Unfair contests

Real-world contests are often “unfair” in the sense that outperforming all rivals may not be enough to be the winner, because some contestants are favored by the allocation rule, while others are handicapped. This paper analyzes an unfair, two-player discriminatory contest (all-pay auction) with private values. We characterize equilibrium strategies, provide closed form solutions, and illustrate additional strategic issues arising in such unfair contests.     

Creating competition out of thin air: An experimental study of right-to-choose auctions

This paper presents an experimental study of a mechanism that is commonly used to sell multiple heterogeneous goods. The novel feature of this procedure is that instead of selling each good in a separate auction, the seller executes a single auction in which buyers, who may be interested in completely different goods, compete for the right to choose a good. We provide experimental evidence that a Right-to-Choose (RTC) auction can generate more revenue than the theoretically optimal auction. Moreover, in contrast to the “optimal” auction, the RTC auction is approximately efficient in the sense that the surplus it generates is close to the maximal one. Furthermore, a seller who would like to retain some of his goods can generate more revenue with a restricted RTC auction in which not all rights-to-choose are sold, than with the theoretically optimal auction.     

Equilibrium in a Market Game

This paper studies the equilibrium of an exchange economy with the same number of agents and commodities. It is shown that under rather mild conditions on demand the market have a price equilibrium—independently of the divisibility of the commodities. The result extends Gale’s equilibrium theorem for indivisible commodities to the case where some commodities are perfectly divisible. The proof is based on a topological lemma contained in previous paper of one of the authors.     

Robustness of the Incentive Compatible Combinatorial Auction

Goods are said to be combinatorial when the value of a bundle of goods is not equal to the sum of the values of the same goods unbundled. Investigations of combinatorial allocation problems should recognize that there are two separate aspects of such problems: anenvironmental distinction between multiple-unit allocation problems which involve combinatorial goods and those which do not do so, and aninstitutional distinction between auctions in which combinatorial values can be expressed as part of the bidding rules and those in which they cannot. Forsythe and Isaac (Research in Experimental Economics, Vol. 2 (1982). Greenwich, Conn.: JAI Press, Inc.) reports the extension of the Vickrey auction into a demand-revealing, multiple unit, private goods auction that can incorporate combinatorial values. This current paper places that theoretically demand-revealing institution in a series of experimental environments in order to generate results (e.g. efficiencies) which may serve as a benchmark for other auctions (combinatorial or otherwise) whose implementation characteristics may be more favorable. To aid in interpretation of our Vickrey experimental results, we also provide results of alternatives to Vickrey allocations from both institutional and heuristic sources, as well as a discussion of the source of the Vickrey auctions high efficiencies even in the presence of misrevelation.     

Optimal sale across venues and auctions with a buy-now option

We characterize the optimal selling mechanism for a seller who faces demand demarcated by a high and a low end and who can access an (online) auction site (by paying an access cost) in addition to using his own store that can be used as a posted price selling venue. We first solve for the optimal mechanism of a direct revelation game in which there is no venue-restriction constraint. We find that the direct optimal mechanism must necessarily incorporate a certain kind of pooling. We then show that even with the venue constraint, the seller can use a two stage indirect mechanism that implements the allocation rule from the optimal direct mechanism, and uses the venues in an optimal fashion. The first stage of the indirect mechanism is a posted price at the store. If the object is not sold, we move to stage two, which involves an auction at the auction site. A feature of this auction is a buy-now option which is essential for implementing the pooling feature of the optimal direct mechanism. We also show that the buy-now option in the optimal mechanism is of a “temporary” variety, and that a “permanent” buy-now option, in contrast, cannot implement the optimal mechanism. Auctions with a temporary buy-now option are in widespread use on eBay. We thank the Associate Editor, George Deltas, for his insightful comments. We also thank seminar participants at the University of Basel and the SAET conference 2007.     

The Effect of Bidder Heterogeneity on Combinatorial Conservation Auction Designs

In an iterative combinatorial auction, bidders can submit bids on individual and/or on combinations of projects in a series of intermediate rounds, where bid prices are revised before a final allocation is made. The iterative format is useful for conservation service procurement as landholders can rely on market information revealed through the rounds to evaluate their choices of projects and bid prices. However, there is no single way of providing the market information. Different designs for generating price information have been proposed. Little is known about the performance of iterative combinatorial auction designs when heterogeneous bidders, with different cost structures, participate in an auction. Using an agent based model, we evaluate a selected set of designs under different bidder heterogeneity scenarios. We observe that higher degrees of heterogeneity lead to lower auction efficiency and that auction outcomes are highly sensitive to price feedback design choices.     

Auction theory adaptations for real life applications

We develop extensions to auction theory results that are useful in real life scenarios.1. Since valuations are generally positive we first develop approximations using the log-normal distribution. This would be useful for many finance related auction settings since asset prices are usually non-negative.2. We formulate a positive symmetric discrete distribution, which is likely to be followed by the total number of auction participants, and incorporate this into auction theory results.3. We develop extensions when the valuations of the bidders are interdependent and incorporate all the results developed into a final combined realistic setting.4. Our methods can be a practical tool for bidders and auction sellers to maximize their profits. The models developed here could be potentially useful for inventory estimation and for wholesale procurement of financial instruments and also non-financial commodities.All the propositions are new results and they refer to existing results which are stated as Lemmas.     

Opportunity Cost for Free Allocations of Emissions Permits: An Experimental Analysis

An important feature of emissions trading is how emissions permits are allocated. The choice between an auction and free allocation should not influence firms’ production choices nor consumer prices according to economic theory. However, many parties expect the method of allocation to affect product prices. This paper describes an experimental investigation into price determination under a cap-and-trade program with different allocation methods. Participants initially display diverse pricing strategies. However, given a simple economic setting in which earnings depend on behavior, we find that subjects learn to consider the opportunity cost of permits and overall behavior moves toward the economic prediction.     

Determining damages from the operation of bidding rings: An analysis of the post-auction `knockout' sale

Summary. This paper studies ‘knockout’ auctions, typically organized by bidding rings, in which the winning bidder makes side-payments to all losing bidders. These side-payments provide an incentive for the ring members to bid higher than they would have in an identical public auction. As a consequence, neither the realized price nor the total payments of the winner are unbiased estimates of the item's price in the absence of collusion. This paper evaluates the extent of this overestimate in the independent private values case, for first and second price post-auction knockouts. Bids are not independent of the sharing rule but transfers from the winning bidder are. Further, bidder payoffs are independent of both the auction format and the sharing rule. The “overbidding” in the knockout is increasing with the dispersion of bidder valuations and of significant empirical relevance. This paper's results can be used to obtain an unbiased assessment of the damages inflicted on the seller. Received: May 1, 1996; revised version: September 7, 2000     

Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies

In this paper we consider a class of economies with a finite number of divisible commodities, linear production technologies, and indivisible goods and a finite number of agents. This class contains several well-known economies with indivisible goods and money as special cases. It is shown that if the utility functions are continuous on the divisible commodities and are weakly monotonic both on one of the divisible commodities and on all the indivisible commodities, if each agent initially owns a sufficient amount of one of the divisible commodities, and if a “no production without input”-like assumption on the production sector holds, then there exists a competitive equilibrium for any economy in this class. The usual convexity assumption is not needed here. Furthermore, by imposing strong monotonicity on one of the divisible commodities we show that any competitive equilibrium is in the core of the economy and therefore the first theorem of welfare also holds. We further obtain a second welfare theorem stating that under some conditions a Pareto efficient allocation can be sustained by a competitive equilibrium allocation for some well-chosen redistribution of the total initial endowments. Journal of Economic Literature Classification Numbers: D4, D46, D5, D51, D6, D61.     

An Optimal Auction for Complements

This paper considers the optimal selling mechanism for complementary items. When buyers are perfectly symmetric, the optimal procedure is to bundle the items and run a standard auction. In general, however, bundling the items is not necessarily desirable, and the standard auctions do not maximize revenue. Moreover, the optimal auction allocation may not be socially efficient since the auction must discriminate against bidders who have strong incentives to misrepresent their true preferences.Journal of Economic LiteratureClassification Number: D44.     

Breaking Collusion in Auctions through Speculation: An Experiment on CO2 Emission Permit Markets

The European Emission Trading Scheme (EU‐ETS) has chosen to adopt an auctioning procedure to initially allocate CO₂ emission permits. Free allocation of permits will become an exception for the third phase (2013–2020) and most firms will have to buy all their permits on the market or via auctions. The ability of bidders to collude is a key concern about the design of the auction format. To counter collusion, the auction can be open to bidders without compliance obligations (speculators). This paper aims at studying experimentally speculation as a collusion‐breaking device in two different auction mechanisms: the uniform‐price sealed‐bid auction and the ascending clock auction. Our results suggest that a uniform sealed‐bid auction open to speculators should be chosen from a revenue maximization point of view. In this mechanism, compliance agents adopt an aggressive strategy toward speculators. This strategy significantly increases the seller's revenue, compared to the more collusive clock auction. In the latter, on the contrary, bidders accommodate speculators, letting them buy permits in the auction and buying their necessary permits on the secondary market. However, as opening the auction to speculators deteriorates efficiency, the regulator faces a trade‐off between these two objectives.     

Equilibrium uniqueness with perfect complements

The present note analyzes the simultaneous ascending-bid auction with arbitrarily many asymmetric bidders with decreasing marginal valuations under complete information. We show that the game is solvable by iterated elimination of weakly dominated strategies if the efficient allocation assigns at least one unit to every player and if bid increments are sufficiently small. In that unique equilibrium, bidders immediately reduce their demand to the efficient allocation, and the auction ends in the first round of bidding.We would like to thank seminar participants at UC Davis, in particular Klaus Nehring and Louis Makowski for comments. Financial support by the Alexander–von–Humboldt Foundation through a Feodor–Lynen grant and by the Deutsche Forschungsgemeinschaft, SFB Transregio 15, “Governance and Efficiency of Economic Systems” is gratefully acknowledged.     

On ascending Vickrey auctions for heterogeneous objects

We construct an ascending auction for heterogeneous objects by applying a primal-dual algorithm to a linear program that represents the efficient-allocation problem for this setting. The auction assigns personalized prices to bundles, and asks bidders to report their preferred bundles in each round. A bidder's prices are increased when he belongs to a “minimally undersupplied” set of bidders. This concept generalizes the notion of “overdemanded” sets of objects introduced by Demange, Gale, and Sotomayor for the one-to-one assignment problem. Under a submodularity condition, the auction implements the Vickrey-Clarke-Groves outcome; we show that this type of condition is somewhat necessary to do so. When classifying the ascending-auction literature in terms of their underlying algorithms, our auction fills a gap in that literature. We relate our results to various ascending auctions in the literature.     

Lottery or waiting-line auction?

This paper studies the efficiencies of the two most widely used non-price allocation mechanisms: lotteries and waiting-line auctions. As our analysis suggests, in addition to the fairness of the mechanism, the use of lotteries in lieu of waiting-line auctions can be also justified from an efficiency point of view. In particular, we show that the less dispersed consumers’ time valuations are, the more efficient is a lottery relative to a waiting-line auction. In addition, we identify four conditions under which a lottery dominates a waiting-line auction in expected social surplus preserving. Furthermore, the numerical simulations we conduct indicate that over a predominantly wide range of circumstances, a lottery is more socially efficient than a waiting-line auction as an allocative mechanism in the absence of a conventional price system.     

Commodity price cycles and heterogeneous speculators: a STAR–GARCH model

We propose an empirical commodity market model with heterogeneous speculators. While the power of trend-extrapolating chartists is constant over time, the symmetric impact of stabilizing fundamentalists adjusts endogenously according to market circumstances: Using monthly data for various commodities such as cotton, sugar or zinc, our STAR–GARCH model indicates that their influence positively depends on the distance between the commodity price and its long-run equilibrium value. Fundamentalists seem to become more and more convinced that mean reversion will set in as the mispricing enlarges. Commodity price cycles may thus emerge due to the nonlinear interplay between different trader types. The paper represents the authors’ personal opinion and does not necessarily reflect the views of the Deutsche Bundesbank.     

Biased procurement auctions

In a complex procurement a buyer may consider biasing the auction rules in order to account for differences in product characteristics offered by the sellers. This paper studies the gathering, disclosure and use of information about this bias. While we also describe the optimal procurement auction in our setting, the main focus of the paper is on the case where the buyer does not have commitment power. We find that without commitment full disclosure of the buyer’s preferences is optimal. Furthermore, lack of commitment distorts the buyer’s incentives to learn about its preferences: unlike the commitment case, without commitment the value of this information can be negative. Based on Chapter 3 of my Ph.D. dissertation at Stanford University. I gratefully acknowledge the support of a John M. Olin Dissertation Fellowship and a Melvin and Joan Lane Stanford Graduate Fellowship. Thanks to Pat Bajari, Tim Bresnahan, Vinicius Carrasco, George Deltas, Jonathan Levin, Paul Milgrom, Ilya Segal and an anonymous referee for valuable suggestions.     

Cournot-Nash and Lindahl equilibria in pure public “bad” economies

Summary. Using a general equilibrium framework, this paper analyzes the equilibrium provision of a pure public bad commodity (for example pollution). Considering a finite economy with one desired private good and one pure public “bad” we explicitly introduce the concept of Lindahl equilibrium and the Lindahl prices into a pure public bad economy. Then, the Lindahl provision is analyzed and compared with the Cournot-Nash provision. The main results for economies with heterogeneous agents state that the asymptotic Lindahl allocation of the pure public bad is the null allocation. In contrast, the asymptotic Cournot-Nash provision of the public bad might approach infinity. Other results were obtained in concert with the broad analysis of the large finite economies with pure public bad commodities. Received: July 26, 2001; revised version: March 12, 2002 RID="*" ID="*" We are indebt to Nicholas Yannelis and anonymous referee for their valuable comments and suggestions. Correspondence to: B. Shitovitz     

Optimal accumulation in a small open economy with technological uncertainty

Summary. This paper analyzes the optimal allocation problem of a small trading country facing an uncertain technology. It is involved in production of many commodities. Differentiability cannot be guaranteed, hence, the Ramsey-Euler condition of optimality needs to be modified. From the optimality criterion, we derive a pair of conditions, which does not require differentiability. If “enough” uncertainty is allowed, the sequence of the distribution functions of investment expenditure converges uniformly to a unique invariant measure. In addition to the weak convergence of the stochastic process of investment expenditure we also have the sequences of the stochastic process of investment expenditure converging weakly. Received: September 8, 1994; revised version: September 25, 1997     

基于SWOT分析下的安徽省拍卖行业的发展建议

拍卖作为有效的市场配置资源的交易方式，越来越多地受到人们的关注和重视。虽然拍卖近几年发展迅速，但也存在着许多阻止拍卖业进一步发展的问题：本文利用SWOT分析的框架，结合当前安徽省拍卖业的问题，提出了完善安徽省拍卖行业的建议和措施。