Bidder Strategies, Valuations, and the Winner s Curse: An Empirical Investigation Robert F. Easley and Charles A. Wood Department of Management, Mendoza College of Business University of Notre Dame, Notre Dame, IN 46556-5646 reasley@nd.edu (574) 631-6077, cwood1@nd.edu (574) 631-4943 INTRODUCTION In recent years it has become possible to argue that Internet auctions and ebay auctions in particular can be regarded as the dominant public market for certain goods, and thus as fertile grounds for empirical evaluation of auction theory. Many studies to date have sampled auctions for a particular market, though the same advances in Internet technology that have transformed the auction industry also permit researchers to go beyond the sampling of a particular market to capturing every bid in every auction. Comprehensive data sets of this type, comparable to the full intra-day bid-ask data used in some financial market studies, are critical to examining some of the more nuanced predictions of recent theories addressing bidder behavior. In this paper, we examine a number of predictions from economic theory that relate to bidder strategies, both for developing their valuations, for bidding itself, and for avoiding the winner s curse. We do this using a complete record of all auctions in a three-month period for US coins that are rare enough to be collectible, and yet traded frequently enough to constitute and active market, analyzing 317,556 bids from 90,309 auctions. We are thus able to empirically investigate a number of both longstanding and relatively recent theoretical predictions. Building not only on long-standing theoretical predictions concerning the Winner s Curse, but also on more recent auction research, including Bajari and Hortescu (2003); Bapna, Goes, and Gupta (2003);, Dellerocas, Fan, and Wood (2004); Easley and Tenorio (2004); Rassmussen (2001); Roth and Ockenfels (2002) and others, we make the following contributions in this research: We clearly establish the existence of the predicted winner s curse adjustment for the number of bidders through robust statistical analysis. The past two decades have seen numerous studies of the prediction that bidders will increasingly shade their bids as the number of bidders grows. Though these studies have generally supported this prediction, this is the first study to have enough data to show the effect directly in a population-level data set.
Because a published book value was available for most (90%) but not all coins in our study, we are also able to establish two distinct levels of certainty with respect to market valuation. We are thus able to confirm another well-known predicted winner s curse adjustment shading bids as valuation uncertainty increases that has not received much empirical study. Because we have data on all bids in all auctions, we are able to distinguish between bidder strategies in a manner that allows us to shed light on recent theoretical models of strategies that have emerged in Internet auctions. Much research attention has been focused on the phenomenon of snipe bidding, or bidding at the last moment, that has emerged in response to ebay s fixed termination time for auctions. We examine snipe bidding, but find that this does not distinguish bidders by winner s curse adjustment, perhaps in part because it is such a commonly adopted strategy. Looking instead at the number of bids placed per bidder, we are able to distinguish a subgroup of bidders who bid multiple times, and thus appear willing to pay for valuation information, at increased risk of incurring the winner s curse. PARTIAL RESULTS In Table 1 we show the results of our least squares regression analysis, which is weighted for the number of auctions participated in by each bidder, such that each bidder has equal impact on the results. The number of bidders is an instrument variable based on the following values, all readily observable at the time the bid is placed: number of previous bids, hours left, and current bid amount. As expected for the full auction (Panel A), there is a significant negative adjustment of the final bid amount for each bidder as the estimated number of bidders increases. The published book value of each coin is used as a control, and absorbs most of the variance, as would be expected when predicting bid values. When the book value is not available we develop an estimated value using the known convex function for other coins where the same coin grade and bracketing grades with published book values are available. We call these values Interpolated, and the negative coefficient confirms the predicted adjustment in bids for higher uncertainty regarding the coin s value. Since we estimate a convex function, bidders comfortable with simple linear interpolation would obtain a higher estimate of book value than ours, so the adjustment we detect is a conservative measure.
Table 1. WLS Many vs. One Bid All Records Panel A: All Records Panel B: Bids Many Times Panel C: Bids Only Once Coeff Err t-stat Coeff Err t-stat Coeff Err t-stat Constant (α) -1.634 0.084-19.48*** -1.346 0.171-7.90*** -1.628 0.096-16.91*** Number -0.022 0.001-38.92*** 0.010 0.001 8.47*** -0.030 0.001-46.18*** Bidders ab Snipe 0.222 0.003 66.29*** 0.225 0.007 33.60*** 0.405 0.005 89.25*** ManyBids ab 0.358 0.004 94.78*** N/A N/A N/A N/A N/A N/A Interpolated c -0.056 0.005-11.67*** -0.043 0.009-4.93*** -0.058 0.006-10.03*** Seller 1.947 0.084 23.21*** 1.801 0.171 10.55*** 1.963 0.096 20.39*** Reputation a Picture a 0.027 0.004 6.33*** 0.010 0.008 1.20*** 0.035 0.005 6.91*** LN(Bidder 0.005 0.001 4.83*** 0.023 0.002 12.46*** -0.001 0.001-0.95*** Experience ab ) LN(Book 0.720 0.001 645.50*** 0.680 0.002 318.00*** 0.729 0.001 559.18*** Value c ) Observations 317,556 82,473 235,083 Adjusted R 2 64.6% 66.1% 63.5% Weighting Bidder Has Participated Bidder Has Bid Many Times Bidder Has Bid Only Once * = p-value <.05; ** = p-value <.01; *** = p-value <.001; Dependent variable is LN (FinalBidAmount abc) Two other controls that affect other aspects of uncertainty are seller reputation, which, when higher, is seen to raise the bid value, and inclusion of a picture, which also reduces uncertainty regarding whether the coin is as advertised, and thus leads to higher bid values. The control for snipe bidding, defined here as bidding in the last 5 minutes of the auction, indicates that those sniping tend to bid higher, which is natural since on average there will be very few lowball bids accepted that late in the auction. Snipe bidders are examined in more detail below. Those who bid more than once, indicated as Many Bids also are seen to bid more on average in Panel A. The effect of multiple bidding is examined in more detail in Panel B, showing only bidders who place multiple bids in a single auction, and Panel C, which shows those bidders who bid only once. It is notable that those who bid multiple times (Panel B) do not make the predicted common value adjustment for the number of bidders, and in fact bid more in the presence of more bidders. This is consistent with the interpretation (e.g., of Rasmussen 2001) that some bidders may be willing to pay for information that helps them reach their valuation. When a multiple bidder faces another bidder, he can ratchet against the bid in order to determine its value, and thus obtain a data point for his own estimated value. This behavior leaves him at greater risk of suffering the winner s curse, and thus does extract a price.
Table 2. WLS Many vs. One Bid Snipe Only Panel A: Snipe Bids Panel B: Snipe Bids, Bids Many Times Coeff Err t-stat Coeff Panel C: Snipe Bids, Bids Only Once Err t-stat Err t-stat Coeff Constant (α) -1.584 0.187-8.47*** -1.321 0.358-3.69*** -1.667 0.221-7.55*** Number 0.000 0.001 0.35*** 0.013 0.002 6.38*** -0.003 0.001-2.32*** Bidders ab ManyBids ab 0.064 0.007 8.74*** N/A N/A N/A N/A N/A N/A Interpolated c -0.061 0.011-5.68*** -0.064 0.018-3.57*** -0.060 0.013-4.48*** Seller 1.985 0.187 10.63*** 1.911 0.358 5.33*** 2.012 0.220 9.13*** Reputation a Picture a 0.058 0.010 5.99*** 0.078 0.018 4.43*** 0.052 0.012 4.45*** LN(Bidder 0.012 0.002 4.81*** 0.003 0.004 0.65*** 0.016 0.003 5.29*** Experience ab ) LN(Book 0.755 0.003 300.78*** 0.705 0.005 150.83*** 0.771 0.003 256.94*** Value c ) Observations 39,192 13,139 26,053 Adjusted R 2 75.4% 73.0% 76.3% Weighting Bidder Has Sniped Bidder Has Sniped and Bidder Has Sniped and Has Bid Only Once Has Bid Many Times * = p-value <.05; ** = p-value <.01; *** = p-value <.001; Dependent variable is LN (FinalBidAmount abc) Looking only at snipe bidders, we note that in Panel A of Table 2 there is no statistical relationship between the estimated number of bidders and the final bid price. Taken at face value, one might conjecture that this is due to the compression of the bid range between the highest bid going into the snipe period, and the final high bid. However, when the snipe bids are divided between those who bid multiple times (Panel B) and those who bid just once (Panel C) we see the common value adjustment for number of bidders reemerge for bidders who bid just once. This is consistent with the recent interpretations (e.g., of Roth & Ockenfels 2002) concerning the advisability of sniping for experts who want to hide their valuations (and who would only bid once) and those who snipe for other reasons, such as wanting to see what other people have bid prior to placing their own bids (and who would thus be more inclined to bid more than once to determine other bid values). In addition to the analyses discussed above, we examine a number of other bidding strategy issues that emerge from the data. For example, Table 3 shows a cross-sectional analysis of winning bids only, which reveals the extent to which those who bid many times suffer the winner s curse, especially when sniping. Here again we see a more dramatic difference between those who bid once (knowing their valuation) and those who bid many times (seeking valuation information), than between those who snipe
and those who bid early. However it is also clear that those who snipe do not incur the winner s curse at a higher rate on average, suggesting that it is an effective strategy. These results are consistent with other analyses (not shown) that reveal an increased preference for the best strategy in Table 3 (one snipe bid), at the expense of the worst (many early bids) as bidder experience increases. Table 3. Percentage of Winning Bid Amount to Book Value Bidder Bids Many Times Bidder Bids One Time Bidder Only Submits Early Bids 108% 93% Bidder Snipes 99% 91% Based upon winning bid observations from 90,309 Auctions CONCLUSIONS The major original contribution of this research involves its use of complete bid-level data to examine a number of implications drawn from recent theoretical work on online auctions. We are thus able not only to establish robust support for the well-known predictions for winner s curse adjustments in the number of bidders and valuation uncertainty, but also to demonstrate the impact of bidding strategies (in particular placing snipe and single bids) and valuation strategies (such as multiple bids to determine other valuations) on the winner s curse adjustments undertaken by the bidders. We also derive a number of interesting results on the ultimate impact of these bidder behaviors on realized prices, leading ultimately to conjectures, requiring further study, concerning bidder learning and the evolution of online auction markets. REFERENCES Bajari, P. and Hortaçsu, A. (Summer 2003), "Winner's Curse, Reserve Prices and Endogenous Entry: Empirical Insights from ebay Auctions," RAND Journal of Economics 34 (2), 329-355. Bapna, R., Goes, P., and Gupta, A. (January 2003), Analysis and Design of Business-To-Consumer Online Auctions, Management Science 49 (1), 85-101. Dellarocas, C., Fan, M., and Wood, C. A. (2004). Reciprocity and Participation in Online Reputation Systems, Working paper, University of Notre Dame, Notre Dame, IN. Easley, R. F., and Tenorio, R. (2004) "Jump Bidding Strategies in Internet Auctions." Management Science, forthcoming. Rasmusen, E. B., (April 7, 2001) "Strategic Implications of Uncertainty Over One's Own Private Value in Auctions". http://ssrn.com/abstract=267932 Roth, A. E., and Ockenfels, A. (September 2002). Last-Minute Bidding and the Rules for Ending Second-Price Auctions: Evidence from ebay and Amazon Auctions on the Internet, American Economic Review 92 (4), 1093-1103.