Auctions with Financial Externalities

We study auctions with financial externalities, i.e., auctions in which losers care about how much the winner pays. In the first-price auction, larger financial externalities result in a lower expected price; in the second-price auction, the effect is ambiguous. Although the expected price in the second-price auction may increase if financial externalities increase, the seller is not able to gain more revenue by guaranteeing the losers a fraction of the auction revenue. With a reserve price, we find that both auctions may have pooling at the reserve price. This finding suggests that identical bids need not be a signal of collusion, in contrast to what is sometimes argued in anti-trust cases. We gratefully acknowledge financial support from the Dutch National Science Foundation (NWO 510.010.501 and NWO-VICI 453.03.606). For valuable discussions and comments, we would like to thank Eric van Damme, Jacob Goeree, Thomas Kittsteiner, Marta Kolodziejczyk, seminar participants at Tilburg University, Humboldt University Berlin, and National University of Singapore, and audiences at ESEM 2001 in Lausanne, and the FEEM 2002 conference in Milan on auctions and market design. The suggestions of an anonymous referee of this Journal greatly improved the article. The usual disclaimer applies.     

How to subcontract?

Firms compete for a contract and subcontract part of the work. If subcontracting takes place before the award of the contract, the revenue equivalence result breaks down, as subcontractors anticipate that their bids influence the probability of the firm winning the contract. Properties of the optimal subcontracting mechanism are discussed.     

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     

Auctions with costly information acquisition

We characterize optimal selling mechanisms in auction environments where bidders must incur a cost to learn their valuations. These mechanisms specify for each period, as a function of the bids in previous periods, which new potential buyers should be asked to bid. In addition, these mechanisms must induce the bidders to acquire information about their valuations and to reveal this information truthfully. Using a generalized Groves principle, we prove a very general “full extraction of the surplus” result: the seller can obtain the same profit as if he had full control over the bidders’ acquisition of information and could have observed directly their valuations once they are informed. We also present appealing implementations of the optimal mechanism in special cases. For helpful comments we thank George Deltas, David Martimort, an anonymous referee, and seminar participants in Mannheim, Rutgers, Tel Aviv, Toulouse, the Society for Economic Design 2002 conference in New York, and the 2003 North American Summer Meetings of the Econometric Society in Evanston, IL. Yossi Spiegel thanks the IIBR for financial assistance and Charles Zheng thanks the NSF for grant SES-0214471.     

投标与拍卖的决策理论方法

本文介绍国内很少涉及的国际投标和拍卖中的一些重要概念和基本问题，重点综述国际投标与拍卖的决策理论模型与方法的发展历史与现状。     

信誉的价值:以网上拍卖交易为例

本文使用网上拍卖交易数据,就卖者信誉对市场交易的影响进行了实证研究。我们发现,卖者的信誉评价一方面影响物品成交的价格,另一方面还对物品拍卖成功的概率有着显著的正面影响;但相对来说,卖者的信誉评价对后者的效果比对前者要更显著。这是本文的主要发现。该结果验证了在一个没有政府干预、近乎自由放任的“虚拟”市场上信誉机制的积极作用。     

密封价格拍卖或招标中的有限腐败

本文研究了密封价格拍卖或招投标中的有限腐败问题,探讨了当行贿者通过行贿招标主持人获得多次出标机会,而其他竞标者不知道这种有限腐败行为时,对拍卖结果所产生的影响。在第二价格拍卖机制下,由于竞标者按真实估价报价总是弱占优策略,该有限腐败行为在此拍卖机制下不会产生影响。但对于密封的第一价格拍卖机制来说,由于行贿者的多个标价中的最高标价比其他竞标者的标价更强势(aggressive),导致其他竞标者获胜的概率减少,行贿者获胜的概率增加。而行贿者的其他出标机会所用的出标策略比其他竞标者的出标策略要弱势,所以在保证期望收益增加的情况下所付出的期望支付有可能比在没有腐败情形下的期望支付要低。特别地,当行贿者获得更多的出标机会时所采用的出标策略与我们的直觉是有差异的。有限腐败对于物品所有者来说是不利的,他的期望收益随着行贿者的特权的增强而减少。     

Auctions for social lending: A theoretical analysis

Prosper, today the second largest social lending marketplace with nearly 1.5 million members and $380 million in funded loans, employed an auction mechanism amongst lenders to finance each borrower's loan until 2010. Given that a basic premise of social lending is cheap loans for borrowers, how does the Prosper auction do in terms of the borrower's payment, when lenders are strategic agents with private true interest rates? We first analyze the Prosper auction as a game of complete information and fully characterize its Nash equilibria, and show that the uniform-price Prosper mechanism, while simple, can lead to much larger payments for the borrower than the VCG mechanism. We next compare the Prosper mechanism against the borrower-optimal auction in an incomplete information setting, and conclude by examining the Prosper mechanism when modeled as a dynamic auction, and provide tight bounds on the price for a general class of bidding strategies.     

Asymptotic Revenue Equivalence in Auctions

We study the revenue in auctions of a single object when the number of bidders becomes large. We show that all sequences of auctions belonging to a class of mechanisms have limiting expected revenue equal to the expected best-use value of the object. An important special case that is covered is common value auctions, but more generally not even affiliation of values is assumed. This provides an asymptotic revenue equivalence result for settings beyond that of private values. Journal of Economic Literature Classification Numbers: D44, C72.     

我国网上拍卖中竞买者出价行为的实证分析

本文从竞买者出价频率与出价水平特征、出价时间过程的自相似性、出价水平的动态变化,以及出价水平的影响因素效应等四个方面,对我国网上拍卖中竞买者的出价行为进行了实证分析,结果发现:与eBay网上竞买者的出价行为相比,我国网上竞买者具有很高的倾向在后期出价,潜在影响因素易于在拍卖后期对竞买者的出价水平产生较大的影响;竞买者具有较强的投机心理,其出价行为存在较大的个体差异,缺乏规范、典型的模式。     

Equilibrium transformations and the Revenue Equivalence Theorem

I develop a method that transforms an equilibrium strategy profile from one auction to another. The method is constructive and does not require complicated computation. This provides a new approach to revenue equivalence and extends the theorem to domains where it had not previously been known, in particular to simultaneous multiple object auctions with complete information and to auction environments having correlated private values and common values.     

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.     

Abstract types and distributions in independent private value auctions

A large body of the mechanism design literature relies on convexity assumptions on the set of types (that is, on the domain of the mechanism). In this note I show that, at least for auction mechanisms with independent signals, it is always possible to extend incentive compatible mechanisms to incentive compatible mechanisms defined on any larger set of types. I acknowledge the comments of Luis Braido, Sérgio Orioli, Humberto Moreira, Frank Page and an anonymous referee. The financial support of Edital Universal 02/06, CNPq is gratefully acknowledged.     

The role of varying risk attitudes in an auction with a buyout option

Summary. An auction with a buyout option is modelled. Such an option allows a bidder to purchase the item being auctioned at a pre-specified buyout price, instead of attempting to obtain the item through the traditional auction procedure. This analysis is motivated by internet auctions where such options are present. If all auction participants are risk neutral, the seller will choose a buyout price high enough so that the option is never exercised. However, a risk averse seller facing risk neutral bidders will choose a price low enough so that the option is exercised with positive probability. Further, if bidders are risk neutral and the seller is risk averse, this option may result in a Pareto improvement compared to a sealed bid second price auction.Received: 3 December 2002, Revised: 28 September 2004, JEL Classification Numbers: D44, L86, D8. Correspondence to: Timothy MathewsWe would like to thank Yair Tauman, Thomas Jeitschko, Pradeep Dubey, Konstantinos Serfes, Abraham Neyman, Qihong Liu, and an anonymous referee, as well as participants of the 2001 Canadian Economic Association Conference and the 2001 Stony Brook International Conference on Game Theory. This paper is based upon Chapter Two of Mathews doctoral dissertation.     

Allocating multiple units

Summary. This paper studies the allocation and rent distribution in multi-unit, combinatorial-bid auctions under complete information. We focus on the natural multi-unit analogue of the first-price auction, where buyers bid total payments, pay their bids, and where the seller allocates goods to maximize his revenue. While there are many equilibria in this auction, only efficient equilibria remain when the truthful equilibrium restriction of the menu-auction literature is used. Focusing on these equilibria we first show that the first-price auction just described is revenue and outcome equivalent to a Vickrey auction, which is the multi unit analogue of a second-price auction. Furthermore, we characterize these equilibria when valuations take a number of different forms: diminishing marginal valuations, increasing average valuations, and marginal valuations with single turning points. Received: December 23, 1999; revised version: December 10, 2001     

A short proof of the Bulow-Klemperer auctions vs. negotiations result

Summary. Bulow and Klemperer [1] have provided an upper bound on the value of bargaining power for a seller of an indivisible object. Specifically, negotiating optimally with N buyers yields lower revenue than an English auction with N + 1 buyers. In this paper, a short and intuitive proof of this result is presented.Received: 2 August 2004, Revised: 6 December 2004, JEL Classification Numbers: C78, D44, D82.I would like to thank Per B. Overgaard and an anonymous referee for many valuable comments.     

Auctions with online supply

Online advertising auctions present settings in which there is uncertainty about the number of items for sale. We study mechanisms for selling identical items when the total supply is unknown but is drawn from a known distribution. Items arrive dynamically, and the seller must make immediate allocation and payment decisions with the goal of maximizing social welfare. We devise a simple incentive-compatible mechanism that guarantees some constant fraction of the first-best solution. A surprising feature of our mechanism is that it artificially limits supply, and we show that limiting the supply is essential for obtaining high social welfare. Although common when maximizing revenue, commitment to limit the supply is less intuitive when maximizing social welfare. The performance guarantee of our mechanism is in expectation over the supply distribution; We show that obtaining similar performance guarantee for every realization of supply is impossible.     

Spectrum allocation in Latin America: An economic analysis

As elsewhere, wireless markets play a crucial role in Latin American economic growth. Mobile telephone networks increasingly provide the communications infrastructure that has largely been lacking throughout the region. Yet, governments have generally made only modest allocations of bandwidth available to Latin American wireless operators, either absolutely (in terms of spectrum each country could allocate at modest opportunity cost) or relative to countries in North America, Asia and the European Union. Using an empirical model estimated on mobile phone data for international markets, we show that very large social benefits are available to countries that make more spectrum available for mobile phone markets. We conduct simulations using our calibrated model to provide lower bounds for country-by-country gains from larger allocations. We also discuss the impact of alternative regulatory regimes on the feasibility to achieve those social gains.     

Auctions with endogenous valuations: the snowball effect revisited

Summary. This paper looks at the determination of ownership of capacity when there are two ex-ante symmetric agents bidding for many units of capacity which are sold sequentially. It is shown that convexity of payoffs in the final stage of the game is sufficient to ensure monopolization of capacity, but that increasing returns to scale are not sufficient to ensure monopolization. Received: March 14, 1997; revised version: December 1, 1997     

Auctions with shill bidding

Summary. Shill bidding has increased substantially in recent years since the technology employed to conduct on-line auctions enables many sellers to disguise their identities and bid. Although their intent is to gain by misleading the bidders on the value of the object, we show that in a common value auction sellers are worse off shill bidding. In fact, any out-of-auction mechanism that makes it difficult for them to shill bid increases their revenues. In addition, shill bidding reduces the surplus of the bidders and the surplus from trade. It is only the auctioneer who could gain from this activity and in that sense he may not have an incentive from within the auction to discourage shill bidding.Received: 1 February 2002, Revised: 12 August 2003JEL Classification Numbers: D44.Correspondence to: Georgia KosmopoulouWe thank Timothy Dunne, Kevin Grier and the anonymous referees of this journal for helpful comments.