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.     

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.     

An experimental study of precautionary bidding

Auctions often involve goods exhibiting a common-knowledge ex-post risk. In such auctions, precautionary bidding predicts that under expected utility, DARA bidders reduce their bids by more than the appropriate risk premium. Because the degree of riskiness of an auctioned good and bidders׳ levels of risk aversion are difficult to observe in field settings, we conduct experimental auctions that allow us to identify the precautionary premium directly. We find strong evidence for precautionary bidding. The effect is robust to changes in experimental design features. Our experiment provides the first empirical demonstration of precautionary motives in a strategic setting.     

Optimal shill bidding in the VCG mechanism

This paper studies shill bidding in the Vickrey?CClarke?CGroves (VCG) mechanism applied to combinatorial auctions. Shill bidding is a strategy whereby a single decision-maker enters the auction under the guise of multiple identities (Yokoo et?al. Games Econ Behav, 46?pp. 174?C188, 2004). I formulate the problem of optimal shill bidding for a bidder who knows the aggregate bid of her opponents. A key to the analysis is a subproblem??the cost minimization problem (CMP)??which searches for the cheapest way to win a given package using shills. An analysis of the CMP leads to several fundamental results about shill bidding: (i) I provide an exact characterization of the aggregate bids b such that some bidder would have an incentive to shill bid against b in terms of a new property Submodularity at the Top; (ii) the problem of optimally sponsoring shills is equivalent to the winner determination problem (for single minded bidders)??the problem of finding an efficient allocation in a combinatorial auction; (iii) shill bidding can occur in equilibrium; and (iv) the problem of shill bidding has an inverse, namely the collusive problem that a coalition of bidders may have an incentive to merge (even after competition among coalition members has been suppressed). I show that only when valuations are additive can the incentives to shill and merge simultaneously disappear.     

Auctions with a buy price

eBay and Yahoo allow sellers to list their auctions with a buy price at which a bidder may purchase the item immediately. On eBay, the buy-now option disappears once a bid is placed, while on Yahoo the buy-now option remains in effect throughout the auction. We show that when bidders are risk averse, both types of auctions raise seller revenue for a wide range of buy prices. The Yahoo format raises more revenue than the eBay format when bidders have either CARA or DARA. Bidders with DARA prefer the eBay auction, while bidders with CARA are indifferent between the two. Part of this work was completed while Reynolds was a visitor at Instituto de Analisys Economico in Barcelona and while Wooders was a visitor at Hong Kong University of Science and Technology. We are grateful to these institutions for their hospitality.     

Bidder collusion

We analyze bidder collusion at first-price and second-price auctions. Our focus is on less than all-inclusive cartels and collusive mechanisms that do not rely on auction outcomes. We show that cartels that cannot control the bids of their members can eliminate all ring competition at second-price auctions, but not at first-price auctions. At first-price auctions, when the cartel cannot control members’ bids, cartel behavior involves multiple cartel bids. Cartels that can control bids of their members can suppress all ring competition at both second-price and first-price auctions; however, shill bidding reduces the profitability of collusion at first-price auctions.     

Nonparametric panel estimation of online auction price processes

In this study, we examine the price process of eBay online auctions. We pool sparse and unevenly spaced bidding histories of individual auctions, resulting in an unbalanced panel of bids. Since the price processes of online auctions are monotonically increasing within individual auctions and exhibit a substantial degree of heterogeneity, we propose a monotone series estimator for panel data with auction-specific slopes for a common relative price growth curve. We generalize Ramsay’s (1998, J R Stat Soc B 60(2):365–375) monotone series estimator to fit our panel model of the price process. We apply the proposed model and estimator to eBay auctions of a popular hand-held device (a Palm PDA). The results are shown to capture closely the overall pattern of observed price dynamics. In particular, the early bidding, mid-auction bidding drought, and end-auction bid sniping are well approximated by the estimated price curve.     

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.     

Bidding behavior and experience in internet auctions

We study the role of experience in internet art auctions by analyzing repeated bidding by the same bidder in a unique longitudinal field dataset. Our results show that experience significantly lowers the level of bids suggesting that bidders change their bidding behavior throughout time. Participating in more than ten auctions brings down average bids by up to 26%. We further test several possible explanations for the observed learning behavior and show that the change in bidding strategy is a result of a change in within-auction behavior that is generated with experience. Our results are robust to concerns of endogenous participation as well as bidder fixed effects.     

Empirical Implications of Equilibrium Bidding in First-Price, Symmetric, Common Value Auctions

This paper studies federal auctions for wildcat leases on the Outer Continental Shelf from 1954 to 1970. These are leases where bidders privately acquire (at some cost) noisy, but equally informative, signals about the amount of oil and gas that may be present. We develop tests of rational and equilibrium bidding in a common values model that are implemented using data on bids and ex post values. We also use data on tract location and ex post values to test the comparative static prediction that bidders may bid less aggressively in common value auctions when they expect more competition. We find that bidders are aware of the "winner's curse" and their bidding is largely consistent with equilibrium.     

Collusion in one-shot second-price auctions

Summary. Most of the literature on collusive behavior in auctions ignores two important issues that make collusion difficult to sustain at least in one-shot interactions: the detection of cheating and the verification of bids. Colluding bidders may deceive each other by using shill bidders. Also, if the identities of the bidders and their bids are not published then it would be difficult to verify the bid of a colluding bidder. This paper addresses these problems in one shot second price auctions where one bidder offers another bidder a side payment in exchange for not participating in the auction, while the number of other bidders is stochastic. In spite of the barriers to collusion mentioned above, a simple side payment mechanism which depends only on the auction price is introduced. It induces a successful collusion, eliminates the verification problem, provides no incentive for the use of shill bidders and guarantees that the proponent obtains ex-post non-negative payoff. The colluding bidders are ex-ante strictly better off compared with the competitive case, irrespective of their types.Received: 27 November 2002, Revised: 28 January 2005, JEL Classification Numbers: C72, D44, D82.Yair Tauman: Correspondence toWe would like to thank an anonymous referee for very valuable comments and suggestions that significantly improved the paper. We thank Shmuel Zamir for a helpful discussion.     

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.     

Competition in the economic crisis: Analysis of procurement auctions

We study the effects of the recent economic crisis on firms׳ bidding behavior and markups in sealed bid auctions. Using data from Austrian construction procurements, we estimate bidders׳ construction costs within a private value auction model. We find that markups of all bids submitted decrease by 1.5 percentage points in the recent economic crisis, markups of winning bids decrease by 3.3 percentage points. We also find that without the government stimulus package this decrease would have been larger. These two pieces of evidence point to pro-cyclical markups.     

Optimistic irrationality and overbidding in private value auctions

Bidding one’s value in a second-price, private-value auction is a weakly dominant solution (Vickrey in J Finance 16(1):8–37, 1961), but repeated experimental studies find more overbidding than underbidding. We propose a model of optimistically irrational bidders who understand that there are possible gains and losses associated with higher bids but who may overestimate the additional probability of winning and/or underestimate the potential losses when bidding above value. These bidders may fail to discover the dominant strategy—despite the fact that the dominant strategy only requires rationality from bidders—but respond in a common sense way to out-of-equilibrium outcomes. By varying the monetary consequences of losing money in experimental auctions we observe more overbidding when the cost to losing money is low, and less overbidding when the cost is high. Our findings lend themselves to models in which less than fully rational bidders respond systematically to out-of-equilibrium incentives, and we find that our model better fits the effects of our manipulations than most of the existing models we consider.     

Auctioning Risky Conservation Contracts

Conservation auctions have the potential to increase the efficiency of payments to farmers to adopt conservation-friendly management practices by fostering competition among them. The literature considers bidders that have complete information about the costs of adoption and optimal bidding behavior reflects this information advantage. Farmers seek information rents and bids decrease when risk aversion increases because farmers are more averse to losing the auction. We contribute to the literature by allowing for cost risk. Our paper shows that farmers must balance the risk of losing the auction (thus foregoing information rent) with the risk of submitting a bid that is not high enough to pay the costs of adopting conservation practices (thus incurring losses). We design an experiment to trade off these two risks and examine how risk aversion affects bidding behavior when participants face different sources and levels of risk. Our experiment contributes to a small literature on experimental auctions with risky product valuations. We find that participants decrease their bids as risk aversion increases, even in auctions with cost risk, suggesting that the risk of losing the auction dominates. These findings uncover new challenges for the practical implementation of conservation auctions as an efficient policy instrument.     

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.     

Multi-unit demand auctions with synergies: behavior in sealed-bid versus ascending-bid uniform-price auctions

We construct a relatively simple model of bidding with synergies and solve it for both open outcry and sealed-bid uniform-price auctions. The essential behavioral forces involved in these auctions are: (1) A demand reduction force resulting from the monopsony power that bidders with multiple-unit demands have when synergies are relatively inconsequential, and (2) Bidding above stand-alone values in order to capture significant complementarities between units. The latter creates a potential “exposure problem,” as bidders may win only parts of a package and earn negative profits. Bidding outcomes are closer to equilibrium in clock compared to sealed-bid auctions. However, there are substantial and systematic deviations from equilibrium, with patterns of out-of-equilibrium play differing systematically between the two auction formats. These patterns of out-of-equilibrium play are analyzed, along with their effects on revenue and efficiency.     

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.     

Renegotiation on incomplete procurement contracts

This article examines the impact of incomplete contracts on procurement costs in road construction auctions. Ex ante contracts in these auctions often fail to specify all of the potential construction contingencies, and consequently, changes in scope are necessary after construction begins. Using Vermont road construction contract data, this study finds evidence that there is a statistically significant difference in costs of firms between auctions with and without extra work adjustments. Substantial adaptation costs are responsible for the higher procurement outlays in incomplete contract. I also find that bidders inflate their bids to incorporate risk premiums in incomplete contracts; however, my estimates suggest that this bidding behaviour does not affect their profit margins.     

Auctions in which losers set the price

We study auctions of a single asset among symmetric bidders with affiliated values. We show that the second-price auction minimizes revenue among all efficient auction mechanisms in which only the winner pays, and the price only depends on the losers' bids. In particular, we show that the kth price auction generates higher revenue than the second-price auction, for all k>2. If rationing is allowed, with shares of the asset rationed among the t highest bidders, then the (t+1)st price auction yields the lowest revenue among all auctions with rationing in which only the winners pay and the unit price only depends on the losers' bids. Finally, we compute bidding functions and revenue of the kth price auction, with and without rationing, for an illustrative example much used in the experimental literature to study first-price, second-price and English auctions.