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Squatting, Sniping, and Online Strategy: Analyzing Early and Late
Bidding in eBay Auctions
Philip Groenwegen
Advised by Professor Philip A. Haile
Yale University
Department of Economics
April 3, 2017
Abstract: This essay builds on previous studies of bidding strategies in online auctions. Many studies have observed an increase in bidding activity close to the ending time of eBay auctions, despite the fact that such behavior is not predicted by economic theory and is explicitly discouraged by eBay. There is also some evidence that bidding very close to the beginning of an eBay auction is another widely used strategy, although this too is unexpected. I use bid data from eBay to examine the conditions under which early and late bidding is most prevalent. I then study the effect of these strategies on the likelihood of a bidder winning an auction and the closing price of an auction. I am sincerely grateful to Professor Philip A. Haile for his thoughtful advising. I also thank Joshua Dull at the Center for Science and Social Science Information and Sachith Gullapalli for their technical advice.
1. Introduction and Literature Review
The explosive growth of the Internet over the past two decades has afforded researchers new opportunities to test theories of economic behavior on a large scale. Online bidding sites like eBay have made research on auctions particularly fruitful. In 2015, the British newspaper The Daily Telegraph estimated that eBay handled nearly $83 billion in sales per year and had about 800 million items for sale at any given time. The scale of eBay and the diversity of items sold on the platform make it a useful tool for testing economic theory. Studying eBay and other online auctions has also revealed many cases of unexpected bidding behavior. One of the most important of these observations is the fact that bidding tends to occur in clusters, with some bids at the beginning of the auction, relatively few in the middle, and a large spike in activity in the last few minutes. The exact rules of an auction on eBay can vary, but one of the most prevalent methods of selling is a second-price auction. 1 When a bidder enters an auction, eBay prompts her to bid at least a minimum increment—set by the seller—over the standing price. There is no maximum on the amount a bidder can enter. If the bidder expresses a willingness to pay above the minimum price, eBay automatically raises the bid of the bidder who submitted a higher willingness to pay, such that the bidder with the highest valuation wins by paying marginally more than the second- highest bid. Thus if the minimum bid is $10, the bid increment is $0.50, and the first bidder enters a maximum willingness to pay of $20, eBay will show that the first bidder has bid $10. If a second bidder enters a willingness to pay of $15, the standing bid will be raised to bidder two’s $15 plus the $0.50 increment to $15.50, the minimum amount required for bidder one, the bidder with the highest willingness to pay, to win. Therefore, at any given point, participants know the (^1) Many auctions on eBay have a “But It Now” option that allows a bidder to end the auction by paying a high, posted price. These auctions are excluded from my analysis.
among more experienced bidders on eBay, suggesting that bidders learn this behavior. Moreover, although eBay discourages sniping, many online forums encourage bidders to engage in the practice, and there even exist services that will automatically submit sniping bids. None of this is to say that bidders ignore the implications of the rules of eBay auctions. In fact, Ariely, Ockenfels, and Roth ( 2003 ) compare the prevalence of late bidding on eBay, which has a fixed closing time, to that on Amazon, which extends the closing time by a few minutes after a bid is placed. As expected, there is less of a flurry of activity close to the expected closing time of an Amazon auction. Previous studies have produced evidence of a modest return to sniping. Ely and Hossain (2009) find that sniping leads to a roughly 5% increase in the probability of winning an auction, as well as a small yet statistically significant decrease in the price paid for the item. Gray and Reiley (2007) perform a similar study and find an even smaller and statistically insignificant benefit to sniping. The statistical insignificance is likely due to the small sample sized used in their study. Gray and Reiley speculate that the observed decrease in the magnitude of the benefit of sniping could be due to the fact that markets have become more competitive or bidders more sophisticated over time. However, they find no evidence of different returns to sniping in markets of different sizes and find that sniping is just as frequent in their study as in previous ones. Both of these studies use field experiments to evaluate the returns to sniping. The authors place both early and late bids on items and compare the prices they pay under the two strategies. Ely and Hossain compare the price they pay to a hypothetical valuation corresponding to their bid in order to find the surplus of winning a given auction. By looking at data from previously completed auctions instead of actually bidding in auctions, I do not estimate the surplus of the
winner, but rather the difference in closing price associated with sniping. On average, this should reflect the change in surplus a winner would receive if she were to snipe. One popular explanation for the prevalence of sniping is the presence of “naïve” bidders. eBay has thousands of active bidders, not all of whom may be well-versed in theoretically optimal bidding strategies. Ku, Malhotra, and Murnighan (2005) demonstrate that competition can cause bidders to become more aggressive, in what they call “competitive arousal.” Similarly, Ariely and Simonson (2003) argue that bidders may enter an auction when the price is relatively low and then become attached not necessarily to the item but to the prospect of winning, leading them to increase their bids many times, perhaps at the last minute, after being outbid. Indeed, Ariely and Simonson find that bidders often buy common retail items like DVDs for more than a brick and mortar store would charge. This may suggest that bidders value winning per se, even if they must overpay to win. Moreover, as Bajari and Hortaçsu (2004) suggest, bidders may participate in auctions to have fun rather than to buy important items. Another potential explanation for sniping is that bidders likely derive more pleasure from bidding in real time than from learning that their bid has been raised automatically. No matter the reason why these “naïve” bidders behave as they do, the presence of these bidders could influence the strategies of better-informed bidders. Ockenfels and Roth (2006) show that late bidding by experienced bidders is a best response to the existence of at least one naïve bidder, who does not initially bid his valuation but instead raises it incrementally. By sniping, sophisticated bidders avoid starting a bidding war with incremental bidders. Indeed, the authors find that bidders who bid only once tend to submit their bids later than the last bids placed by incremental bidders, which is further evidence to suggest that sniping is favored by experienced bidders as a response to their naïve competitors.
however, a possibility once some bidders snipe.^4 Ely and Hossain’s and Roth and Ockenfels’ models are satisfying because they empirically show benefits to sniping and offer explanations for why rational bidders would engage in such a practice. Nevertheless, their models rely on the existence of at least some naïve, incremental bidders in an auction. Other literature has attempted to explain sniping through the lens of imperfect information, such as common values auctions or cases where bidders are uncertain of their own private values. Rasmussen (2006) and Hossain (2008) propose models where bidders have independent private values, but some bidders do not know their exact valuation and must incur a cost to learn it. These bidders submit a relatively low bid and reconsider whether to bid again each time they are outbid, effectively using other bids to “learn” their own private valuations. In response, experienced bidders may prefer to snipe, so they avoid giving away any information that could raise the bid of a competitor. Similar results have been predicted in auctions with common values, where a knowledgeable bidder’s bid may convey information to less well- informed bidders. As outlined in Section 2, Bajari and Hortaçsu (2003) propose that sniping is an equilibrium behavior in second-price sealed-bid auctions with common values. Being outbid early in an auction could inform the lower bidder that she has underestimated the true value and cause her to raise her bid to something she previously believed was too high. In general, theories of information asymmetry are attractive because they do not rely on the presence of naïve bidders to give a rational basis for sniping. While the presence of common values may theoretically provide an incentive to snipe, testing this hypothesis rigorously is possible thanks to relatively recent work formalizing the nature private and common values auctions. Milgrom and Weber (1982) propose models of (^4) This is shown in more detail in Section 2. In short, a sniper may cause bidders other than those with the highest valuations to win a group of simultaneous auctions for similar goods.
private and common values bidding in addition to offering qualitative descriptions of factors that might influence the presence of private or common values. They also propose what they call an “intermediate” model of affiliated values. While the authors link the common values framework with auctions for things like mineral rights and private values with non-durable consumer goods, they claim that an affiliated values model is suitable for goods like paintings. With affiliated values, bidders’ valuations are correlated, but they still reflect the individual preferences of the bidder. This differs from a pure common values auction, where bidders’ valuations are estimates of one true, unknown valuation. Later work attempts to distinguish between private and common values empirically. Paasrsch (1992) derives models of private and common values and tests their applicability to tree planting auctions, yet as Haile, Hong, and Shum (2003) note, this method requires modeling bidding behavior based on one’s assumption about the suitability of a private or common values framework. Instead, Haile, Hong, and Shum show that in first-price sealed-bid auctions with equilibrium bidding, the presence of common values is testable against the null hypothesis of private values. This test relies on the fact that the “winner’s curse” is present under common values but not under private values. As more bidders arrive in a common values auction, there is an increased probability that the winner’s estimate of the actual, unknown value of the item is too high. To compensate for this, bidders should decrease their bids as more bidders arrive. This is not the case under private values, since a bidder’s valuation depends only on her own preferences and information. Under private values, then, there should be no relationship between the number of bidders and an individual’s expectation of winning, conditional on the number of bidders, and bidders should not adjust their bids depending on the number of competitors of they face.
auction by observing only some of the bids, Bajari and Hortaçsu examine the relationship between the levels of the observed bids and the number of bidders. 6 Bajari and Hortaçsu also adopt the instrumental variables approach to endogenous bidder participation explained by Haile, Hong, and Shum (2003). They use the minimum bid as an instrument for participation. The authors find that the minimum bid is negatively correlated with the number of bids, and they assume that it is uncorrelated with any other factors that could affect the value of the bids. The latter assumption may not be particularly strong, given that lower minimum bids could simply be associated with less valuable items. Finally, although Bajari and Hortaçsu provide qualitative evidence that auctions for coins have a common values element and find statistical backing for their claim, they note that they merely reject a pure private values model. Indeed, as Goeree and Offerman (2002) claim, the extreme cases of pure private and common values are likely quite rare. Rather, most auctions probably have some elements of both cases. In the present study, I attempt to improve on Bajari and Hortaçsu’s analysis by using a new instrument. I also test the relationship between the median bid—rather than the average bid, the closing price, or all the observed bids—and the number of bidders in order to limit the effect of the unknown winning bid. Recognizing that a mixture of private and common values is likely, I attempt to examine not just whether a private or common values model prevails, but also the magnitude of these effects. Many previous studies have investigated sniping and squatting by placing bids in auctions or by tracking individual bidders, in addition to studying the characteristics of completed auctions. As Ariely, Ockenfels, and Roth ( 2003 ) note, one would obtain stronger 6 Bajari and Hortaçsu (2003) also claim that Athey and Haile (2002) imply that under eBay’s rules, the number of bidders should have a positive relationship with the levels of the bids, rather than no relationship, under the null hypothesis of private values.
results in an experimental setting where researchers can control for factors like bidders being unaware of their true valuations. Similarly, Einav, Kuchler, Levin, and Sundaresan (2015) note the difficulty of using real auction data: While heterogeneity among items, bidders, and sellers can obscure important bidding patterns, considering bidding for only certain items under certain conditions can make it difficult to generalize one’s results. For reasons of practicality, I rely solely on data from completed eBay auctions in which I did not bid. Despite the challenges this presents, the size of the dataset should help solve the power problems seen in work like Gray and Reiley’s (2007). Instead of following bidders or conducting an experiment where I place bids myself, I rely on information about the good being sold and about each bidder’s identity, experience, and bids in completed eBay auctions. Like in previous work, I create indicator variables to show sniping and squatting. I use them to study the prevalence of these behaviors and whether they have an effect on the probability of winning and on the price the winner pays. I compare the behavior I observe to the null hypothesis that there is no benefit to bidding at any particular time, and that bidders should simply bid their valuation when they see an item in which they are interested. The present study will examine the prevalence of sniping and squatting in auctions for a number of different goods. The purpose of this part of the study will be to determine if either type of unexpected bidding is more common in auctions for goods where a common values framework may be appropriate. For each type of good that I study, I test whether it might be appropriate to assume common values and compare my finding to the prevalence of early or late bidding in auctions for that type of good. For each type of good, I will examine the effect of bidding behavior on the probability that a given bidder wins an auction. I then develop a new
second highest bidder’s valuation. Since the highest bid at any given point is unknown to the other bidders, eBay auctions are very similar second-price sealed-bid auctions. In second-price sealed-bid auctions, it is a weakly dominant strategy to bid one’s valuation. Assuming private values, the time that a sealed bid is placed also should not affect its magnitude, since bidders do not know the valuations of their competitors. One possible equilibrium in eBay auctions is that all bidders will bid their valuations, as is traditionally predicted for second-price sealed-bid auctions. However, this is complicated by the fact that only the highest bid in an eBay auction is sealed. To be sure, this is the most important bid to know, since it is the one that must be beaten in order to win, but knowledge of lower bids could reveal information about how one’s competitors behave, help bidders learn their own private valuation, or, in the case of common values, help improve their estimate of an item’s true value. This additional information allows for incremental bidding in during the auction. As a result, bidding one’s value at the beginning of an auction is just one equilibrium strategy. Bajari and Hortaçsu (2003) and Roth and Ockenfels (2000) show that other equilibria, including one where bidders place multiple bids and bid their valuations only at the last moment, exist. The key to these analyses is dividing an eBay auction into two stages: The first comprises almost the entire auction, from the beginning to just before the end. The second is the last moment of the auction—the moment in which sniping takes place. During the first period, bidders have time to react to other bids that come in, while in the second period they do not. The second period of the auction is exactly like a second price sealed bid auction, since even if one were to see the last-minute bids, it would be impossible to use the information they might bring. Bajari and Hortaçsu (2003) also note that this two-stage model also implies that when a bidder
stops bidding or “drops out” of the first stage, it does not necessarily indicate that the price has reached the bidder’s valuation, as it would in a typical ascending auction. Roth and Ockenfels’ (2000) model incorporates another element of uncertainty in the brief final period of the auction. In their model, while bids are submitted with certainty in the first period, there is a possibility in the second period that a bid will not be processed in time to be counted. This is an apt modification; bidders frequently complain that their snipes are not processed in time, and online services compete by advertising their success in transmitting snipes. The authors show that it is an equilibrium strategy for bidders to bid the minimum bid at the beginning of the auction and then to bid their valuation in the last second. This strategy allows a bidder to increase the probability that, should she win, she must pay only the starting price or the minimum increment over the starting price. If two bidders submit the minimum bid at the beginning of the auction, eBay will count whichever bidder submitted the bid first as the current high bidder. When the players bid their valuations at the end of the auction, the bidder with the higher valuation could lose if her snipe fails and if the low bidder had submitted the minimum bid first. In this equilibrium, players risk that their final bid equal to their valuation will not go through. This creates the possibility that the bidder will lose against a competitor simply due to chance, rather than because she has the lower valuation than her competitor. Alternatively, bidders can mitigate the risk that their high bids will lose simply due to chance by bidding their valuation in the first stage of the auction, eliminating the possibility that the bid will not be transmitted in time. One’s opponent may know that one is following this strategy. For example, when an opponent arrives, he sees that there is one bidder and the standing price is the minimum bid. He must bid at least an increment above the minimum. If he does this, he will find out that the first bidder has not bid the minimum, since eBay’s proxy
uninformed bidder’s valuation and the minimum bid. The uninformed bidder uses information from the informed bidder’s actions to determine if her own valuation of an object is accurate. The authors claim that an informed bidder will never bid above her valuation for an object, so the presence of an informed bid shows an uninformed bidder that the object must have some value. In order to avoid a bidding war, the informed bidder may submit her bid equal to her valuation in the second stage of the auction, preventing her information from being shared with uninformed bidders. The authors also define the case when it is profitable for the uninformed bidder to snipe. In particular, if the ratio of the probability of an item being “fake” to the probability of an item being “genuine” is greater than the ratio of the uninformed bidder’s valuation to the minimum price, then the uninformed bidder should not snipe, assuming there is no signal from the informed bidder that the object is genuine. Ely and Hossain’s (2009) model takes a different approach by predicting sniping as well as squatting in the context of competing price effects and simultaneous auctions. They speculate that the presence of a squatting bid will encourage potential entrants to consider simultaneous auctions for the same good in order to avoid competition and to win at a lower price. Intuitively, the earlier a bid is placed, the longer it has this deterrent effect. This is what they call the “competition effect” that promotes squatting. This effect trades off with the “escalation effect,” which hurts the case for squatting and instead is an incentive to snipe. The escalation effect holds that entry into an auction can provoke a bidding war. The authors acknowledge that this relies on the existence of naïve bidders who do not bid their valuations: A bidder could win against a naïve competitor with a higher valuation if the bidder snipes and prevents the competitor from raising his bid in response.
Further, Ely and Hossain replace the two-period models of Roth and Ockenfels and Bajari and Hortaçsu by dividing eBay auctions into N +2 periods, where N is the number of bidders. Each bidder bids in her own period. The authors create a final period, N +1, when sniping can occur. Sophisticated bidders will submit two bids in their model. First, they will incrementally raise their bids in different auctions for the same good to find the one with the lowest high bid. A sophisticated bidder succeeds once her incremental bid makes her the high bidder in an auction. She then bids her valuation in that auction, maximizing her chance of winning the auction at the lowest price. The authors claim that naïve bidders will do the same thing but will not realize that bidding need not be incremental. As a result, once the naïve bidder becomes the high bidder in an auction, she will do nothing until she is outbid. Thus if all bidders are naïve, the authors predict auctions with sniping to have a lower closing price, while they make no such prediction if all bidders are sophisticated and bid incrementally only to uncover their competitors’ bids. Moreover, as mentioned earlier, the authors show that sniping can lead to an inefficient allocation of goods. If a sophisticated bidder gradually raises her bid in two auctions, Auction 1 and Auction 2, she will stop bidding once she is the highest bidder in the auction with the lower standing bid, say Auction 2. If the sniper bids in and wins Auction 1, and the sophisticated squatter wins Auction 2, then inefficient allocation is possible. In this case, the bidder whom the sniper beats in Auction 1 has a higher valuation than the sophisticated squatter who wins Auction
- Thus the bidders with the highest and third highest valuations win the two auctions. This is even more clearly the case with naïve bidders who not bid their valuations and do not have the chance to respond to a snipe.
effects of costly information acquisition and asymmetrical information between bidders on the prevalence and effectiveness of alternative bidding strategies, as in Bajari and Hortaçsu (2003) and Ockenfels and Roth (2006). The Canadian coins are relatively homogenous in terms of age, but there are relatively few observations. The Indian Head pennies, on the other hand, have a much broader range in age but are a much larger market, allowing for more observations and more powerful results. Harry Potter DVDs are widely sold and typically have an easily knowable retail value. I chose a specific computer processor in order to have very homogenous group and one with very expensive items. Unfortunately, this traded off with the sample size; there are relatively few observations in this group. Finally, the iPhone 6 market is relatively large and, although the products are all essentially the same, they have varying degrees of wear and tear, adding a degree of uncertainty to the item’s true value. My final data set sampled thousands of auctions that occurred in January and February
- After eliminating Buy It Now auctions, auctions not denominated in U.S. dollars, and auctions where all bidder information was private, my data set contained 1,973 auctions with 9,830 bidders who placed 18,452 distinct bids (i.e., not counting as separate bids all the times a bid was automatically raised). None of the auctions in the final data set had reserve prices. It is important to have information about individual bidders in order to track whether they submit multiple bids and to consider the effect of their experience on their behavior. As in much of the literature, I use a bidder’s feedback rating as a proxy for her experience on eBay. 7 Table 1 shows the distribution of bids and bidders into the categories discussed previously. 7 Each time a bidder completes a transaction, the seller can rate her as good, bad, or neutral, which correspond to changes in her feedback rating of +1, - 1, or 0. Previous literature has noted that bidders generally receive positive feedback, so their rating is a decent measure of how many transactions they have completed.
Table 1. Number of bids by item type Frequency Percentage Processor 234 1. Harry Potter 668 3. Canadian coin 1722 9. Indian Head 9396 50. iPhone 6 6432 34. Total 18452 100 Observations 18452 Sellers set the duration and starting price of the auction in advance, and these are known to all bidders. Auctions can be 1, 3, 5, 7, or 10 days long. All of these lengths are represented in my data, although 7-day auctions are by far the most common, as demonstrated in Table 2. To account for the fact that the auctions are of varying lengths, I usually consider the time elapsed in an auction as the percentage of the auction that has elapsed. Table 2. Number of auctions by duration Frequency Percentage 1 14. 3 57 2.8890 02 5 359 18. 7 1379 69. 10 164 8. Total 1973 100 Observations 1973 The data show extremely clear patterns of bidding, with most bidding occurring at the beginning or end of an auction and very little in the intermediate hours and days. There is also evidence of multiple bidding, that is, cases where bidders ignore eBay’s advice to bid their maximum willingness to pay when they first bid and instead bid different amounts at different times. Of the 18,452 individual bids collected, 8,6 22 , almost 47%, were not the first bid the bidder had placed for a particular item. In some cases, incremental bidding does not even appear
