An experimental study of auctions with a buy price under private and common values

eBayʼs Buy It Now format allows a seller to list an auction with a “buy price” at which a bidder may purchase the item immediately and end the auction. When bidders are risk averse, then theoretically a buy price can raise seller revenue when values are private (but not when values are common). We report the results of laboratory experiments designed to determine whether in practice a buy price is advantageous to the seller. We find that a suitably chosen buy price yields a substantial increase in seller revenue when values are private, and a small (but statistically insignificant) increase in revenue when values are common. In both cases a buy price reduces the variance of seller revenue. A behavioral model which incorporates the winnerʼs curse and the overweighting by bidders of their own signal explains the common value auction data better than the rational model.     

Auctions with endogenous participation and an uncertain number of bidders: experimental evidence

Attracting bidders to an auction is a key factor in determining revenue. We experimentally investigate entry and bidding behavior in first-price and English clock auctions to determine the revenue implications of entry. Potential bidders observe their value and then decide whether or not to incur a cost to enter. We also vary whether or not bidders are informed regarding the number of entrants prior to placing their bids. Revenue equivalence is predicted in all four environments. We find that, regardless of whether or not bidders are informed, first-price auctions generate more revenue than English clock auctions. Within a given auction format, the effect of informing bidders differs. In first-price auctions, revenue is higher when bidders are informed, while the opposite is true in English clock auctions. The optimal choice for an auction designer who wishes to maximize revenue is a first-price auction with uninformed bidders.     

Behavior in second-price auctions by highly experienced eBay buyers and sellers

We report on sealed-bid second-price auctions that we conducted on the Internet using subjects with substantial prior experience: they were highly experienced participants in eBay auctions. Unlike the novice bidders in previous (laboratory) experiments, the experienced bidders exhibited no greater tendency to overbid than to underbid. However, even subjects with substantial prior experience tended not to bid their values, suggesting that the non-optimal bidding of novice subjects is robust to substantial experience in non-experimental auctions. We found that auction revenue was not significantly different from the expected revenue the auction would generate if bidders bid their values. Auction efficiency, as measured by the percentage of surplus captured, was substantially lower in our SPAs than in previous laboratory experiments.     

The Relevance of a Choice of Auction Format in a Competitive Environment

We examine the relevance of an auction format in a competitive environment by comparing uniform and discriminatory price auctions with many bidders in a private values setting. We show that if the number of objects for sale is small relative to the number of bidders, then all equilibria of both auctions are approximately efficient and lead to approximately the same revenue. When the number of objects for sale is proportional to the number of bidders, then the particulars of the auction format matter. All equilibria of the uniform auction are efficient, while all of the equilibria of the discriminatory auction are inefficient. The relative revenue rankings of the auction formats can go in either direction, depending on the specifics of the environment. These conclusions regarding the efficiency and revenue ranking are in contrast to the previous literature, which focused on the case of independent information across agents.     

CHARITY AUCTIONS*

In a charity auction the public‐goods nature of auction revenue affects bidding incentives. We compare equilibrium bidding and revenue in first‐price, second‐price, and all‐pay charity auctions. Bidding revenue typically varies by selling format. First‐price auctions are less lucrative than second‐price and all‐pay auctions, and with sufficiently many bidders the all‐pay auction has the highest bidding revenue. However, revenue equivalence applies when the auctioneer can set a reserve price and fees plus threaten to cancel the auction. If the auctioneer cannot threaten cancellation, a reserve and bidding fee can augment revenue but again revenue varies by auction format     

Large common value auctions with risk averse bidders

We analyze large symmetric auctions with conditionally i.i.d. common values and risk averse bidders. Our main result characterizes the asymptotic equilibrium price distribution for the first- and second-price auctions. As an implication, we show that with constant absolute risk aversion (CARA), the second-price auction raises significantly more revenue than the first-price auction. While this ranking seems robust in numerical analysis also outside the CARA specification, we show by counterexamples that the result does not generalize to all risk averse utility functions.     

Revenue in first-price auctions with a buy-out price and risk-averse bidders

Journal of Economics - We model the “Buy-It-Now or Best Offer” eBay listing option as a first-price auction with a buy-out price and consider seller revenue when bidders are...     

Standard Auctions with Financially Constrained Bidders

We develop a methodology for analyzing the revenue and efficiency performance of auctions when buyers have private information about their willingness to pay and ability to pay. We then apply the framework to scenarios involving standard auction mechanisms. In the simplest case, where bidders face absolute spending limits, first-price auctions yield higher expected revenue and social surplus than second-price auctions. The revenue dominance of first-price auctions over second-price auctions carries over to the case where bidders have access to credit. These rankings are explained by differences in the extent to which financial constraints bind in different auction formats.     

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.     

Premium auctions and risk preferences: An experimental study

In premium auctions, the highest losing bidder receives a reward from the seller. This paper studies the private value English premium auction (EPA) for different risk attitudes of bidders. We explicitly derive the symmetric equilibrium for bidders with CARA utilities and conduct an experimental study to test the theoretical predictions. In our experiment, subjects are sorted into risk-averse and risk-loving groups. We find that revenues in the EPA are significantly higher when bidders are risk loving rather than risk averse. These results are partly consistent with theory and confirm the general view that bidders' risk preferences constitute an important factor that affects bidding behavior and consequently also the seller's expected revenue. However, individual subjects rarely follow the equilibrium strategy and revenue in our experiment is lower than in the symmetric equilibrium.     

Late and multiple bidding in second price Internet auctions: Theory and evidence concerning different rules for ending an auction

In second price Internet auctions with a fixed end time, such as those on eBay, many bidders submit their bids in the closing minutes or seconds of an auction. We propose an internet auction model, in which very late bids have a positive probability of not being successfully submitted, and show that late bidding in a fixed deadline auction can occur at equilibrium in auctions both with private values and with uncertain, dependent values. Late bidding may also arise out of equilibrium, as a best reply to incremental bidding. However, the strategic advantages of late bidding are severely attenuated in auctions that apply an automatic extension rule such as auctions conducted on Amazon. Field data show that there is more late bidding on eBay than on Amazon, and this difference grows with experience. We also study the incidence of multiple bidding, and its relation to late bidding.     

不同一口价组合拍卖机制下的卖方收益比较研究

随着电子商务的发展,作为网上拍卖方式之一的一口价拍卖逐渐盛行起来。网上一口价拍卖打破了时间和空间的限制,因而被广泛应用于组合拍卖中。笔者针对目前拍卖网站所采用的两种不同拍卖规则:固定一口价和持久一口价,在独立私人估价模型下分析比较了上述两种规则下的卖方期望收益。     

Bidding behavior in competing auctions: Evidence from eBay

Much of the existing auction literature treats auctions as running independently of one another, with each bidder choosing to participate in only one auction. However, in many online auctions, a number of substitutable goods are auctioned concurrently and bidders can bid on several auctions at the same time. Recent theoretical research shows how bidders can gain from the existence of competing auctions, the current paper providing the first empirical evidence in support of competing auctions theory using online auctions data from eBay. Our results indicate that a significant proportion of bidders do bid across competing auctions and that bidders tend to submit bids on auctions with the lowest standing bid, as the theory predicts. The paper also shows that winning bidders who cross-bid pay lower prices on average than winning bidders who do not.     

Simultaneous use of auctions and posted prices

I consider a model in which several identical objects are sold simultaneously via an auction and a posted price mechanism. The model explains several empirical regularities regarding bidding behavior in eBay auctions such as the finding that some bidders bid multiple times over the course of the auction, and that bidders tend to bid with greater frequency near the end of the auction than the beginning. I also show that sellers prefer to simultaneously use auctions and posted prices than to use either mechanism individually.     

Demand reduction and preemptive bidding in multi-unit license auctions

Multi-unit ascending auctions allow for equilibria in which bidders strategically reduce their demand and split the market at low prices. At the same time, they allow for preemptive bidding by incumbent bidders in a coordinated attempt to exclude entrants from the market. We consider an environment where both demand reduction and preemptive bidding are supported as equilibrium phenomena of the ascending auction. In a series of experiments, we compare its performance to that of the discriminatory auction. Strategic demand reduction is quite prevalent in the ascending auction even when entry imposes a (large) negative externality on incumbents. As a result, the ascending auction performs worse than the discriminatory auction both in terms of revenue and efficiency, while entrants’ chances are similar across the two formats.     

The high/low divide: Self-selection by values in auction choice

Most prior theoretical and experimental work involving auction choice has assumed bidders find out their value after making a choice of which auction to enter. We examine whether or not bidders knowing their value prior to making a choice of which among multiple alternative auction formats to enter impacts their choice decision and/or the outcome of the auctions. The results show a strong impact on auction choice. Subjects with low values choose the first price sealed bid auction more often while subjects with high values choose the ascending auction more often. The number of bidders in each auction, revenue, efficiency and average bidder surplus all end up equalized.     

Asymmetric information about rivals'' types in standard auctions

We study auctions in which bidders may know the types of some rival bidders but not others. This asymmetry in bidders' knowledge about rivals' types has different effects on the two standard auction formats. In a second-price auction, it is weakly dominant to bid one's valuation, so the knowledge of rivals' types has no effect, and the good is allocated efficiently. In a first-price auction, bidders refine their bidding strategies based on their knowledge of rivals' types, which yields an inefficient allocation. We show that the inefficient allocation in the first-price auction translates into a poor revenue performance. Given a standard regularity condition, the seller earns higher expected revenue from the second-price auction than from the first-price auction, whereas the bidders are better off from the latter.     

Equilibrium reserve prices in sequential ascending auctions

We study a model where bidders have perfectly correlated valuations for two goods sold sequentially in two ascending-price auctions. The seller sets a reserve price before the beginning of each auction. Despite the lack of commitment by the seller, we characterize an equilibrium and study its properties. Strategic non-disclosure of information takes the form of non-participation in the early auction by low-valuation bidders, while high-valuation bidders bid up to their true valuations. Some buyers who would profitably buy at the reserve price refrain from participating in order to decrease the second-auction reserve price.     

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.     

Second chance offers in auctions

This paper examines situations in which a seller might make a second chance (take-it-or-leave-it) offer to a non-winning bidder at a price equal to their bid at auction. This study is motivated by the take-it-or-leave-it second chance offer rules used by eBay and a number of state procurement agencies. Equilibrium bidder behavior is determined for IPV sealed bid first price, second price, English, and Vickrey auctions when a second chance offer will be made with an exogenous probability $p$ . In all but the Vickrey auction (which elicits the dominant strategy of bidding one’s value) equilibrium bids are lower than if there were no possibility of a second chance offer and higher than if a second chance offer will be made for certain. Further, the possibility of a second chance offer erodes the strategic equivalence between second price bids and English auction drop out levels. If bidders are risk averse (with CRRA preferences), this difference leads to expected revenue dominance of the second price over the English auction, both of which dominate the Vickrey auction. The first price auction is also shown to revenue dominate the Vickrey auction, and moreover, numerical results and intuition from existing literature suggest that the first price auction revenue dominates the second price auction.