A Mechanism Design Approach to Ranking Asymmetric Auctions

I propose a new mechanism design approach to the problem of ranking standard auctions with two heterogeneous bidders. A key feature of the approach is that it may be possible to rank two auctions even if neither dominates the other for all combinations of types. The approach simplifies the analysis and unifies results in the existing literature. Roughly speaking, the first‐price auction is more profitable than the second‐price auction when the strong bidder's distribution is flatter and more disperse than the weak bidder's distribution. Applications include auctions with one‐sided externalities. Moreover, contrary to previous work, reserve prices are easily handled. Finally, the method can be extended to some environments with many bidders.     

Speculation in Standard Auctions with Resale

In standard auctions resale creates a role for a speculator—a bidder who is commonly known to have no use value for the good on sale. We study this issue in environments with symmetric independent private‐value bidders. For second‐price and English auctions the efficient value‐bidding equilibrium coexists with a continuum of inefficient equilibria in which the speculator wins the auction and makes positive profits. First‐price and Dutch auctions have an essentially unique equilibrium, and whether or not the speculator wins the auction and distorts the final allocation depends on the number of bidders, the value distribution, and the discount factor. Speculators do not make profits in first‐price or Dutch auctions.     

Reputation and Mechanism Choice in Procurement Auctions: An Experiment

We experimentally study the role of reputation in procurement using two common mechanisms: price‐based and buyer‐determined auctions. While buyers are bound to buy from the lowest bidder in price‐based auctions, they can choose between bidders in buyer‐determined auctions. Only the latter buyers can consider the reputation of bidders. We find that bidders supply higher quality in buyer‐determined auctions leading to higher market efficiencies in these auctions. Accordingly, buyers prefer the buyer‐determined auction over the price‐based auction, while only half of the bidders do so. A more detailed analysis of buyers' and bidders' behavior and profits provides insights into their mechanism choice.     

基于幂效用函数的多属性英式拍卖研究

以采购问题为背景研究多属性拍卖问题,其中拍卖问题的特点是：（1）包含任意有限个属性;（2）买卖双方的效用函数均具有加性结构,且在除价格以外的单个属性上,买方的效用函数和卖方的成本函数均为一般幂函数形式。首先,设计了一种买方事先公布评分函数而卖方轮流提交投标的多属性英式拍卖机制;其次,在卖方对称的假设下分析了拍卖机制中的最优投标策略,确定了最优投标价格和最优非价格属性值;然后,分析得出了最具成本优势的卖方最终胜出的条件以及最优多属性投标;最后,计算了该拍卖机制中买方的期望收益,并求出了使其期望收益最大化的最优评分函数权重。     

An Experimental Investigation of Procurement Auctions with Asymmetric Sellers

Electronic reverse auctions are a commonly used procurement mechanism. Research to date has focused on suppliers who are ex ante symmetric in that their costs are drawn from a common distribution. However, in many cases, a seller's range of potential costs depends on their own operations, location, or economies of scale and scope. Thus, understanding how different bidder types impact auction outcomes is key when designing an auction. This study reports the results of the first controlled laboratory experiment designed to compare prices between first‐price and second‐price procurement auctions for homogeneous goods when seller cost types are asymmetric and the number of bidders varies. The results indicate that first‐price auctions generate lower prices regardless of market composition. The results also reveal that first‐price auctions are at least weakly more efficient than second‐price auctions despite the theoretical prediction that the reverse should hold in asymmetric auctions. Post hoc analysis of individual bidders' behavior in first‐price auctions revealed evidence that bidders systematically underbid when their cost realizations were close to the lower bound. Furthermore, bidders adjust their behavior based on the type of the other bidders in the market in a manner inconsistent with theory. Consequently, adding a third bidder to a two‐bidder market is not advantageous to the buyer unless that third bidder is a low‐cost type.     

Collusion via Resale

The English auction is susceptible to tacit collusion when post‐auction interbidder resale is allowed. We show this by constructing equilibria where, with positive probability, one bidder wins the auction without any competition and divides the spoils by optimally reselling the good to the other bidders. These equilibria interim Pareto‐dominate (among bidders) the standard value‐bidding equilibrium without requiring the bidders to make any commitment on bidding behavior or postbidding spoil division.     

在线拍卖中的“托”出价研究

本文分析了独立的私人估价环境下最优保留价格与竞买人数之间的关系,纠正了最优保留价格与竞买人数无关的传统观点.在此基础上,讨论了卖者可能递交"托"出价的条件以及拍卖中只剩下一个竞买人时卖者的最优"托"出价.     

Design of Auction Parameters to Reduce the Effect of Collusion

Government departments are increasingly turning to auctions to procure goods and services. Collusion among bidders, however, reduces competition and raises winning bid prices. Since conventional collusion control measures based on the redesign of auction mechanisms are less effective in government procurement auctions, there is a need to devise control measures that decrease the effect of collusion. This article demonstrates how the principles of design of experiments can be applied in a system dynamics model to find the auction parameter values that substantially reduce the effect of collusion in government procurement auctions. This research makes a number of contributions. First, it develops a feedback‐based dynamic mechanism of collusion in government procurement auctions. The mechanism proposes the winning bid price as being determined not by the total number of bidders but by the number of independent bidders. It defines each cartel as one independent bidder regardless of the number of bidders in the cartel. Second, the mechanism is tested by developing a system dynamics model to government auctions for procuring contracts for roadwork projects in India. Third, the principles of experimental design are applied to find the auction parameter values that ensure high bid participation and low winning price‐to‐reserve price ratios.     

Transparency in Buyer‐Determined Auctions: Should Quality be Private or Public?

We study buyer‐determined procurement auctions where both price and non‐price characteristics of bidders matter for being awarded a contract. Although, in scoring auctions bidders perfectly know how price and non‐price attributes determine the awarding of the contract, this remains uncertain in buyer‐determined auctions where the buyer is free to choose once all bids have been submitted. We analyze the impact of information bidders have with respect to the buyer's awarding decision. As we show theoretically whether it is in the buyer's interest to conceal the impact of non‐price characteristics depends on how important the quality aspects of the procured good are to the buyer: The more important quality aspects are, the more interesting concealment becomes. In a counterfactual analysis using data from a large European procurement platform, we analyze the reduction of non‐price information available to the bidders. Confirming our hypothesis, for auction categories where bidders’ non‐price characteristics strongly influence buyers’ decisions concealment of non‐price information leads to an increase in buyers’ surplus of up to 15% due to higher competitive pressure and lower bids. Conversely, for categories where bidders’ non‐price characteristics are of little importance concealment of non‐price information leads to a decrease in buyers’ surplus of up to 6%.     

Keyword Auctions,Unit‐Price Contracts,and the Role of Commitment

Motivated by the enormous growth of keyword advertising, this paper explores the design of performance‐based unit‐price contract auctions, in which bidders bid their unit prices and the winner is chosen based on both their bids and performance levels. The previous literature on unit‐price contract auctions usually considers a static case where bidders' performance levels are fixed. This paper studies a dynamic setting in which bidders with a low performance level can improve their performance at a certain cost. We examine the effect of the performance‐based allocation on overall bidder performance, auction efficiency, and the auctioneer's revenue, and derive the revenue‐maximizing and efficient policies accordingly. Moreover, the possible upgrade in bidders' performance level gives the auctioneer an incentive to modify the auction rules over time, as is confirmed by the practice of Yahoo! and Google. We thus compare the auctioneer's revenue‐maximizing policies when she is fully committed to the auction rule and when she is not, and show that the auctioneer should give less preferential treatment to low‐performance bidders when she is fully committed.     

Optimal Nonparametric Estimation of First‐price Auctions

This paper proposes a general approach and a computationally convenient estimation procedure for the structural analysis of auction data. Considering first‐price sealed‐bid auction models within the independent private value paradigm, we show that the underlying distribution of bidders' private values is identified from observed bids and the number of actual bidders without any parametric assumptions. Using the theory of minimax, we establish the best rate of uniform convergence at which the latent density of private values can be estimated nonparametrically from available data. We then propose a two‐step kernel‐based estimator that converges at the optimal rate.     

组合拍卖与议价谈判机制设计研究

设计了一种先组合拍卖再议价谈判的多物品出售两阶段机制.论文分析表明,机制的组合拍卖阶段保持了VCG机制的激励相容性质,在机制的议价谈判阶段,存在4种不同类别的获胜投标者,就拍卖者将采取的不同价格策略,可将其区分为第1类投标者和第2类投标者.据此,找到了拍卖者采取不同价格策略的相应条件.给出了该机制中拍卖者与任意获胜投标者之间的博弈均衡路径.就买卖双方的总估价而言,存在不同相对关系下的不同交易结果.对比该机制和经典VCG机制,该机制改进社会交易福利值为:第1类投标者在议价价格和VCG价格下带给拍卖者利润的变化值.此结果表明,该机制的社会交易福利优于经典VCG机制.     

Increasing Revenue by Decreasing Information in Procurement Auctions

We report on results of several laboratory experiments that investigate on‐line procurement auctions in which suppliers bid on price, but exogenous bidder quality affects winner determination. In procurement auctions, bidder quality may or may not be publicly known to all bidders, and the effect of this quality transparency on the auction outcome is one aspect of auction design that we examine. The second aspect of auction design that we examine is the effect of price visibility on the auction outcome, and the interaction between price visibility and quality transparency. In terms of price visibility, we consider two extreme cases: the sealed bid request for proposals (RFPs), and the open‐bid dynamic auction event. In terms of bidder quality transparency, we also consider two extreme cases: a setting in which bidder qualities are publicly known and the case in which they are private. We find that in our laboratory experiments, the RFP format is consistent in generating higher buyer surplus levels than does the open‐bid dynamic format. This advantage is independent of the quality transparency. In contrast, the open‐bid format is highly sensitive to quality transparency, generating significantly lower buyer surplus levels when the information about bidder quality is public.     

Ranked Items Auctions and Online Advertisement

We study auctions for a set of commonly‐ranked items where each buyer has unit demand. This setting has promising applications in areas such as keyword auctions in the search engine advertising industry, the sale of quality‐ranked raw materials, etc. An auction mechanism suitable for this setting is the simultaneous pooled auction (SPA), where each bidder simultaneously submits a single bid and is allocated an object based on the rank of his bid among all the bids. We study how to improve the seller's expected revenue by enforcing a reserve price in an SPA. We find that the use of an appropriate reserve price may significantly increase the seller's revenue, especially when the number of items for sale is relatively large compared to the number of participating bidders. One inherent problem in the SPA is that some bidders may incur ex post losses; that is, they pay more than what they value the received objects. We propose a tailored VCG mechanism that generates the same expected revenue as the SPA does, while bidders do not incur any ex post loss. We also discuss the potential applications of this research to keyword auctions.     

An Analysis of Scoring and Buyer‐Determined Procurement Auctions

In procurement auctions, the object for sale is a contract, bidders are suppliers, and the bid taker is a buyer. The suppliers bidding for the contract are usually the current supplier (the incumbent) and a group of potential new suppliers (the entrants). As the buyer has an ongoing relationship with the incumbent, he needs to adjust the bids of the entrants to include non‐price attributes, such as the switching costs. The buyer can run a scoring auction, in which suppliers compete on the adjusted bids or scores, or, he can run a buyer‐determined auction, in which suppliers compete on the price, and the buyer adjusts a certain number of the bids with the non‐price attributes after the auction to determine the winner. Unless the incumbent has a significant cost advantage over the entrants, I find that the scoring auction yields a lower average cost for the buyer, if the non‐price attributes are available. If the non‐price attributes are difficult or expensive to obtain, the buyer could run a buyer‐determined auction adjusting only the lowest price bid.     

建设用地指标和建设用地的序贯拍卖定价机制研究

现行建设用地指标定价机制未能有效反映其真实价值，使得农民缺乏复垦闲置宅基地来提供建设用地指标的意愿。针对指标和建设用地的互补性特点，以及指标价值是开发商私人信息的特征，本文构建第一价格和第二价格两种密封拍卖下的互补品序贯拍卖模型，研究建设用地指标和建设用地的定价机制。理论和仿真分析得出两种拍卖下的建设用地指标和建设用地价格，并通过对比分析得出不同目标下的最优定价机制。研究发现，两种拍卖下，竞标人的建设用地指标报价均随着土地价格增值系数增加而提高，随着竞标人数递增而降低；序贯二价下的竞标人建设用地指标及建设用地的报价均高于序贯一价；序贯二价下，持有建设用地指标的竞标人获得建设用地的概率更高。因此，地方政府可采用适当提高土地闲置费用的方法，以此提高失地农民复垦权益，激励农民复垦闲置宅基地，增加建设用地指标供给；同时，采用序贯二价拍卖，提高建设用地指标和土地的利用效率。     

The Affiliation Effect in First‐Price Auctions

We study the monotonicity of the equilibrium bid with respect to the number of bidders n in affiliated private‐value models of first‐price sealed‐bid auctions and prove the existence of a large class of such models in which the equilibrium bid function is not increasing in n. We moreover decompose the effect of a change in n on the bid level into a competition effect and an affiliation effect. The latter suggests to the winner of the auction that competition is less intense than she had thought before the auction. Since the affiliation effect can occur in both private‐ and common‐value models, a negative relationship between the bid level and n does not allow one to distinguish between the two models and is also not necessarily (only) due to bidders taking account of the winner's curse.     

Collusion in Second‐Price Auctions under Minimax Regret Criterion

Collusion in auctions, with different assumptions on distributions of bidders' private valuation, has been studied extensively over the years. With the recent development of on‐line markets, auctions are becoming an increasingly popular procurement method. The emergence of Internet marketplaces makes auction participation much easier and more convenient, since no physical presence of bidders is required. In addition, bidders in on‐line auctions can easily switch their identities. Thus, it may very well happen that the bidders in an auction have very little, if any, prior knowledge about the distributions of other bidders' valuations. We are proposing an efficient distribution of collusive profit for second‐price sealed bid auctions in such an environment. Unlike some known mechanism, which balance the budget only in expectation, our approach (which we call Random k) balances the budget ex‐post. While truth‐telling is not a dominant strategy for Random k, it is a minimax regret equilibrium.     

网上逢低买入拍卖形式下的买方策略

逢低买入是一种新型的基于网络的动态定价方式。这种定价方式将不同的投标人联合起来以便获得数量折扣,它的一个特点就是商品的价格随着中标人数的增加而降低。本文采用独立私有估价假设,建立了一个不完全信息的动态博弈模型来解释在逢低买入机制下的买方的投标策略问题。通过求解发现,对于买方而言,存在一个弱占优策略:投标人投低于他估价的最大被允许投标值,这表明逢低买入拍卖是一种弱激励相容的机制。     

ASSESSING SOCIAL COSTS OF INEFFICIENT PROCUREMENT DESIGN

This paper considers the social costs implied by inefficient allocation of contracts in a first‐price, sealed‐bid procurement auction with asymmetric bidders. We adopt a constrained (piecewise linear) strategy equilibrium concept and estimate the structural parameters of the bidders' distribution of costs. We estimate social costs defined as the predicted cost difference between the winning firm and the most efficient bidding firm. We also compare the expected procurement costs under two different auction formats. The data is collected from procurement auctions of road painting in Sweden during 1993–1999. The results indicate that the social costs of inefficient contract allocation is about 2% of total potential production cost and that an efficient second‐price auction would lower the expected procurement cost by 2.5%. (JEL: D44, H57, C15)