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  • 1. Bidding Strategies and the eBay Auction: Does Bidding Late Eliminate Paying Great? March 2003 Karl W. Einolf Mount Saint Mary’s College Emmitsburg, MD 21727 (301) 447-5396 x4068 fax (301) 447-5335 einolf@msmary.edu http://faculty.msmary.edu/einolf The author is very grateful for a grant from Mount Saint Mary’s College to help fund this research. He also thanks April Parreco for her extensive and diligent research assistance.
  • 2. Abstract: The eBay auction is a cross between the traditional open outcry auction and a second- price sealed bid auction. The eBay auction has a timed ending, so bidders may participate in an open outcry auction until the final seconds of the auction. During this final period the eBay auction becomes a second-price sealed bid auction as bidders may enter a bid that will not be countered by other bidders. Bidders often employ the snipe strategy, a single bid placed at the very end of the auction. This paper shows that the dominance of the snipe strategy increases as a good becomes scarcer and has increasingly unknown value. Using 3,801 bids from 300 auctions, the paper shows that bidding closer to the end of the auction is more prevalent with scarcer goods. However, only 32% of bids placed in the final five minutes in the auctions were snipe bids. Most bidders on eBay do not bid optimally and some auction winners end up overpaying by bidding too early.
  • 3. 1. Introduction More consumers every day are purchasing goods and services through online auction houses. The eBay auction website reported 61.7 million registered users at the end of December 2002. eBay transferred $14.9 billion dollars in product during 2002 and retained $1.2 billion in revenue through auction related fees. The eBay auction is unique in that it is a cross between a traditional English open outcry auction and a sealed bid auction. The eBay auction is conducted over a fixed time period – typically conducted over three to ten days. Each auction has a specific beginning and ending time. While the auction for a good is in progress, bidders may enter a bid by indicating to eBay their maximum willingness to pay. This is the “open- outcry” period in the auction. eBay sets the bid price slightly above the second-highest bid, so essentially eBay is a second-price auction. However, during the last seconds of the auction, bidders may enter a bid that will not be countered by another bidder. It is during this period that eBay works like a second-price sealed bid auction. Bidding strategies in traditional auctions are understood and well established. In an English open outcry auction, bidders should be careful not to increase the bid beyond the bid increment. A large “jump” may push the bid price well beyond the second- highest bidder’s maximum willingness to pay and force the bidder to pay more than she had to. In a second-price sealed bid auction, bidders have a dominant strategy to bid their valuation of the good (Vickrey’s truth serum). In a first-price sealed bid auction, bidders must determine an optimal “shaded” bid. The lower the shaded bid is then the greater potential profit, but a bid too low will decrease the chance of winning the auction. 1
  • 4. Most analysis of the eBay auction suggests that the optimal strategy for bidders is to ignore the “open-outcry” period in the auction and bid during the final seconds. The practice of bidding during the last seconds is known as “sniping”. Roth and Ockenfels (2000) show that bidders tend to use the snipe strategy in the eBay auction where there is a fixed ending to the auction. The snipe strategy is not used at other internet auction sites (Yahoo.com) where auctions are conducted over a fixed period, but only end after a period of bidding inactivity. Other research has considered optimal selling strategies (Kauffman & Wood, 2001) and appropriate auction entries (Bajari & Hortacsu, 2001). This paper considers optimal eBay bidding strategies across a wide class of goods. eBay handles many different types of auctions: from widely available goods with common market prices to scarce collectibles with unknown values. This paper develops a theoretical model of the eBay auction. As a good becomes increasingly scarce and its value becomes less known, bidders have an increasing incentive to use the snipe strategy. However, the snipe strategy is not necessary for a good that is widely available with a common market price. Data from three hundred auctions are used to test the theoretical results. The paper shows that bidders do tend to bid more frequently toward the end of an auction the scarcer the good. However, most bidders for scarce goods still bid earlier than they should and simply enter bidding wars that occur closer the end of the auction. 2. Theoretical Model of the eBay Auction Consider an eBay auction for a commodity. Each of the i=1…n bidders has a private valuation, vi, for the commodity where vi∈ [0,V]. A special case occurs when the commodity has a known and common valuation where vi= vj for all i and j. The auction 2
  • 5. is conducted during a fixed time period [0,T]. The auction begins at time t=0 and ends at time t=T. Any bidder, i, in the auction will bid, bi∈[0,V], at time, ti∈(0,T]. A bidder may place multiple bids as long as subsequent bids are higher than previous bids. The probability that the commodity is available through another auction is defined as Pa. When Pa=1, the commodity is available in many markets and it is certain that the commodity is available in another auction. When Pa=0, the commodity is unique and is not available in any other market. Bidder i will win the auction if bi>bj for any other bidder j at the end of the auction. Bidder i also wins if bi=bj and ti<tj for any other bidder j. If bi is the highest bid and bj is the second highest bid, then bidder i receives a profit of vi – (bj + ε) where ε is the bid increment. Each bidder has a private belief of the probability that any bid, bi, will be the highest (and winning) bid in the auction such that bi – bj=ε where bj is the second highest bid. This belief is dependent upon bidder i’s determination of the highest possible valuation of all other bidders, vm. The belief is represented by the cumulative density function, Piwin(bi,vm). Using this model, the following sections describe optimal bidding strategies for three different types of commodities auctioned on eBay. eBay Auction for an available commodity with known and common value (Pa=1): When a commodity, like a popular consumer electronics good, is available in other auctions (Pa=1), it is typically available in other markets outside of eBay. A common market price, p, for the commodity develops. Thus, the commodity will have a known and common valuation such that vi= vj = p for all i and j. Because the commodity 3
  • 6. is available in alternative markets, most bidders enter the eBay auction looking to pay a discounted price below the common market price. Each bidder wants to maximize their profit (p – (bj + ε)) where bj is the second highest bid placed by a bidder j. A bidder’s expected profits for a bid, bi, is Piwin(bi,p)( p – (bj + ε)) or Piwin(bi,p)( p – bi). The bidder selects a bid, bi*, that solves max Pi win (bi , p )( p − bi ) . Figure 1 presents bi an example with two bidders and shows how an optimal bid depends on each bidder’s private cumulative density function, Piwin(bi,p). [Insert Figure 1 here] In this case, there is no risk of bidder i not obtaining the commodity at some point. The probability that they do not win the initial auction is (1-Piwin(bi,p)). The probability that they do not win the first two auctions is (1-Piwin(bi,p))2. As the number of potential auctions increases (and with Pa=1 there will always be another available), the probability of not obtaining the item approaches zero. Theorem 1: When a commodity is available in other auctions (Pa=1) and the commodity has a known and common value, p, a bidder’s optimal strategy is to bid bi* = max Pi win (bi , p )( p − bi ) at any time ti∈(0,T]. (There is no advantage to bidding at time bi t=T.) Proof: Assume that bidder i places a bid of bi* at time ti<T. Consider bidder j’s best response. If bj* ≤ bi*, then bidder j will abandon the current auction and bid in another as Pa=1. The expected profit at another auction is greater than the current auction: 4
  • 7. The expected profit at another auction with bid of bj* is Pa(Pjwin(bj*,p)( p – bj*)). The expected profit at current auction with bid of bj2 > bi* > bj* is Pjwin(bj2,p)(p –bj2). With Pa=1, by the definition of bj*, (Pjwin(bj*,p)( p – bj*)) > Pjwin(bj2,p)( p – bj2). If bj* > bi*, bidder j will place a bid of bj* at time tj>ti because (Pjwin(bj*,p)( p – bj*))>0. Consider bidder i’s best response. Because bi* < bj*, bidder i will abandon the current auction and bid in another as Pa=1. The expected profit at another auction is greater than the current auction: The expected profit at another auction with bid of bi* is Pa(Piwin(bi*,p)( p – bi*)). The expected profit at current auction with bid of bi2 > bj* > bi* is Piwin(bi2,p)(p –bi2). With Pa=1, by the definition of bi*, (Piwin(bi*,p)( p – bi*)) > Piwin(bi2,p)( p – bi2). During the period t∈(0,T), the winner of the auction depends solely on the value of the optimal bid and not on the timing of the bids. At time t=T, the winner of the auction also depends solely on the value of the optimal bid. There is no advantage to bidding at time t=T. 5
  • 8. eBay Auction for a unique commodity with completely private value (Pa=0): Theorem 2: When a commodity is unique and unavailable in other auctions (Pa=0) where each of the i=1…n bidders has a private valuation, vi∈ [0,V], a bidder’s optimal strategy is to bid bi*=vi at time ti=T. Proof: Under this scenario of a second price auction with Pa=0 (there will be no subsequent auctions), from Vickrey each bidder’s optimal strategy is to bid their valuation bi*=vi. What needs to be shown is that this bid must come at time ti=T. Assume vi > vj for all j, then bi* > bj* for all j. If bidder i bids bi* at ti=T, then bidder i wins the auction and pays bk*+ε where k is the second highest bidder. Let bidder i place a bid of bi* at time ti<T. Bidder k has time to reevaluate her valuation to vk2 and bid bk2. Suppose bidder k bids bk2 at tk=T. If bk2 > bi*, then bidder i loses the auction and receives a profit of zero. If bk2 ≤ bi*, then bidder i still wins the auction but pays bk2+ε > bk*+ε . In either case, bidder i is worse off than when a bid was placed at ti=T. eBay Auction for a marginally available commodity with a private value: Theorem 3: As the probability, Pa, that a commodity is available in another auction decreases, where each of the i=1…n bidders has a private valuation, vi∈ [0,V], more bidders in an auction have an optimal strategy to bid bi* at time ti=T. 6
  • 9. Proof: Bidder i places a bid of bi* at time ti<T. Consider bidder j’s best response. If bj* ≤ bi*, whether bidder j abandons the current auction and bids in another depends on Pa. The expected profit at another auction with bid of bj* is Pa(Pjwin(bj*,vm)(vj – bj*)). The expected profit at current auction with bid of bj2 > bi* > bj* is Pjwin(bj2,vm)(vj –bj2). Bidder j abandons the current auction when Pa(Pjwin(bj*,vm)(vj – bj*)) > Pjwin(bj2,vm)(vj – bj2). ˆ There exists some critical value Pja for bidder j such that: ˆ Pja (Pjwin(bj*,vm)( vj – bj*)) = Pjwin(bj2,vm)(vj – bj2). ˆ If Pa< Pja , then bidder j reevaluate her valuation to vj2 and bids bj2. Suppose bidder j bids bj2 at tj=T. If bj2 > bi*, then bidder i loses the auction and receives a profit of zero. If bj2 ≤ bi*, then bidder i still wins the auction but pays bj2+ε > bj*+ε. In either case, bidder i is worse off than if bi* was placed at ti=T. As Pa →0, it is more likely that some bidder j will reevaluate her valuation and bid again. Thus as Pa →0, it becomes increasingly more important for bidder i to bid at ti=T. 3. Data The theoretical results were tested by examining eBay auctions from three distinct categories: consumer electronics, family-signed and dated Longaberger baskets, and 7
  • 10. dated Longaberger baskets. Auctions were selected at random from May through December of 2001. An auction was included if it had at least three bids. The consumer electronics auctions were collected to represent widely available goods with a common market price. Data from 100 auctions with a total of 1,460 bids were collected on auctions for brand new digital cameras, DVD players, and CD players. All of the goods were widely available on eBay at the time of the auction and were also available at both CircuitCity.com and Amazon.com. Each of the goods had a common market price at both internet retailers. The Longaberger basket auctions were collected to represent less available goods with unknown values. The Longaberger Company, located in Dresden, Ohio, manufactures collectible baskets in many different styles. The baskets are not sold in stores. Instead, they are sold through sales consultants who hold “home shows” in customers’ houses similar to the “Tupperware Party”. The baskets are marked and dated by the weaver, and only current year baskets are available from Longaberger sales consultants. Dated baskets are sold in secondary markets at antique and craft shops, but since its inception eBay has captured much of this secondary market. eBay offers sellers a worldwide consumer base. A search for “Longaberger basket” on eBay will generate over 3,000 auctions on any given day. Members of the Longaberger family sign baskets made by their company during factory tours. A very limited number of family-signed baskets are available on eBay. A search for “signed or autographed Longaberger basket” will generate about 30 auctions on any given day. Given the numerous styles of baskets, finding a specific basket with signatures made in a certain year can be difficult. 8
  • 11. The family-signed and dated Longaberger basket auctions were collected to represent scarce goods with unknown values. Data from 100 auctions of this type with a total of 1,174 bids were gathered. Each of the 100 baskets being auctioned off was unique. eBay did not have another basket like each of these during a thirty-day period before and after the auction was completed. Unsigned and dated Longaberger basket auctions were collected to represent goods in between the previous two categories. A group of 100 auctions with a total of 1,167 bids were collected. These baskets are available on a small scale and prices are known to vary within a specific range. A price guide is available (Bentley Guide) that details the range of prices found for any particular dated basket. 4. Results Theorems 1 through 3 suggest that bidders are more concerned with bidding at the end of an auction the more a commodity is scarce and has an unknown value. Examining the distribution of bids for each of the three categories of goods indicates that bidders tended to bid closer to the end of the auction for scarce goods. Figure 2 shows the distribution of bids over each 10% period in the auction. In the final 10% of the time remaining in the consumer electronics auctions, 24.8% of the bids were entered. In the final 10% of the dated Longaberger basket auctions, 36.7% of the bids were entered. In the final 10% of the family-signed and dated Longaberger basket auctions, over half (51.9%) of the bids were placed during this late stage of the auction. [Insert Figure 2 here] 9
  • 12. The difference in the distribution of bids appears to indicate that bidders are bidding optimally as the Theorems suggest they should. Although over half of the bidders for the family-signed baskets place their bids in the final 10% of the auction, most are not using the optimal “snipe” strategy. Closer inspection of the bids indicates this. The final 10% of a seven-day auction is a 16 hour 48 minute period. Bidding with 16 hours to remain certainly provides other bidders ample time to reevaluate their valuations and to place another bid. Figure 3 illustrates the percentage of bids that were placed in the final 60, 5, and 1 minute periods. The pattern of bidding remains; bidders tended to place their bids later in the auction the scarcer the commodity. However, very few bids were placed in true “snipe” fashion during the final minute of the auction. [Insert Figure 3 here] A LOGIT regression was employed to gain a better understanding of what determines whether a bidder places a bid during the final minutes of an auction. The dependent variable LESS5 is a dummy variable with a value of 1 when a bid was placed in the final five minutes in the auction and 0 otherwise. A bidder using the “snipe” strategy optimally will bid only once during the final minutes of the auction. The independent variable ONEBID is a dummy variable that has a value of 1 when a bid is the only one placed by a bidder and has the value of 0 when a bid is one of two or more placed by the same bidder. The theory indicates that the “snipe” strategy becomes more necessary as the commodity is increasingly scarce. Although bidders in the consumer electronics auctions could place an optimal single bid at any time during the auction, they are no worse off by placing these bids at the end of the auction. The ONEBID variable tests to see whether single bids are more likely to 10
  • 13. placed in the final five minutes. The a priori hypothesis is that single bids will be more likely to be placed in the final minutes as “snipe” bids. Experience may also dictate whether a bidder has learned that bidding at the end of an auction is optimal. When a bidder places a bid, eBay reports the bidder’s feedback rating. Every time a bidder participates in an eBay transaction, the other party may offer positive, neutral, or negative feedback. The rating is an accumulation of positive reports from other eBay members. eBay deems a bidder “experienced” when the bidder achieves 10 feedback points. The independent variable EXP10 is a dummy variable that has a value of 1 when a bidder has 10 or more feedback points and 0 otherwise. Again, the a priori hypothesis is that bids in the final five minutes will be more likely placed by experienced bidders. A bidder will be more likely to bid at the end of an auction if the auction ends at a convenient time. The dummy variables DAYTIME and WEEKEND were defined to represent convenient auction ending times. The DAYTIME variable has a value of 1 when an auction ends between nine o’clock in the morning and midnight Eastern Standard Time and a 0 otherwise. The buyers and sellers in the auctions were all from the United States, so the DAYTIME variable represents daytime on the west coast as six o’clock in the morning to nine o’clock in the evening. The WEEKEND variable has a value of 1 when an auction ends from Friday at midnight to Sunday at midnight on the east coast. Finally, two independent dummy variables were created to represent the type of good on the auction block. The SLONG variable has a value of 1 when the bid was for a family-signed Longaberger basket and a 0 otherwise. The LONG variable has a value of 11
  • 14. 1 when the bid was placed for a regular dated Longaberger basket and a 0 otherwise. The a priori hypothesis is that bidders will be more likely to bid in the final five minutes for a dated Longaberger basket and even more likely to do so for a family-signed basket. The output of the multinomial logit model is illustrated in Table 1. The model is statistically significant with p<0.0000. Bidder experience and a convenient auction ending time had no statistically significant effect on whether a bidder placed a bid in the final five minutes. However, the type of good on the auction block did have a statistically significant effect. A bidder placing a bid in the final five minutes is 1.5 times more likely to be placing the bid on a dated Longaberger basket than a consumer electronics good. A bidder placing a bid in the final five minutes is 1.8 times more likely to be placing the bid on a family-signed and dated Longaberger basket than a consumer electronics good. Finally, a surprising result is that the ONEBID variable is statistically significant with a negative coefficient. Bidders that bid only one time during an auction are 1.6 times less likely to bid in the final five minutes. Table 1: Logit results – characteristics in numerator of Prob[LESS5=1] Variable Coefficient P-value Constant -3.32 0.0000 ONEBID -0.47 0.0008 EXP10 0.17 0.2024 DAYTIME 0.53 0.1483 WEEKEND -0.40 0.8109 LONG 0.40 0.0184 SLONG 0.58 0.0006 12
  • 15. 5. Discussion and Conclusion Bidders tend to bid closer to the end of an auction the scarcer the good. However, most bidders on eBay do not bid optimally by bidding only one time. Even those bidders that do bid at the end of the auction tend to bid with enough time left to enter a bidding war with other bidders. A closer examination of the bids placed in the final five minutes reveals that the majority of the bids are not placed optimally. As Figure 4 indicates, 68% of the bids placed in the final five minutes are from bidders who bid multiple times during the auction. Only 27% of the bids were placed as a “snipe” in the final five minutes. An additional 5% of the bids were also placed optimal “snipe” bids even though the bidders placed two bids. Often a bidder will purposely place a very small bid when they first discover an auction in order to keep track of the auction. eBay provides a summary screen of auctions that each bidder has participated in. Many bidders place a low bid to put the auction on their “radar” screen and then implement an optimal “snipe” bid in the final seconds of the auction. [Insert Figure 4 here] Only about one-third of the last minute bidders were actually bidding optimally. Most bidders do not use an optimal bidding strategy and they treat eBay as if it was an open outcry auction. The timed ending of the eBay auction causes it to be a second-price sealed auction in the final seconds. Bidders should wait until the end to bid and not reveal their maximum valuation until then. Other bidders will not have an opportunity to reevaluate their maximum willingness to pay and raise the bid price. 13
  • 16. In the auctions examined for this paper 10% of the consumer electronics auction winners, 15% of the dated Longaberger basket auction winners, and 5% of the family- signed and dated Longaberger basket auction winners overpaid by bidding too early. Other bidders had a chance to respond to the winner’s early bid and ratchet up the bid price. For the less scarce goods, bidders are looking to make a specific profit. They wish to pay a specific amount below their maximum valuation. If the bid price exceeds this amount, the bidders move on to another auction. So these bidders may not be concerned that the amount they actually pay as long as they get the profit they intended. Bidders should also be wary that sellers on eBay have hired shill bidders to increase the bid price. Although the practice is illegal and eBay has prosecuted a few cases, it is difficult to regulate. Bidders should simply bid at the very end and not give shill bidders an opportunity to raise the price. The damage to early winning bidders increased significantly as the item up for bids became scarcer. Consumer electronics winners overpaid an average 8.5% more than they needed to. Dated Longaberger basket winners overpaid an average 15.4%, and family-signed basket winners overpaid an average 20.1%. The message is simple: bid late or pay great! 14
  • 17. References Bajari, Patrick and Ali Hortacsu. 2000. “Winner’s Curse, Reserve Prices and Endogenous Entry: Empirical Insights from eBay Auctions.” Working Paper, Stanford University. Fershtman, Chaim and Daniel Seidmann. “Deadline Effects and Inefficient Delay in Bargaining with Endogenous Commitment.” Journal of Economic Theory, August 1993, 60(2), 306-321. Harstad, Ronald M., “Alternative Common Value Auction Procedures: Revenue Comparisons with Free Entry,” Journal of Political Economy, 1990, 98, pp. 421-429. Hendricks, K., and Paarsch, H., “A Survey of Recent Empirical Work Concerning Auctions,” Canadian Journal of Economics, 1995, 28, pp. 403-426 Levin, Dan and James Smith. “Equilibrium in Auctions with Entry.” American Economic Review, June 1994, 84 (3), 585-99. Lucking-Reiley, David. “Using Field Experiments to Test Equivalence Between Auction Formats: Magic on the Internet.” American Economic Review, December 1999, 89 (5), pp. 1063-80. Malhotra, Deepak, and Murnighan, J.K., “Milked for all Their Worth: Competitive Arousal and Escalation in the Chicago Cow Auctions,” working paper, Kellogg School of Management, Northwestern University, April 2000. McAfee, R. Preston, “Mechanism Design by Competing Sellers,” Econometrica, 1993, 61, pp. 1281-1312. Milgrom, P and Weber, R.J. (1982). A Theory of Auctions and Competitive Bidding. Econometrica, 50, pp. 1089-1122. Myerson, Roger, B., “Optimal Auction Design,” Mathematics of Operation Research, 1981, 6, pp. 58-73. Roth, Alvin E., Murnighan, J.K., and Schoumaker, F. “The Deadline Effect in Bargaining: Some Experimental Evidence,” American Economic Review, September 1988, 78(4), pp. 806-23. Roth, Alvin, E., and Ockenfels, Axel, “Last Minute Bidding and the Rules for Ending Second-Price Auctions: Theory and Evidence from a Natural Experiment on the Internet,” June 2000. Working paper, Harvard University. 15
  • 18. Roth, Alvin E., and Xing, Xiaolin. “Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions,” American Economic Review, September 1994, 84, pp. 992-1044. Simpson, Glenn R. “eBay Coin Auctions Produce Allegations of ‘Shill’ Bidding,” Wall Street Journal, Monday, June 12, 2000, A3, A6. Wilcox, Ronald T. “Experts and Amateurs: The Role of Experience in Internet Auctions,” Marketing Letters, 2000. Forthcoming. 16
  • 19. Figure 1 Figure 1a: Cumulative Probability Density Function (Piwin(bi,vm)) 1 P1win(b1,vm) Probability of winning bid P2win(b2,vm) 0 V bid bi Figure 1b: Actual Profit (p - bi) V Profit 0 V bid bi Figure 1c: Expected Profit V P1win(b1,vm)( p – b1) Expected Profit P2win(b2,vm)( p – b2) 0 b1* b2* V bid bi
  • 20. Figure 2 Distribution of Bid Timing 60% Consumer Electronics Longaberger Baskets Signed Longaberger Baskets 50% 40% % of total bids 30% 20% 10% 0% 100-90 90-80 80-70 70-60 60-50 50-40 40-30 30-20 20-10 10-0 % of Time Remaining in Auction
  • 21. Figure 3 Bidding in the Final Minutes 25% 21.72% Consumer Electronics 20% 17.40% Longaberger Baskets % of total bids 15% Signed Longaberger Baskets 10.68% 10% 9.54% 8.05% 5.21% 5% 3.75% 2.67% 2.74% 0% Last 60 minutes Last 5 minutes Last 1 minute
  • 22. Figure 4: Types of Bids in the Final Five Minutes Optimal 27% Bidding War 68% Radar 5%