应商数目和第二合同新引入的供应商数目满足一个不等式时,拆分招标的采购成本小于整体招标的采购成本,并且指出了拆分比例对拆分招标的采购成本的影响。     

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.     

Wars of attrition and all-pay auctions with stochastic competition

We extend the war of attrition and all-pay auction analysis of Krishna and Morgan (1997) to a stochastic competition setting. We determine the existence of equilibrium bidding strategies and discuss the potential shape of these strategies. Results for the war of attrition contrast with the characterization of the bidding equilibrium strategies in the first-price all-pay auction as well as the winner-pay auctions. Furthermore we investigate the expected revenue comparisons among the war of attrition, the all-pay auction and the winner-pay auctions and discuss the linkage principle as well. Our findings are applicable to future works on contests and charity auctions.     

Capacity constraints and the winner's curse in multi-unit common value auctions

We explore the role of capacity constraints in establishing efficient pricing in multi-unit common value auctions in a setting relevant to auction-based equity IPOs. The method of inquiry is experimental economics. We find that sufficiently large capacity constraints mitigate the overbidding that plagues single-unit auctions and is one of the most robust laboratory findings. We also uncover a puzzling propensity for most bidders to place a portion of their bids at prices above their signals. This disequilibrium behavior persists with experience and in cases with substantial losses in previous auctions. Our results suggest caution is warranted in promoting auction based IPOs that allow unrestricted access by the non-professional investing public.     

Optimal auctions with multidimensional types and the desirability of exclusion

Within the context of a single-unit, independent private values auction model, we show that if bidder types are multidimensional, then under the optimal auction exclusion of a positive measure of bidder types occur. The results complements Armstrong’s (1996) exclusion of types result.     

A dynamic equilibrium model of search, production, and exchange

We study a general equilibrium model where agents search for production and trading opportunities, that generalizes the existing literature by considering a large number of differentiated commodities and agents with idiosyncratic tastes. Thus, agents must choose nontrivial exchange as well as production strategies. We consider decreasing, constant, and increasing returns to scale in the matching technology, and characterize the circumstances under which there exist multiple steady state equilibria, or multiple dynamic equilibria for given initial conditions. We also characterize the existence of dynamic equilibria that are limit cycles. Equilibria are not generally optimal, and when multiple equilibria coexist they may be ranked. We analyze comparative statics and find that certain intuitive results do not necessarily hold without restrictions on the stochastic structure.