Auctions typically involve the sale of many related goods. Treasury, spectrum and electricity auctions are examples. In auctions where bidders pay the market-clearing price for items won, large bidders have an incentive to reduce demand in order to pay less for their winnings. This incentive creates an inefficiency in multiple-item auctions. Large bidders reduce demand for additional items and so sometimes lose to smaller bidders with lower values. We demonstrate this inefficiency in an auction model which allows interdependent values. We also establish that the ranking of the uniform-price and pay-as-bid auctions is ambiguous in both revenue and efficiency terms. Bidding behavior in spectrum auctions, electricity auctions, and experiments highlights the empirical importance of demand reduction.

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Recently, economists have developed methods for structural estimation of auction models. Many researchers object to these methods because they find the rationality assumptions used in these models to be implausible. In this paper, we explore whether structural auction models can generate reasonable estimates of bidders’ private information. Using bid data from auction experiments, we estimate four alternative structural models of bidding in first-price sealed-bid auctions: 1) risk neutral Bayes-Nash, 2) risk averse Bayes-Nash, 3) a model of learning and 4) a quantal response model of bidding. For each model, we compare the estimated valuations and the valuations assigned to bidders in the experiments. We find that a slight modification of Guerre, Perrigne and Vuong’s (2000) procedure for estimating the risk neutral Bayes-Nash model to allow for bidder asymmetries generates quite reasonable estimates of the structural parameters.

This paper proposes a semiparametric estimation procedure of the first-price auction model with risk averse bidders within the independent private values paradigm. We show that the model is nonidentified in general from observed bids. Moreover, any distribution of bids can be rationalized by an auction model with either constant relative risk aversion or constant absolute risk aversion. Thus identification of the model must be achieved through additional restrictions. We then establish semiparametric identification under a common but unknown support condition and parameterization of the bidders' utility function. Next we propose a semiparametric method for estimating the corresponding auction model using local polynomial estimators. This method involves several steps and allows to recover the parameters of the utility function as well as the bidders' private values and their distribution. An attractive computational advantage of our method is that it does not require solving the differential equation characterizing the equilibrium strategy. An illustration of the method on U.S. Forest Service timber sales is proposed. In particular, a test of bidders' risk neutrality is performed.

The accurate assessment of participants’ private information may critically affect policy recommendations in auction markets. In many auction environments estimation of the private information distribution may be complicated by the presence of unobserved heterogeneity. This problem arises when some of the information available to all bidders at the time of the auction is subsequently not observed by the researcher. This paper develops a semi-parametric method that allows a researcher to uncover the distribution of bidders’ private information in a standard First-Price procurement auction when unobserved auction heterogeneity is present. Sufficient identification conditions are derived and a two-stage estimation procedure to recover bidders’ private information is developed. The procedure is applied to data from Michigan highway procurement auctions and compared to the estimation procedures traditionally used in the context of highway procurement auctions. The estimation results suggest that ignoring unobserved auction heterogeneity is likely to result in substantially biased estimates and may lead to erroneous policy recommendations.

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We consider a dynamic Bertrand game, in which prices are publicly observed and each firm receives a privately observed cost shock in each period. Although cost shocks are independent across firms, within a firm costs follow a first-order Markov process. We analyze the set of collusive equilibria available to firms, emphasizing the best collusive scheme for the firms at the start of the game. In general, there is a tradeoff between productive efficiency, whereby the low-cost firm serves the market in a given period, and high prices. We show that when costs are perfectly correlated over time within a firm, if the distribution of costs is log concave and firms are sufficiently patient, then the optimal collusive scheme entails price rigidity: firms set the same price and share the market equally, regardless of their respective costs. Productive efficiency can be achieved in equilibrium under some circumstances, but such equilibria are not optimal. When serial correlation of costs is imperfect, partial productive efficiency is optimal. For the case of two cost types, first-best collusion is possible if the firms are patient relative to the persistence of cost shocks, but not otherwise. We present numerical examples of rfist-best collusive schemes.

We consider parametric examples of 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. In such multidimensional private value auction environments, we show that the revenue equivalence between the first and second price auctions breaks down and there is no definite revenue ranking; while the second price auction is always efficient allocatively, the first price auction may be inefficient and the inefficiency may increase as the signal becomes more informative; equilibria may fail to exist for the first price auction. We also show that auction mechanisms provide different incentives for bidders to acquire costly information about opponents ’ valuation.

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COWLES FOUNDATION DISCUSSION PAPER NO. 1279