Anticipation of Auction Fever: Entry Decision,Reserve Price and the Choice of Auction Design

This paper analyzes the entry decision of rational bidders who expect to experience auction fever in English auctions. It shows that nonparticipation decision reduces seller's expected profit and this effect may outweigh the positive effect of the auction fever. We analyze the choice between English and second‐price sealed‐bid auctions and the optimal reserve price in English auctions. We show that it might be optimal for the seller to set a reserve price below her own valuation of the object. Finally, we show that the order in which bidders place their bids matters and the first bidder always has an advantage. Copyright © 2011 John Wiley & Sons, Ltd.     

Auctions with endogenous participation

We study endogenous-participation auctions where bidders only know the number of potential participants. After seeing their values for the object, potential participants decide whether or not to enter the auction. They may not want to enter the auction since they have to pay participation costs. We characterize equilibrium bidding strategies and entry decisions for both first- and second-price sealed-bid auctions when participation is endogenous. We show that there is a pure strategy entry equilibrium where only bidders with values greater than a certain cut-off point actually bid. In this context, both types of auctions generate the same expected revenue. We also show that, contrary to the predictions of the fixed number of bidders literature, the seller's expected revenue may decrease when the number of potential participants increases. In addition, we show that it is optimal for the seller to charge an entry fee, which contrasts with results from the existing literature on auctions with entry. As in the fixed-n literature, we show that first-price auctions generate more expected revenue than second-price auctions when buyers are risk-averse. Finally, we characterize the optimal auction – the auction that maximizes the seller's expected revenue – by using a direct revelation mechanism. The optimal auction involves a reserve price larger than the optimal reserve price in the fixed-n literature. The winner's payment is the second highest bid less the participation cost and losers receive a subsidy equal to the participation cost. Received: 17 August 1998 / 21 September 1999     

On the Sub-optimality of Entry Fees in Auctions With Entry

We study a variation of Myerson’s (1981) model in which we allow for uncertainty about the number of bidders. In our set-up, an appropriate reserve price in a standard auction maximizes the auctioneer’s expected revenue. However, entry fees can be optimal only under some special conditions. Basically, there must be some homogeneity in bidders’ beliefs about the number of bidders and the auctioneer must know, to some extent, these beliefs.     

The impact of reserve prices on the perceived bias of expert appraisals of fine art

We examine whether expert appraisals provided to bidders before major art auctions are unbiased indicators of value. Despite a strong grounding in theory, this aspect of optimal auction design has been frequently challenged in previous empirical research, particularly in the market for fine art. We adopt a valuation benchmark that incorporates sellers' reserve prices as well as high bids, and recognize censoring of works that fail to make reserve. Although the auction houses never divulge reserve prices, we exploit the fact that they can be observed indirectly via their impact on buy‐in rates. Using the set of French Impressionist paintings brought to auction from 1985 to 2001, we estimate the distribution of reserve prices, establish their link to a proper valuation benchmark, and isolate the selection bias due to bought‐in works on the perceived market value of fine art works. After controlling for the impact of reserve prices, and considering all works brought to auction, we find no evidence of bias in the experts' pre‐sale estimates. Copyright © 2010 John Wiley & Sons, Ltd.     

Empirical implementation of nonparametric first-price auction models

Nonparametric estimators provide a flexible means of uncovering salient features of auction data. Although these estimators are popular in the literature, many key features necessary for proper implementation have yet to be uncovered. Here we provide several suggestions for nonparametric estimation of first-price auction models. Specifically, we show how to impose monotonicity of the equilibrium bidding strategy; a key property of structural auction models not guaranteed in standard nonparametric estimation. We further develop methods for automatic bandwidth selection. Finally, we discuss how to impose monotonicity in auctions with differing numbers of bidders, reserve prices, and auction-specific characteristics. Finite sample performance is examined using simulated data as well as experimental auction data.     

Bundling and the Reduction of the Winner's Curse

The paper studies the effects of bundling on the bidding strategies and seller revenues in auctions when the bidders have common values for the objects. Bundling of objects before the auction reduces the problem of the winner's curse, and the bidders bid more aggressively. This does not mean that a bundled auction is always better for the seller's revenue. Indeed, there is another effect that makes the bundled auction preferable (from the seller's standpoint) if and only if the number of bidders is small. While this is the only effect present in an independent-private-values model, it does not vanish when bidders have pure common values for the objects. The paper concludes that a bundled auction is unambiguously better for the seller than separate auctions when the number of bidders is small.     

Bids as a Vehicle of (Mis)Information: Collusion in English Auctions with Affiliated Values

In an English auction, a bidder’s strategy depends on the prices at which his competitors drop out, because these convey information on the value of the object on sale. A ring of colluding bidders can strategically manipulate the information transmitted through its members’ bids, in order to mislead other bidders into bidding less aggressively and thus allow a designated bidder to bid more aggressively. Collusion increases the probability that the ring wins the auction and reduces the price it pays. The presence of a ring harms other bidders (as well as the seller) and reduces efficiency.     

Learning through Simultaneous Play: Evidence from Penny Auctions

This paper contributes to the emerging empirical literature on penny auctions, a particular type of all‐pay auctions. We focus on the potential learning effects that bidders may experience over time but also (and particularly) across auctions as a result of their auction participation. Using detailed bid‐level information, we find that, similarly to earlier literature, bidders suffer from a sunk cost fallacy, whereby their probability of dropping out of an auction is decreasing in the number of bids they have already placed in that auction. Although we do find that learning through repeated participation alleviates the sunk cost fallacy, participation in simultaneous penny auctions emerges as a much more effective learning mechanism, ultimately contributing toward bidders earning higher individual surpluses.     

Advertising a second-price auction

This study examines a symmetric private-value second-price auction model in which the seller solicits bidders at a cost, sets a reserve price, and receives a payoff which is a convex combination of revenue and welfare. The bidder’s valuations are drawn from a distribution with a decreasing hazard rate and non-decreasing virtual valuations. We find that at equilibrium the seller adopts an advertising policy which minimizes the uncertainty over the number of participants, and sets a reserve price which only depends on the distribution of valuations and the weight on revenue in the objective function. A welfare-maximizing seller is shown to advertise more than a revenue-maximizing seller, and a ceteris paribus increase in the advertising level is proved to increase the expected winner’s rent.     

Information acquisition and/or bid preparation: A structural analysis of entry and bidding in timber sale auctions

Recently, several auction models with entry have been proposed: in one model ( and ), bidders are assumed to draw their private values after they decide to enter. In another model ( and ), bidders are assumed to learn their values before their entry decisions are made. The entry cost in the latter model can be interpreted as bid preparation cost, while the entry cost in the former model consists of both costs from information acquisition and bid preparation. Moreover, these two models have different implications for important policies, e.g., the optimal reserve price. In this paper we provide a unified structural framework where the two models can be estimated and distinguished using the Bayesian method. We apply our method to analyze Michigan timber sale auctions.     

Synergies in Wireless Telephony: Evidence from the Broadband PCS Auctions

We examine bid data from the first two broadband PCS spectrum auctions for evidence of value synergies. First, we estimate a benchmark regression for the determinants of final auction prices. Then, we include variables reflecting the extent to which bidders ultimately won or already owned the adjacent wireless properties. Consistent with geographic synergies in an ascending-bid auction, prices were higher when the highest losing bidder had adjacent licenses. The footprints of winning bidders suggest that they were often successful in realizing these synergies.     

多单位网上拍卖中的托投标分析

在独立私有价值的多单位网上英式拍卖中，诚实的竞标者能够采用对抗性的竞标策略来降低卖者参与托投标的激励，然而即使考虑了诚实竞标者对于托投标的策略性响应，托投标对于卖者而言依然是有利可图的。更为有效地阻止托投标的措施可能包括吸引更多的潜在竞标者，并限制在单次拍卖中销售的物品数量。同时考虑了卖者对于这种对抗性竞标策略的策略响应，求解了卖者的最优托投标，结论表明无论最优的托投标是唯一的还是多重的，卖者的最优策略是在开始使用低的托投标，在观察到之前的竞标信息之后通过动态调整将托投标设定到最优水平。     

The public release of information in first-price sealed-bid auctions

We determine the conditions under which the seller in a first-price sealed-bid auction has an incentive to reveal his private information about the mean of bidders’ valuations in order to increase his expected revenue. With risk-neutral bidders, we show that the seller’s expected revenue is higher when information is revealed. However, when bidders are risk-averse, this result does not necessarily hold; it depends on the bidders’ risk-aversion level and on the number of bidders.     

Keyword auctions with budget-constrained bidders

We study a keyword auction model where bidders have constrained budgets. In the absence of budget constraints, Edelman et al. (Am Econ Rev 97(1):242–259, 2007) and Varian (Int J Ind Organ 25(6):1163–1178, 2007) analyze “locally envy-free equilibrium” or “symmetric Nash equilibrium” bidding strategies in generalized second-price auctions. However, bidders often have to set their daily budgets when they participate in an auction; once a bidder’s payment reaches his budget, he drops out of the auction. This raises an important strategic issue that has been overlooked in the previous literature: Bidders may change their bids to inflict higher prices on their competitors because under generalized second-price, the per-click price paid by a bidder is the next highest bid. We provide budget thresholds under which equilibria analyzed in Edelman et al. (Am Econ Rev 97(1):242–259, 2007) and Varian (Int J Ind Organ 25(6):1163–1178, 2007) are sustained as “equilibria with budget constraints” in our setting. We then consider a simple environment with one position and two bidders and show that a search engine’s revenue with budget constraints may be larger than its revenue without budget constraints.     

Charity auctions as assets: Theory and simulations of fundraising risk management in mean-variance space

This paper demonstrates how the risk over auction revenue at fundraising events can be managed with modern portfolio theory. Within the independent private values (IPV) framework, it is shown that auction mechanisms offer charities an inherent mean-variance tradeoff over revenue when contributions produce a public good benefit among bidders. This allows the fundraiser to construct a “portfolio” of auction mechanisms for their event so as to manage auction revenue outcomes according to the charity's risk preferences. Simulations provide support for the empirical prominence of the second-price winner-pay (i.e. English) auction, as this is often the portfolio's most heavily weighted mechanism under reasonable risk preferences.     

基于边际成本递增的多属性反向拍卖最优策略

针对当前传统的基于单一价格属性的逆向拍卖机制已难以满足企业日益复杂的采购需求的现状,需要研究采购环境下的多属性英式拍卖机制。首先,文中提出了基于边际成本递增的多属性拍卖模型。然后运用多属性效用理论,进一步研究了在多属性英式拍卖机制下投标人的最优投标策略及拍卖人最优评分规则。最后,基于边际成本递增的多属性拍卖模型,研究了不同因素及边际成本对拍卖人最优评分规则的影响。     

A model for sealed-bid auctions with independent private value and common value components

This paper shows how a decision-making model can be applied to a sealed-bid auction with both independent private value (IPV) and common value (CV) components. The model yields estimates for the winning bid and for the actual value and error components of the winning bid as functions of the number of bidders and the underlying value and error distributions, assuming that these distributions are normal. The winner's curse and the special cases of IPV and CV auctions are examined using the model.     

Common-value auction versus posted-price selling: an agent-based model approach

Previous theoretical work has compared a private-value auction and posted-price market, and an affiliated-value auction and a posted-price market to determine the selling method preferred by sellers. Much less, however, is known about the seller’s preferred selling method when the buyers have a common value of the item. Our objective is to determine if a first-price auction or a posted-price market provides a seller with the larger expected revenue when buyers have a common value of the item being sold. An agent-based posted-price market and an agent-based first-price common-value auction with a reserve price are developed to compare these selling methods. Holding the buyers’ uncertainty about the value of the item constant, the seller prefers the posted-price market when the seller has no uncertainty about the item’s value. When the seller has an equal level of uncertainty as the buyers, the seller’s expected revenue for each market is similar. As the seller’s uncertainty increases beyond the level of the buyers’ uncertainty, the auction with a reserve price eventually becomes the preferred choice.     

Money Out of Thin Air: The nationwide Narrowband pcs Auction

The Federal Communications Commission held its first auction of radio spectrum at the Nationwide Narrowband PCS Auction in July 1994. The simultaneous multiple-round auction, which lasted five days, was an ascending bid auction in which all licenses were offered simultaneously. This paper describes the auction rules and how bidders prepared for the auction. The full history of bidding is presented. Several questions for auction theory are discussed. In the end, the government collected $617 million for ten licenses. The auction was viewed by all as a huge success an excellent example of bringing economic theory to bear on practical problems of allocating scarce resources.