Investment Incentives in Procurement Auctions

This paper investigates firms' incentives to invest in cost reduction in the first price sealed bid auction, a format largely used for procurement. Two central features of the model are that we allow firms to be heterogeneous and that investment is observable. We find that firms will tend to underinvest in cost reduction because they anticipate fiercer head-on competition. Using the second price auction as a benchmark, we also find that the first price auction will elicit less investment from market participants and that this is socially inefficient. These results have implications for market design when investment is important.     

On the road to the Golden Age

Summary To find a pattern leading to the Golden Age it is necessary to introduce a principle for the division of consumption between generations.The Golden Rule result gives the fraction of G. N. P. that each generation saves on behalf of future generations but since this fraction is constant, previous generations have made an identical sacrifice on behalf of the present one.In a similar fashion it is postulated here that every generation chooses the proportion of G. N. P. which it wishes to save while requiring previous generations to save in exactly the same way. This means that although very generations would like to increase its consumption, it does not wish earlier generations to do so since that would leave less total G. N. P. in the present.The part of G. N. P. to be invested is assumed to be a certain, to be determined, function of time. The production function is taken to be Cobb-Douglas with constant returns to scale. The optimal growth path is determined under various assumptions about labour supply. It is shown that the Golden Age results are obtained as time approaches infinity.With 1 FigureThis research has been financed by a grant from the Tri-Centennial Fund of the Bank of Sweden.     

Entry of painters in the Amsterdam market of the Golden Age

We analyze the evolution of the entry of painters and price of paintings in the XVII century Amsterdam art market. In line with evolutionary theory, demand-driven entry in the market was first associated with product innovations and a rapid increase in the number of painters. After reaching a peak, the number of painters started to decrease in parallel with a price decline and the introduction of process innovations. To test for the role of profitability in the art market as a determinant of endogenous entry of painters, we build a price index for the representative painting inventoried in Dutch houses. This is based on hedonic regressions controlling for characteristics of the paintings (size, genre, placement in the house), the owners (job, religion, value of the collection, size of the house) and the painters. After a peak at the beginning of the century, the real price of paintings decreased until the end of the century. We provide anecdotal evidence for which high initial prices attracted entry of innovators, and econometric evidence on the causal relation between price movements and entry.     

Creative Destruction, Investment Volatility, and the Average Age of Capital

In this article, a new numerical procedure is used to compute the equilibrium of a vintage capital growth model with nonlinear utility, where the scrapping time is nonconstant. We show that equilibrium investment and output converge nonmonotonically to the balanced growth path due to replacement echoes. We find that the average age of capital is inversely related to output, which is consistent with recent micro evidence reinforcing the importance of the embodied question. We also find that an unanticipated permanent increase in the rate of embodied technological progress causes labor productivity to slowdown in the short run.     

Entry and Competition Effects in First-Price Auctions: Theory and Evidence from Procurement Auctions

Motivated by several interesting features of the highway mowing auction data from the Texas Department of Transportation (TDoT), we study three competing procurement auction models with endogenous entry. Our entry and bidding models provide several interesting implications. For the first time, we show that even within an independent private value paradigm, as the number of potential bidders increases, bidders' equilibrium bidding behaviour can become less aggressive, and the expected procurement cost may rise because the "entry effect" is always positive and may dominate the negative "competition effect". We then develop structural models of entry and bidding corresponding to the three models under consideration, controlling for unobserved auction heterogeneity, and use the recently developed semi-parametric Bayesian estimation method to analyse the data. We select the model that best fits the data, and use the corresponding structural estimates to quantify the "entry effect" and the "competition effect" with regard to the individual bids and the procurement cost.     

Auctions in which losers set the price

We study auctions of a single asset among symmetric bidders with affiliated values. We show that the second-price auction minimizes revenue among all efficient auction mechanisms in which only the winner pays, and the price only depends on the losers' bids. In particular, we show that the kth price auction generates higher revenue than the second-price auction, for all k>2. If rationing is allowed, with shares of the asset rationed among the t highest bidders, then the (t+1)st price auction yields the lowest revenue among all auctions with rationing in which only the winners pay and the unit price only depends on the losers' bids. Finally, we compute bidding functions and revenue of the kth price auction, with and without rationing, for an illustrative example much used in the experimental literature to study first-price, second-price and English auctions.     

Optimal Information Disclosure in Auctions and the Handicap Auction

We analyse a situation where a monopolist is selling an indivisible good to risk-neutral buyers who only have an estimate of their private valuations. The seller can release, without observing, certain additional signals that affect the buyers' valuations. Our main result is that in the expected revenue-maximizing mechanism, the seller makes available all the information that she can, and her expected revenue is the same as it would be if she could observe the part of the information that is "new" to the buyers. We also show that this mechanism can be implemented by what we call a handicap auction in interesting applications. In the first round of this auction, each buyer picks a price premium from a menu offered by the seller (a smaller premium costs more). Then the seller releases the additional signals. In the second round, the buyers bid in a second-price auction where the winner pays the sum of his premium and the second highest non-negative bid. In the case of a single buyer, this mechanism simplifies to a menu of European call options.     

Difference-Form Contests and the Robustness of All-Pay Auctions

In much of the existing literature on rent-seeking games, the outcome of the contest is either infinitely sensitive or relatively insensitive to contestants' efforts. The current paper presents a family of contest games that permit characterization of equilibrium for all levels of sensitivity of the outcome to contestants' efforts. Specifically, the outcome of the contest depends on the difference between efforts, which encompass the lottery and the all-pay auction as polar cases. The equilibrium converges to that of the all-pay auction as the probability of winning the prize grows infinitely sensitive to one's effort, and the main qualitative features of equilibrium persist over a large parameter region. Journal of Economic Literature Classification Numbers: D44, D72.     

Bottom-Fishing and Declining Prices in Sequential Auctions

We study standard sequential auctions, in which the seller chooses the order of sale, and right-to-choose auctions, in which the winner chooses her preferred item from the remaining items. Empirically, prices in sequential auctions tend to decline, and sellers often hold right-to-choose auctions. In our setting, the right-to-choose format guarantees declining prices and efficiency. In the standard auction, a buyer may submit a low bid for the first item ("bottom-fishing") despite its being her less-preferred item. An example shows that the standard auction has declining prices, is inefficient, and gives lower expected revenue than the right-to-choose. Journal of Economic Literature Classification Numbers: D44, D82.     

Auctions of licences and market structure

Summary. This paper studies sequential auctions of licences to participate in a symmetric market game. Assuming that the rate at which industry profits decrease with repeated entry is not too large, at the unique solution either a single firm preempts entry altogether or entry occurs in every stage, depending on the net benefit of complete preemption to an incumbent. If we relax the assumption, a third outcome can occur: two firms may coordinate their choices to avoid further entry. The analysis employs a new refinement of Nash equilibrium, the concept of recursively undominated equilibrium. Received: February 25, 2000; revised version: September 12, 2000     

Endogenous Entry and Exit in Common Value Auctions

We develop and experimentally test a model of endogenous entry, exit, and bidding in common value auctions. The model and experimental design include an alternative profitable activity (a safe haven) that provides agentspecific opportunity costs of bidding in the auction. Each agent chooses whether to accept the safe haven income or forgo it in order to bid in the auction. Agents that enter the auction receive independently-drawn private signals that provide unbiased estimates of the common value. The auctioned item is allocated to the high bidder at a price that is equal to the high bid. Thus the market is a first-price sealed-bid common value auction with endogenous determination of market size.     

Quantal Response Equilibrium and Overbidding in Private-Value Auctions

This paper applies the quantal response equilibrium (QRE) model to study overbidding in private-values auctions. Experimental evidence shows that the prevalence of overbidding depends on the cost of overbidding relative to underbidding, as predicted theoretically. We use QRE as an error structure to estimate parameters of several competing models of overbidding. A QRE model based on risk averse bidders closely tracks the exact distribution of bids. The estimated parameters are significant and consistent across treatments. Journal of Economic Literature Classification Numbers: C72, C92, D44.     

Profit Maximizing in Auctions of Public Goods

A profit-maximizing auctioneer can provide a public good to a group of agents. Each group member has a private value for the good being provided to the group. We investigate an auction mechanism where the auctioneer provides the good to the group only if the sum of their bids exceeds a reserve price declared previously by the auctioneer. For the two-bidder case with private values drawn from a uniform distribution we characterize the continuously differentiable symmetric equilibrium bidding functions for the agents, and we find the optimal reserve price for the auctioneer when such functions are used by the bidders. We also examine another interesting family of equilibrium bidding functions for this case, with a discrete number of possible bids, and show the relation (in the limit) to the differentiable bidding functions.     

A Study of Collusion in First-Price Auctions

This paper examines the bidding for school milk contracts in Florida and Texas during the 1980s. In both states firms were convicted of bid-rigging. The data and legal evidence suggest that the cartels in the two states allocate contracts in different ways: One cartel divides the market among members, while the other cartel also uses side payments to compensate members for refraining from bidding. We show that both forms of cartel agreements are almost optimal, provided the number of contracts is sufficiently large.
In the auction the cartel bidder may face competition from non-cartel bidders. The presence of an optimal cartel induces an asymmetry in the auction. The selected cartel bidder is bidding as a representative of a group and has on average a lower cost than a non-cartel bidder. The data support the predicted equilibrium bidding behaviour in asymmetric auctions in accordance with optimal cartels.     

Bundling and Optimal Auctions of Multiple Products

We study the optimal ( i.e. revenue maximizing) auction of multiple products. We make three major points. First, we extend the relationship between price discrimination and optimal auctions from the single-product case to the multiple-product case. A monopolist setting prices for multiple products may offer discounts on purchases of bundles of products; similarly, the optimal auction of multiple products facilitates price discrimination by allocating products inefficiently to customers who are willing to purchase both products. Second, we demonstrate that optimal auctions are qualitatively distinct from monopoly sales of multiple products. Because of uncertainty about the values of other consumers, two products are bundled probabilistically in an optimal auction for a customer who is willing to buy both of them. A customer may then receive a discount on a lower-valued product without receiving a higher-valued product. Third, we show that in an optimal auction of two products the allocation of one product may vary with the amount of competition for the other product.     

First Price Auctions in the Asymmetric N Bidder Case

I consider the first price auction when the bidders' valuations may be differently distributed. I show that every Bayesian equilibrium is an 'essentially' pure equilibrium formed by bid functions whose inverses are solutions of a system of differential equations with boundary conditions. I then prove the existence of an equilibrium. I prove its uniqueness when the valuation distributions have a mass point at the lower extremity of the support. I give sufficient conditions for uniqueness when every valuation distribution is one of two atomless distributions. I establish inequalities between equilibrium strategies when relations of stochastic dominance exist between valuation distributions.     

Asymmetric Information and Adverse Selection in Mauritian Slave Auctions

Information asymmetry is a necessary prerequisite for testing adverse selection. This paper applies this sequence of tests to Mauritian slave auctions. The theory of dynamic auctions with private and common values suggests that when an informed participant is known to be active, uninformed bidders will be more aggressive and the selling price will be higher. We conjecture that observable family links between buyer and seller entailed superior information and find a strong price premium when a related buyer purchased a slave, indicative of information asymmetry. We then test for adverse selection using sale motivation. Our results indicate large discounts on voluntary as compared to involuntary sales. Consistent with adverse selection, the market anticipated that predominantly low-productivity slaves would be brought to the market in voluntary sales.     

Designing Multi-unit Multiple Bid Auctions: An Agent-based Computational Model of Uniform, Discriminatory and Generalised Vickrey Auctions

Multi-unit auctions are being used by public agencies to allocate resources and to purchase services. These auctions resolve the lumpy bid problem inherent in single-bid auctions by allowing bidders to submit a supply or demand schedule. However, the choice of pricing formats for multi-unit auctions is controversial. Neither economic theory nor laboratory experiments depict a complete picture of how alternative pricing formats perform in terms of budgetary or allocative efficiency. This paper constructs an agent-based computational model to compare uniform, discriminatory and generalised Vickrey pricing formats under different degrees of competition and heterogeneity in the bidder population.     

网上拍卖竞买者出价来到过程的特征研究

本文利用从eBay网站收集的20个子类物品拍卖数据,通过基于MatLab编写的计算机程序,对竞买者出价来到过程的时段性、自相似性和幂律分布特征进行了研究,结果显示网上拍卖竞买者出价来到过程存在显著的后期出价现象,较长期限的拍卖能够减弱竞买者后期出价现象,且各类别拍卖的"冷淡期"呈现一定的规律;竞买者出价来到过程具有自相似性和幂律分布特征,受一自组织过程的驱动,但在不同拍卖时段有着不同的表现