Home-grown values and incentive compatible auction design

The behavioral properties of several auctions designed to elicit individual valuations for an object are studied using controlled laboratory experiments. Our experiments lead us to conclude that there are some behavioral differences between alternative incentive-compatible institutions for eliciting home-grown values, contrary to the theoretical expectation that these institutions are isomorphic. These results are consistent with earlier experimental results using induced values. The most important finding is that English auctions appear to elicit lower bids than Vickrey auctions, after controlling for observable socio-economic characteristics. Moreover, English auction bids also exhibit significantly less residual variance and may be sensitive to the number of rival bidders. It appears that the real-time learning allowed in the English auction significantly affects subject behavior. We also find that values elicited with the Becker, DeGroot and Marshak institution differ from those in both English and Vickrey auctions. Received November 1993/Final version May 1995     

Comparing the Spanish and the discriminatory auction formats: A discrete model with private information

The Spanish Treasury is the only Treasury in the world that uses a hybrid system of discriminatory and uniform price auctions to sell government debt: winning bidders pay their bid price for each unit if this is lower than the weighted average price of winning bids (WAP), and pay the WAP otherwise. Following Gordy [Gordy, M., 1996. Multiple bids in a multiple-unit common-value auction. Board of Governors of the Federal Reserve System], we model the Spanish auction as a common value auction of multiple units with private information, allowing for multiple bids. Numerical analysis shows that bidders spread their bids more in the Spanish than in the discriminatory auction and bid higher for the first unit, and that the expected seller’s revenue is higher in the Spanish than in the discriminatory auction within a reasonable set of parameter values.     

Fraction auctions: The tradeoff between efficiency and running time

This paper studies the sales of a single indivisible object where bidders have continuous valuations. In Grigorieva et al. [14] it was shown that, in this setting, query auctions necessarily allocate inefficiently in equilibrium. In this paper we propose a new sequential auction, called the c-fraction auction. We show the existence of an ex-post equilibrium, called bluff equilibrium, in which bidders behave truthfully except for particular constellations of observed bids at which it is optimal to pretend a slightly higher valuation. We show c-fraction auctions guarantee approximate efficiency at any desired level of accuracy, independent of the number of bidders, when bidders choose to play the bluff equilibrium. We discuss the running time and the efficiency in the bluff equilibrium. We show that by changing the parameter c of the auction we can trade off efficiency against running time.     

All-pay auctions with pre- and post-bidding options

Motivated by the emergence of online penny or pay-to-bid auctions, in this study, we analyze the operational consequences of all-pay auctions competing with fixed list price stores. In all-pay auctions, bidders place bids, and highest bidder wins. Depending on the auction format, the winner pays either the amount of their bid or that of the second-highest bid. All losing bidders forfeit their bids, regardless of the auction format. Bidders may visit the store, both before and after bidding, and buy the item at the fixed list price. In a modified version, we consider a setting where bidders can use their sunk bid as a credit towards buying the item from the auctioneer at a fixed price (different from the list price). We characterize a symmetric equilibrium in the bidding/buying strategy and derive optimal list prices for both the seller and auctioneer to maximize expected revenue. We consider two situations: (1) one firm operating both channels (i.e. fixed list price store and all-pay auction), and (2) two competing firms, each operating one of the two channels.     

An experimental test of alternative models of bidding in ascending auctions

The theory and behavior of the clock version of the ascending auction has been well understood for at least 20 years. The more widely used oral outcry version of the ascending auction that allows bidders to submit their own bids has been the subject of some recent controversy mostly in regard to whether or not jump bidding, i.e. bidders submitting bids higher than required by the auctioneer, should be allowed. Isaac, Salmon & Zillante (2005) shows that the standard equilibrium for the clock auction does not apply to the non-clock format and constructs an equilibrium bid function intended to match with field data on ascending auctions. In this study, we will use economic experiments to provide a direct empirical test of that model while simultaneously providing empirical evidence to resolve the policy disputes centered around the place of jump bidding in ascending auctions.Received: March 2005The authors would like to thank Florida State University for providing the funding for the experiments in this paper and Bradley Andrews for programming assistance.     

A new pricing scheme based on DEA for iterative multi-unit combinatorial auctions

Iterative Multi-unit Combinatorial Auctions are auctions in which: bidders can express bids in successive rounds until a stopping rule is held; there are multiple units of each item; and bids are bundles of items. Data Envelopment Analysis (DEA) is a nonparametric method for measuring the relative efficiency of a set of homogeneous units. In this work, we present an algorithm for solving an iterative multi-unit combinatorial auction in which the auctioneer computes at each round a linear anonymous price for each item by using a DEA model and pushes bidders to express bids according to them. A computational study is carried out in order to check the performance of the proposed design.      

常数相对风险厌恶多单位拍卖的比较静态与定价结构

考虑竞价者具有常数相对风险厌恶时的多单位拍卖问题,讨论均衡出价与风险偏好以及价值分布之间的关系.在竞价者具有相同的风险偏好的对称拍卖情形,利用风险中性等价导出了比较静态的充要条件,这一充要条件综合了风险偏好和价值分布的变化.在竞价者具有不同的风险偏好的非对称拍卖中,导出了均衡出价关于风险偏好的线性定价结构,依据这一结构,对任意给定出价,竞价者要求的剩余是其风险厌恶参数的线性函数,并且可以分解为竞争性剩余和风险厌恶剩余.     

Large auctions with risk-averse bidders

We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction (k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/n ²) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n ²) revenue equivalent. The generalization, that all large auctions are O(1/n ²) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as ${n\longrightarrow \infty }We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction (k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/n ²) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n ²) revenue equivalent. The generalization, that all large auctions are O(1/n ²) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as n? ￥{n\longrightarrow \infty } with risk-averse bidders is strictly below the risk-neutral limit. Therefore, these auction mechanisms are not revenue equivalent to large k-price auctions even to leading-order as n? ￥{n\longrightarrow \infty }.     

Auctions with bidder-determined allowable combinations

Combinatorial auctions are desirable as they enable bidders to express the synergistic values of a group of assets and thus may lead to better allocations. Compared to other types of auctions, they keep bidders from being exposed to risks (of receiving only parts of combinations that would be valuable to them) or from being overly cautious (in order to minimize such risks). However, computation time needed to determine the set of optimal winning combinations in a general combinatorial auction may grow exponentially as the auction size increases, and this is sometimes given as a reason for not using combinatorial auctions. To determine the winning allocation in a reasonable time, a bid taker might try to limit the kinds of allowable combinations, but bidders may disagree on what combinations should be allowed, and this may make limiting the allowable combinations politically infeasible.This paper proposes and tests successfully a new approach to managing the computational complexity of determining the set of winning combinations. The main idea is to let bidders themselves determine and prioritize the allowable combinations. Using bidder-determined combinations has two nice properties. First, by delegating the decision on what is biddable to the bidders who know what combinations are important to them, the bid taker is able to be (and appear) fair. Second, since bidders know their economics and have the incentive to get important combinations included, bidder prioritization of combinations will tend to assure that the most economically-important combinations are included in determining the winning set of bids if the bid taker is not able to consider all of the combinations submitted by bidders. The proposed auction process is useful in situations, such as government auctions, in which the bid taker is reluctant to limit the allowable combinations.     

面向电子逆向拍卖的多属性报价建议模型

针对多属性拍卖中报价的复杂性和现有报价指导模型的局限性,提出了一个以拍卖方的总价值提升为基本约束,以投标人的利润最大化为目标的多属性报价建议模型,并引入二元变量解决了定性属性的推荐问题。当投标人具有不同的投标能力和偏好时,模型可根据投标人的投标要求进行报价推荐;当存在单位价值相同的推荐报价时,模型设置了相应的约束以鼓励早投标行为。最后,还从理论上证明了该模型的稳定性,并通过算例说明了模型的可行性。     

Design of discrete Dutch auctions with an uncertain number of bidders

The focus of this paper is on Dutch auctions where the bidding prices are restricted to a finite set of values and the number of bidders follows a Poisson distribution. The goal is to determine what the discrete bid levels should be to maximize the auctioneer’s expected revenue, which is the same as the average selling price of the object under consideration. We take a new approach to the problem by formulating the descending-price competitive bidding process as a nonlinear program. The optimal solution indicates that the interval between two successive bids should be wider as the Dutch auction progresses. Moreover, the auctioneer’s maximum expected revenue increases with the number of bid levels to be set as well as the expected number of bidders. Numerical examples are provided to illustrate the key results from this study and their managerial implications are discussed.     

Choice of item pricing feedback schemes for multiple unit reverse combinatorial auctions

Recently, interest in combinatorial auctions has extended to include trade in multiple units of heterogeneous items. Combinatorial bidding is complex and iterative auctions are used to allow bidders to sequentially express their preferences with the aid of auction market information provided in the form of price feedbacks. There are different competing designs for the provision of item price feedbacks; however, most of these have not been thoroughly studied for multiple unit combinatorial auctions. This paper focuses on addressing this gap by evaluating several feedback schemes or algorithms in the context of multiple unit auctions. We numerically evaluate these algorithms under different scenarios that vary in bidder package selection strategies and in the degree of competition. We observe that auction outcomes are best when bidders use a naïve bidding strategy and competition is strong. Performance deteriorates significantly when bidders strategically select packages to maximize their profit. Finally, the performances of some algorithms are more sensitive to strategic bidding than others.     

Estimating advertisers' values for paid search clickthroughs

Paid search is an important form of online advertisement. Clickthroughs from slots are bid for by advertisers. The process of formulating bids is a complex one involving bidders in competing against other advertisers in multiple auctions. It would be helpful in managing the bidding process if it were possible to determine the values placed on a clickthrough by different advertisers. The theory of two models for estimating advertiser values and associated parameters is presented. The models are applied to a set of data for searches on the term Personal Loans. The results of the model that fits the data better are evaluated. The utility of the model to practitioners is discussed. Some issues raised by the results about the role of bidding agents and the discriminatory power of Customer Relationship Management systems are considered. Ways to develop the preferred model are outlined. It is suggested that the model has implications for evaluating forecasting methods for use in paid search auctions.     

Flow auctions

Flow goods (like electricity) are sold through auctions in a dynamic framework. An important design question is the frequency of such auctions. We use a simple dynamic auction model in continuous time to answer this question. We focus on the relationship between the persistency of bidders’ valuations and the optimal choice of frequency. If the seller focuses on the equilibrium in which bidders follow a repeated static Nash strategy, then the frequency of auctions should typically increase when persistency declines. However, accounting for the fact that bidders can follow different equilibria that are collusive in nature, the comparative statics are reversed, forcing the seller to reduce the frequency when bidders’ valuations are less persistent. The argument builds on the fact that high frequency auctions are more conducive to collusion among bidders.     

Multi-criteria auctions without full comparability of bids

The emergence of auction mechanisms that support bids characterized by several attributes is one of the most recent evolutions within auction theory. These mechanisms, referred to as multi-attribute, multiple issue or multi-dimensional auctions, are at the intersection between multi-criteria decision and auction theories. The purpose of this paper is to introduce multi-criteria auctions the originality of which is not to require full comparability between bids. We claim that this distinctive feature is of great interest, especially in procurement situations. Furthermore, the existence of potential incomparability between multi-dimensional offers will permit us to manage different bidding niches coexisting within the same bidding space. A theoretical framework based on a general preference structure will be introduced and then referenced to existing approaches such as multi-attribute auctions or new ones such as dominance based multi-criteria auctions or butterfly auctions.     

Constrained equilibrium in a bidding problem

There are a number of situations where firms vie for some constrained total quantity by bidding individual quantities but where the allocation is determined on a ‘pro-rated’ basis. One such example is a licenses-on-demand method of import quota allocation. Bidders are constrained to bid at most the total quantity, and if the sum of all bids exceeds this total, the awards are granted proportional to the fractional amounts that the bidders request. In this note, we identify the (Nash) equilibrium of the model, present some examples, and do a sensitivity analysis of the bids as the total amount available changes. We also look into changes of the bids when a new participant enters the bidding process. In an economic context, such allocation methods are shown to be biased in favor of the least efficient firms.     

Investigating buyer and seller strategies in online auctions

The annual turnover of online auctions is already in tens of billions of dollars and this amount is predicted to grow substantially over the next few years. Hence, it is important to know how buyers and sellers can influence their chances of success. Therefore, data were collected from eBay auctions for three different categories of collectible items, namely those with a published guide price, those with a rough guide price and those having no easily obtainable guide price. The options available to buyers and sellers of items were then analysed. It was found that it was hard for the seller to influence an item's achieved price significantly, apart from items with no guide price where the starting price could have an effect. Most bidders bid close to the current value and so there were insufficient data to determine the consequences of timing on the placing of high bids. For low bids, delaying a bid was found to improve significantly the chances of winning for one of the data sets.     

The buy price in auctions with discrete type distributions

This paper considers second-price, sealed-bid auctions with a buy price where bidders’ types are discretely distributed. We characterize all equilibria in which bidders whose types are less than the buy price bid their own valuations. Budish and Takeyama (2001) analyze the two-bidder, two-type framework. They show that if bidders are risk-averse, then the seller can obtain a higher expected revenue from the auction with a certain buy price than from the auction without a buy price. We extend their revenue improvement result to the n-bidder, two-type framework. In case of three or more types, however, bidders’ risk aversion is not a sufficient condition for a revenue improvement. We point out that even if bidders are risk-averse, the seller cannot always obtain a higher expected revenue from the auctions with a buy price.     

Ranking asymmetric auctions

We compare the expected revenue in first- and second-price auctions with asymmetric bidders. We consider “close to uniform” distributions with identical supports and show that in the case of identical supports the expected revenue in second-price auctions may exceed that in first-price auctions. We also show that asymmetry over lower valuations has a stronger negative impact on the expected revenue in first-price auctions than in second-price auctions. However, asymmetry over high valuations always increases the revenue in first-price auctions.     

Compact bidding languages and supplier selection for markets with economies of scale and scope

Combinatorial auctions have been used in procurement markets with economies of scope. Preference elicitation is already a problem in single-unit combinatorial auctions, but it becomes prohibitive even for small instances of multi-unit combinatorial auctions, as suppliers cannot be expected to enumerate a sufficient number of bids that would allow an auctioneer to find the efficient allocation. Auction design for markets with economies of scale and scope are much less well understood. They require more compact and yet expressive bidding languages, and the supplier selection typically is a hard computational problem. In this paper, we propose a compact bidding language to express the characteristics of a supplier’s cost function in markets with economies of scale and scope. Bidders in these auctions can specify various discounts and markups on overall spend on all items or selected item sets, and specify complex conditions for these pricing rules. We propose an optimization formulation to solve the resulting supplier selection problem and provide an extensive experimental evaluation. We also discuss the impact of different language features on the computational effort, on total spend, and the knowledge representation of the bids. Interestingly, while in most settings volume discount bids can lead to significant cost savings, some types of volume discount bids can be worse than split-award auctions in simple settings.