Collusion via Signalling in Simultaneous Ascending Bid Auctions with Heterogeneous Objects, with and without Complementarities

Collusive equilibria exist in simultaneous ascending bid auctions with multiple objects, even with large complementarities in the buyers' utility functions. The bidders collude by dividing the objects among themselves, while keeping the prices low. In the most collusive equilibrium the complementarities are never realized. The scope for collusion however narrows as the ratio between the number of bidders and the number of objects increases.     

Asymmetric Auctions

The revenue-equivalence theorm for auctions predicts that expected seller revenue is independent of the bidding rules, as long as equilibrium has the properties that the buyer with the highest reservation price wins and any buyer with the lowest possible reservation price has zero expected surplus. Thus, in particular, the two most common auction institutions—the open 'English' and the sealed high-bid auction—are equivalent despite their rather different strategic properties.     

Auctions with cross-shareholdings

Summary. We study the effect of cross-shareholding among two competing firms on their bidding behavior and the expected sales revenue for the seller in an auction environment. The bidders private signals are independent, and the model encompasses the private values model and a particular common value model as special cases. When cross-shareholding is symmetric, the bids decrease towards the collusive level as the degree of cross-shareholding increases. The Revenue Equivalence result no longer holds: the first-price auction generates higher expected revenue for the seller than the second-price auction.With asymmetric cross-shareholding, revenue comparisons are only possible in the common value setting. Expected revenue for the seller is again higher in the first-price than in the second price auction. Bidding behavior in the second-price auction is more sensitive to changes in cross-shareholding and the value environment than in the first-price auction.Received: 18 September 2000, Revised: 27 May 2003, JEL Classification Numbers: C72, D44.Correspondence to: Sudipto DasguptaWe thank Sugato Bhattacharyya, Paul Klemperer, Kunal Sengupta and Guofu Tan for helpful discussions, and an anonymous referee for suggestions that improved the paper. The usual disclaimer, of course, applies.     

Optimal Multi-Object Auctions

This paper analyses optimal auctions of several objects. In the first model bidders have a binary distribution over their valuations for each object, in which case the optimal auction is efficient. The optimal auction takes one of two formats: either objects are sold in independent auctions, or a degree of bundling is introduced in the sense that the probability a bidder wins one object is increasing in her value for the other. The format of the optimal auction may depend upon the number of bidders. In the second model the restriction to binary distributions is relaxed, and the optimal auction is then inefficient.     

Default Service Auctions

In February 2002, New Jersey completed a market process whereby the utilities were able to purchase one-year forward contracts to ensure energy needs for their default service customers for a one-year period. The auction was the first application of the simultaneous descending clock auction to power procurement. We chose this auction format to fit the specific needs of the New Jersey Electric Discount and Energy Competition Act and the New Jersey Board of Public Utilities mandate for a competitive bidding process to procure the electricity to meet the electric utilities default service obligations.     

Sequentially Optimal Auctions

In auctions where a seller can post a reserve price but if the object fails to sell cannot commit never to attempt to resell it, revenue equivalence between repeated first price and second price auctions without commitment results. When the time between auctions goes to zero, seller expected revenues converge to those of a static auction with no reserve price. With many bidders, the seller equilibrium reserve price approaches the reserve price in an optimal static auction. An auction in which the simple equilibrium reserve price policy of the seller mirrors a policy commonly used by many auctioneers is computed.Journal of Economic LiteratureClassification Numbers: C78, D44, D82.     

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.     

Reduced Form Auctions Revisited

This note uses the Theorem of the Alternative to prove new results on the implementability of general, asymmetric auctions, and to provide simpler proofs of known results for symmetric auctions. The tradeoff is that type spaces are taken to be finite.     

k-Price Auctions

In this paper we analyze the equilibria structure of k-price auctions, k ≥ 3, under the independent-private-value assumption. We discuss agents with an arbitrary attitude toward risk. That is, agents may be risk averse or risk seeking, or they may have an alternating attitude toward risk. We provide a characterization of a continuous symmetric equilibrium, prove that there exists at most one such equilibrium, and show that every such equilibrium is differentiable and increasing. We also show some additional general properties of the equilibrium strategies in these auctions. Journal of Economic Literature Classification Numbers: C72, C73, D83.     

Auctions as coordination devices

This paper develops an economic argument relating auctions to high market prices. At the core of the argument is the claim that market competition and bidding in an auction should be analyzed as part of one game, where the pricing strategies in the market subgame depend on the bidding strategies during the auction. I show that when there are two licenses for sale the only equilibrium in the overall game that is consistent with the logic of forward induction is the one where firms bid an amount (almost) equal to the profits of the cooperative market outcome and follow a cooperative pricing strategy in the market game resulting in high prices. With three or more licenses the auction format co-determines whether or not the forward induction argument works.     

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.     

Optimal Complementary Auctions*

This paper considers the situation where two products are sold by the same seller, but to disjoint sets of potential buyers. Externalities may arise from each market outcome to the other. The paper examines the nature of the seller's optimal mechanism, and, for example in the case of positive externalities, it is shown that the allocation decision in either market depends on the highest types in both markets. The optimal mechanism can be implemented by an indirect mechanism that essentially charges winning bidders for the value of their externalities. The analysis is applied to the sale of public sector franchises including exploration and development rights for oil and gas tracts.     

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.     

Strategic Analysis of High-tech Auctions

This paper deals with the security voting structure in an auction mechanism used to sell an item Of high-tech. The design of security voting structure allows the seller to choose between two objectives that are not mutually consistent. However, if the seller wants to maximize his revenue, he should retain some shares to benefit from the future dividends generated by the acquirer. In addition, if he wants to sell his high-tech to the most efficient candidate, he should sell all the shares.     

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.     

Informational Size and Efficient Auctions

We develop an auction model for the case of interdependent values and multidimensional signals in which agents' signals are correlated. We provide conditions under which a modification of the Vickrey auction which includes payments to the bidders will result in an ex post efficient outcome. Furthermore, we provide a definition of informational size such that the necessary payments to bidders will be arbitrarily small if agents are sufficiently informationally small.     

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.     

Auctions for Universal Service Subsidies

The Telecommunications Act of 1996 requires that telephone service be available in high-cost areas at rates that are affordable and reasonably comparable to those charged in low-cost areas. It also requires that carriers serving high-cost areas at below-cost rates be compensated with explicit and sufficient subsidies. This paper analyzes an auction mechanism for the allocation of such subsidies. It shows that in a wide range of circumstances auctions are more efficient than traditional subsidy schemes. It also shows, however, that auction designs aimed at stimulating competition among several subsidized carriers may be particularly vulnerable to collusion.     

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。