Post on 05-Sep-2020
Are Snipers in Danger of Extinction?
By Xavier Del Pozo∗
November 14, 2013
Abstract
Sniping or last-minute bidding is a widely observed phenomenon in the onlineauction site eBay. As a consequence, a non-negligible amount of bids are neversent, nor do they arrive on time; causing both economic and efficiency losses.To eliminate sniping, employing a second-price (descending) Dutch mechanismcan be considered as an alternative to eBay’s. Hence, these two auction types:a second-price Dutch, and one replicating eBay’s are tested in the laboratory.The Dutch format exhibits slightly higher levels of efficiency, whereas in eBaysniping increases the amount of inefficient outcomes. In both formats, morethan half of the bids are close to the predicted value. However, overbidding ismore prevalent in the Dutch mechanism. Selling prices are higher under theDutch format, but not significantly different from the expected ones. Hence,adopting this mechanism could potentially benefit the auction house due to theincrease in fees.
Keywords: experiment, sniping, eBay, second-price Dutch auction
JEL classification: C90, D44
∗Del Pozo: ESEI Center for Market Design, University of Zurich, Switzerland(xavier.del.pozo@esei.ch). I would like to thank the Swiss National Science Foundation (SNSF138162) and the European Research Council (ERC Advanced Investigator Grant, ESEI-249433)for financial support. I gratefully acknowledge helpful conversations on this subject with GiovanniPonti, Isabel del Pozo, Adam Sanjurjo, Marcello Sartarelli, and comments from audiences at thefollowing universities and conferences: Alicante, Valencia, Zurich, SAEe Vigo and IMEBE Madrid.For the latest version, please check: https://sites.google.com/site/xavierdelpozo/research
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1 Introduction
The spread of internet access during the 90s allowed many online auction sites to
flourish in a short period of time. eBay started running auctions in 1995. Despite
tough competition, eBay became the market leader in online consumer auctions.1
As of 2011, eBay had more than 100 million active users and the total amount of
goods sold was $68.6 billion.2 eBay runs second-price (ascending) auctions, employing
a proxy bidding mechanism, with a fixed deadline. The bidder provides the proxy
with his reservation price. Every time a higher bid arrives, the proxy counter-bids
on his behalf and it secures him having the highest bid. The bidder with the highest
reservation price wins the auction and pays a final price equal to the second highest
reservation price plus a small increment.3
Evidence from eBay auctions on computers and antiques shows that around half of
all last bids are received in the last 5 minutes, and even 10-percent arrives within the
last 10 seconds before the auction ends.4 Moreover, the more experienced the bidder
is, the later he submits the bid (Roth and Ockenfels 2002). This type of bidding
behavior is commonly referred as “sniping”.
Bajari and Hortacsu (2004) review different hypotheses, advanced by several au-
thors, for the late bidding behavior. First, to avoid bidding wars with naıve bidders
(Ariely, Ockenfels and Roth 2005, Ockenfels and Roth 2006). Second, to prevent dis-
closing private information to other bidders (Bajari and Hortacsu 2003, Ockenfels and
Roth 2006). Third, when identical items are being auctioned simultaneously, earlier
bidding in an auction can induce an increase in expected price on all of them (Wang
2006, Peters and Severinov 1997). Fourth, when bidders experience uncertainty about
their own private valuation, late-bidding is preferred to the searching costs of inferring
1For a survey comparing different online auction sites for the period 1998-99 refer to Lucking-Reiley (2000).
2Retrieved November 18th, 2012, from www.ebayinc.com/who.3The size of the increment depends on the amount of the second highest reservation price. The
higher the latter, the larger the size of the increment.4Ockenfels and Roth (2006) confirm these findings in a second study on eBay auctions. Bajari
and Hortacsu (2004) find similar late bidding patterns in coin auctions.
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the selling price of similar items previously listed (Rasmusen 2006, Hossain 2008). At
the same time, Ely and Hossain (2009) show that the reduction in the final price
pursued by snipers is on average economically insignificant.5
Irrespective of motive, sniping is a common occurrence. As a result, the auction’s
winner may not necessarily be the bidder with the highest valuation, implying an
inefficient outcome and loss of revenue for the auctioneer. Roth and Ockenfels (2002)
find in a survey that around 10% of the time snipers could not submit their bids. Two
main reasons were cited. First, other activities impeded snipers submitting a late bid.
Second, slow or irregular internet traffic prevented bids reaching eBay on time.
The second-price (descending) Dutch auction posits an alternative to eBay’s auc-
tion format. Vickrey (1961) already suggested this mechanism. The author noted
the strategic equivalence between the second-price Dutch and the second-price sealed
bid auctions where bidding one’s own private valuation remains the weakly dominant
strategy. Under the Dutch modality, there exists no incentive to snipe. Submitted
bids cannot be observed by rival bidders during the course of an auction. Currently,
there are neither experimental studies testing the performance of second-price Dutch
auctions, nor companies or institutions implementing this mechanism.
For this purpose, a laboratory experiment is an ideal environment that allows for
control of other variables such as number of bidders or induced private values. Hence,
in this chapter I compare through a laboratory experiment the two auction formats
described in detail below:
• Second-price Dutch auction: also known as descending or reverse clock auction.
The price descends until two bidders accept a price indicated on the clock.
The bidder accepting the highest price wins the auction. But he only pays the
price accepted by the second bidder. Bidders receive no information on bidding
activity during the auction.
• eBay auction: or second-price (ascending) auction with a proxy bidding mech-
5Gray and Reiley (2004) also find a lower, but statistically insignificant, final price when a par-ticular bidder snipes.
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anism.6 New bids must be higher than the current highest bid and can be
submitted until a fixed deadline. Information on current highest bid and its
bidder is always publicly available.
Albeit both auction formats are second-price based, their rules, beside the descend-
ing/ascending mechanism, make them qualitatively different. For instance, available
information on previous bidding activity differs completely. Nevertheless, there are
important reasons to select these two formats for comparison. First, to establish if
there are differences in bidding behavior, if any, between the second-price Dutch and
experimental evidence of its strategic equivalent, the second-price sealed bid auction.
Second, to determine empirically whether the second-price Dutch posits an alterna-
tive to eBay’s format by performing a comparison in terms of efficiency, prices and
bidders’ earnings.
Previous theoretical works analyzing eBay auctions include Ockenfels and Roth
(2006). The authors model an internet auction where late bids have some probability
of not being transmitted correctly. They prove that bidders may not have a dominant
strategy in this scenario. Nonetheless, sniping can arise at equilibrium and as a best
response to avoid bidding wars.
With respect to laboratory experiments, Kagel and Levin (1993) find on second-
price sealed bid auctions that only a minority of bids (20-30%) are equal to their
private valuation. In contrast, overbidding (60-70% of all bids) seems to be the rule
rather than the exception. Apparently, the weakly dominant strategy is not suffi-
ciently transparent, and the learning feedback to correct the overbidding behavior is
weak. Research on Dutch auctions focuses on the first-price Dutch and its strate-
gic equivalence with the first-price sealed bid auction. Coppinger, Smith and Titus
(1980) and Cox, Roberson and Smith (1982) conclude that prices are lower in the
Dutch format but still above the risk neutral Nash equilibrium. Continuing the study
of first-price Dutch auctions, Katok and Kwasnica (2008) study the effect of clock
6In eBay, when a bid is submitted, providing the proxy bidding mechanism with your reservationprice was optional. Recently, eBay modified the bidding rules. Now, bidders submit exclusively thereservation price.
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speed on bidding behavior. The use of fast clocks results in significantly lower prices
than those of a first-price sealed bid. In contrast, a significant reduction in the clock
speed leads to a price increase. Thus, bidders avoid incurring in the opportunity costs
induced by waiting and prefer to pay higher prices. Katok and Kwasnica’s result seem
to corroborate what Lucking-Reiley (1999) reported earlier in his field experiment on
auctioning cards over the internet. By using a extremely slow clock, (first-price) Dutch
auctions yield higher revenues than any other auction mechanism.
The results of my experiment show that, 57% of all bids in the second-price Dutch,
and 49% in the eBay treatment, are very close to the private value. Overbidding is
more prevalent in the Dutch format but still clearly lower than in previous experiments
on second-price sealed bid auctions. However, it does not translate in higher prices.
On the contrary, selling prices are not significantly different from the expected ones
while they are significantly higher than those in eBay auctions. Time distribution of
bidding activity on the eBay treatment corroborates the sniping behavior hypothesis.
Some 20% of all last bids are received within the last 5 seconds before the auction ends.
Moreover, winning bids submitted in that interval lead to an increase on inefficient
outcomes, compared with those winning bids sent before. Efficiency levels attained
in the Dutch auctions are almost always higher, though they are not significantly
different from eBay’s treatment.
The rest of the chapter continues as follows: Section 2 derives the theoretical
predictions regarding bidding behavior, while Section 3 describes the experimental
design. Results are shown in Section 4 and Section 5 concludes.
2 Theoretical Predictions
Consider an Independent Private Value auction. Two bidders compete for a single
unit. Each bidder’s induced private value v is drawn independently from the same
uniform distribution [v, v].
It is well documented in the literature that to bid your own private value b(v) = v
in second-price sealed bid auctions is a weakly dominant strategy (Vickrey 1961).
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This holds independently of the bidder’s attitude towards risk.
Second-Price Dutch Auction
Recall that, prior to submitting a bid, a bidder cannot infer whether there is ongoing
bidding activity or if any other bidder has already accepted the price on the clock.
Hence, a bidder’s decision is strategically equivalent to that of a second-price sealed
bid auction. Consequently, to bid one’s own private value is still a weakly dominant
strategy:
b2Dutch(v) = v
eBay Auction
eBay employs a proxy bidding mechanism. When a bid is submitted (as in a first-price
ascending auction), a bidder also has to indicate his reservation price or maximum
willingness to pay for the object. As subsequent bids from other contestants arrive,
the proxy mechanism rises his bid just to surpass by a minimum increment the last
bid received.7
Bidders can submit multiple bids during an auction. Strategies that involve bid-
dding above one’s own private value are weakly dominated. As opposed to second-
price sealed bid auctions, Ockenfels and Roth (2006), modelling an internet auction
in discrete time, prove that bidders may not have a dominant strategy in eBay. Nev-
ertheless, in my design, submitting one’s private value (as the reservation price) is
a weakly dominant strategy when sniping.8,9 Incremental bidding is also a plausible
7If the reservation prices of two bids submitted are equal, the bidder, whose bid arrived earlier,holds the highest bid. In this particular case, the price is equal to both reservation prices (withoutany increment above the lowest reservation price).
8When a bidder snipes, it is assumed that the contestant has no time for a counter-bid.9In Ockenfels and Roth (2006)’s model, it is not a weakly dominant strategy. A bidder wants
to avoid paying the whole minimum increment by bidding slightly above the contestant’s bid. Forinstance, if the contestant bids 10, a bidder is better off bidding (as his reservation price) 10.1 than20 (his private value). In the former, the final price is 10.1 while in the latter 10 plus 1 (the minimumincrement). This case is excluded in my design. Bidders are only allowed to bid integer values (seeSection 3).
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scenario. Inexperience or naıve bidders pursue to have the highest bid as in an English
auction. Hence, bids (for the reservation price) should not exceed the private value:
beBay(v) ≤ v
3 Experimental Design
Two subjects participate in each auction. Both participants bid for a single unit of a
fictitious object. The higher bidder’s profit is equal his private valuation minus the
price paid for the object. The lower bidder obtains a zero profit.
Private values, v, are randomly and independently drawn for each bidder in each
auction round. Values are generated from a uniform distribution on the interval
[1, 100]. Bids are restricted to integer values on the previous interval range. After each
auction, bidders are informed about the winner, the price paid and their individual
and accumulated profits so far. The lower bidder cannot thereby infer the highest
bid.10
Within a cohort of 4 bidders, pairs of bidders are randomly rematched after each
auction played. Hence, it is guaranteed that each bidder plays with a different con-
testant in two consecutive auctions. Participants are informed about this.11
Subjects are assigned an initial capital to cover possible losses. Rational bidders
playing the dominant strategy do not incur in losses. However, it is not unusual
in second-price auctions to observe bidding above one’s own private value. This
bidding behavior may lead to negative profits.12 The profit (or loss) in each auction
round is accumulated and added up to (or subtracted from) the initial capital. The
instructions remind participants that a bidding strategy leading to no losses is a
possible outcome.13 In case of bankruptcy, participants can no longer continue the
10The only exception arises when both bidders submit the same bid.11Instructions point out explicitly that the contestant in two consecutive auctions is always a
different person. However, they can infer that they would face the same contestant at some point.The number of participants in each session is lower than the number of auctions played.
12Refer to Kagel, Harstad and Levin (1987) or Kagel and Levin (1993).13Examples in the instructions and cases in the questionnaires covered all possible scenarios: pos-
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experiment. They are asked to leave the room.
All auctions are subject to two treatments: Second-price Dutch auction or eBay’s.
Second-Price Dutch Auction (2Dutch)
The mechanism explained here follows Vickrey (1961)’s description on how one can
take advantage of the (first-price) Dutch format to convert it into a second-price one.
That is, the clock does not stop at the first bid submitted as it occurs in the first-price
Dutch auction. It only stops when the second bidder submits his price-determining
bid.
More specifically, the auction starts with the clock at a price of 100 points and it
descends at a rate of 1 point per second.14 When the higher bidder stops the clock, he
becomes the winner. He alone is informed about this event. Nonetheless, the auction
continues normally for the other bidder. Only when the latter stops the clock, thereby
setting the price, the auction ends. The final price is equal to the lower bid plus one
point. If both bids are the same, a lottery decides the winner and the price is set
equal to both bids.15 If only one bid is submitted, the bidder wins the auction and
pays a price of 1 point. In the absence of bids, there is no winner.
Figure 1 shows a screenshot of the computer interface. The price clock is displayed
on the top left. Bidders can observe their private value and last bid on the top
right. They can stop the clock using the button on the bottom left of the screen.
Alternatively, pressing the button on the right, bidders opt to preselect at which price
to stop the clock. This preselected bid price can be modified as long as the clock
has not reached that preselected price. Bidders are given 10 seconds before the clock
starts to descend. Thus, they have enough time to observe their private value and
make their decision.
In the experiment, when the lower bidder stops the clock, therefore ending the
itive, negative and no profit.14According to Katok and Kwasnica (2008) this speed rate falls into the category of fast clocks.
Similar speed rates, around 1% per second, have been employed by Cox, Smith and Walker (1983)in (first-price) Dutch auctions.
15It is only in this situation that the lower bidder can infer the winner’s bid.
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Figure 1: Screenshot of a Second-Price Dutch Auction
auction, the two bidders involved in it saw a waiting screen on their display. Only when
all auctions (running simultaneously) finished, did they proceed to the results screen.
Thus, there did not exist an incentive to shorten the auction, nor the experiment
duration by stopping the clock earlier. On average, 2Dutch lasted as long as eBay
auctions.
eBay Auction (eBay)
On the online eBay, it is optional to provide the proxy with a reservation price.16 In
this treatment, to make the mechanism equivalent to that of a second-price auction, it
is obligatory to provide the reservation price when submitting a bid. Hence, bidders
have to submit two values when bidding: a normal bid, and their reservation price for
the object. With the latter value, the proxy bids on the bidders’ behalf when being
16Now, bids on eBay are just one value, the reservation price, and the proxy bids on behalf of thebidder according to this value.
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Figure 2: Screenshot of an eBay Auction
outbid. It beats the current highest bid by an increment of one point.
The normal bid has to be higher than the current highest bid, while the reservation
price has to be at least equal to the normal bid. Bidders can modify their last bid as
long as both values are higher than their last two values submitted and higher than
the current highest bid.
Auctions last 100 seconds. Bids are only accepted during this time. Bidders are
therefore provided enough time to engage in different bidding strategies.
The screenshot of the computer interface, shown in Figure 2 basically differs from
the 2Dutch in the specific information displayed in each treatment. On the top left
part, subjects watch the remaining time of the auction, the current highest bid and
its bidder. If the other contestant is the highest bidder, a red color is used. This
facilitates the subject identify when he is not holding the highest bid. The top right
part shows the private value and his last bid. In the bottom part, bidders type in
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the two entry masks their normal bid and reservation price. They submit a bid by
pressing the button underneath.
Procedure
The study was conducted in July 2012 with 12 cohorts of 4 participants at the Labora-
tory for Theoretical and Experimental Economics of the University of Alicante. Four
sessions were run and each session lasted around 90 minutes on average.17 Participants
were undergraduate students from different disciplines.
The experiment run using the z-Tree software (Fischbacher 2007). During an
auction, participants could see private and public information. Final profits were ex-
changed at a rate of 3e per 100 points. No show-up fee was paid. Instead, participants
received an initial capital of 6e (or 200 points in the experimental currency unit).18
Two participants in the same cohort went bankrupt at different points of the ex-
periment. Data from that cohort was excluded in the posterior analysis. The average
payoff was 13.97e, being 7.6 and 20.6e the minimum and maximum amounts.19
Each participant played 26 auctions divided into two phases. Both phases consisted
of 3 training or test auctions followed by 10 payoff-relevant auctions. Participants were
informed that the only difference between phases was the auction rules. The training
rounds were meant for participants to familiarise themselves with the software and
auction rules. Six cohorts played the eBay treatment in the first phase and the 2Dutch
in the second. The remaining six cohorts played the treatments in the reversed order,
2Dutch first and eBay last. The same set of independently generated private values is
employed for each of the two groupings of six cohorts, i.e. two given cohorts playing
treatments in different order are matched with respect to bidders’ private values (Cox
et al. 1982). In this manner, posterior statistical comparisons are more robust and
differences are not just driven by some bias due to the small sample of private values.
17Each session consists of 3 cohorts of 4 participants.18The initial capital amount was higher than the usual show-up fee paid in similar experiments at
the laboratory.19The cohort involved in the bankruptcy was not included in these calculations.
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The order of play was the following: First, the instructions common to both
phases were handed out and read aloud.20 Next, the instructions of phase one were
distributed, read aloud and the auctions played. Finally, the instructions of phase
one were collected, while those of phase two were handed out, read aloud and the
auctions played subsequently. Additionally, participants had to respond correctly to
a questionnaire in the eBay treatment to ensure they understood the mechanism cor-
rectly. In the 2Dutch treatment it was not considered necessary due to its considerably
simpler rules.
4 Results
This section presents the results of the statistical analysis based on the theoretical
predictions described in Section 2. Bidding behavior is analyzed with respect to
bidders’ own private valuations. Specifically, from the data generated in the eBay
treatment, the last bid submitted by each bidder is used. From the two values in each
eBay bid, the reservation price provided for the proxy mechanism is the relevant value
for the theoretical predictions and computations.
If not specified otherwise, the non-parametric Wilcoxon-Mann-Whitney U-test for
comparisons between treatments is employed. For comparisons within treatments,
the non-parametric Wilcoxon signed-rank test is used. Both tests are always based on
aggregated data within a cohort. Data aggregation depends upon the interval used
in the comparison; for instance, all rounds, first or last five rounds, etc. All tests are
two-tailed unless otherwise specified.
There exists no evidence of an order effect in bidding activity (U-test, p=.855
for 2Dutch and p=.273 for eBay). Consequently, bidding observations in the second
phase are considered independent as well. The data from the same treatment in both
phases is therefore pooled together. Posterior tests of null hypotheses are based on
11 independent statistical observations, one from each cohort.
In the two treatments, bidding patterns are fairly robust, so that their bidding dis-
20A copy of the instructions in both treatments can be found in Appendix A.
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020
4060
8010
0Bi
d
0 20 40 60 80 100Private Value
(a) 2Dutch - Rounds 1-5
020
4060
8010
0Bi
d0 20 40 60 80 100
Private Value
(b) 2Dutch - Rounds 6-10
020
4060
8010
0Bi
d
0 20 40 60 80 100Private Value
(c) eBay - Rounds 1-5
020
4060
8010
0Bi
d
0 20 40 60 80 100Private Value
(d) eBay - Rounds 6-10
Figure 3: Bidding Distribution
tributions are similar irrespective of the order of play. The effect seems to be stronger
in the 2Dutch. This result hints at strong bidding incentives in both mechanisms.
Exposure to a different auction format does not seem to alter bidding behavior.
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Rounds b = v b = v ± 1 b > v + 1 b < v + 1
1-5 28.6 55.5 20.9 23.62Dutch 6-10 32 58.9 28.8 12.3
All 30.3 57.2 24.8 18
1-5 20.4 42.7 17.5 39.8eBay 6-10 29.1 55.4 6.1 38.5
All 24.8 49.2 11.7 39.1
Table 1: Percentages of Bidding Distribution
Bidding Behavior
The scatter diagrams in Figure 3 provide a first glance at bidding behavior, sorted
by treatment and first and last 5 rounds. The dots refer to the submitted bids. Bids
on the 45-degree line coincide with participants’ own private value. Underbidding
(overbidding), defined as bidding under (above) own private value, is represented by
the dots below (above) the line. Irrespective of the mechanism, an overwhelming
majority of bids are on or very close to the 45-degree line, especially in the last five
rounds. Nonetheless, bidding values on eBay seem to be more widespread. Comparing
the diagrams of the first and last five rounds, there exists a clear change in bidding
behavior. In 2Dutch, though in the second five rounds bid values cluster even closer
to the prediction line, there are a few outbidding outliers. In eBay, overbidding
is exclusively present in the first five rounds and vanishes thereafter. In contrast,
underbidding becomes a persistent behavior, common in all rounds.
Table 1 illustrates the bidding distribution with respect to the private value. In
2Dutch and eBay, 30% and 25% of all bids are equal to the private value, respectively.
If bids located one point above and below the valuation line are included, then, the
proportion of bids following this strategy increases considerably to 57% and 49%,
respectively.
The largest difference across treatments is characterised by the divergence in the
under- and overbidding behavior. Overbidding in 2Dutch is higher by some 13%,
whereas the percentage difference in underbidding is 21% in favour of eBay. These
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differences become even larger when looking at the last 5 rounds. To confirm this
difference, the null hypothesis that bidding across treatments is equal for all and the
last five rounds is rejected (p=.0197 and p=.0012, respectively).21 Kagel and Levin
(1993) report similar distributions in second-price sealed bid auctions; 27% of all bids
play the weakly dominant strategy (b = v). However, overbidding, which occurs in
67% of all bids, is much larger than in 2Dutch auctions.22
In eBay, underbidding is more frequent, as expected. The two main motives
leading to the 39.1% of underbids are the following. First, the winning bidder (17.4%
of all bids) does not need to raise his bid because the current price is already higher
than his contestant’s private value. Hence, the latter has no incentive to counter-bid.
Second, a sniper (6% of all bids) wins the auction in the last seconds, leaving no time
to the contestant to react and place a counter-bid.
Bidding Dynamics
From the graphs in Figure 3 and the data in Table 1, it is observed that bidders
modify the strategies as they experience a learning effect. Comparing the first and
last five rounds within each treatment shows that bidding is significantly different in
2Dutch but not in eBay (p=.016 and p=.286, respectively).
Figure 4(a),(b) and (c) illustrate the evolution of the bidding activity. Figure
4(a) suggests that the dominant strategy is chosen more often in 2Dutch, irrespective
of the measure and round taken.23 Nonetheless, this difference is not statistically
significant.24 In eBay, selecting the dominant strategy increases significantly between
the first and last five rounds (p=.0099).25 Apparently, while the incentive to bid your
valuation in 2Dutch is clear from the beginning, subjects in eBay need some time to
21Kagel and Levin (1993) use a χ2-test to observe differences in bidding distributions. In my case,this test also confirms that the 2Dutch bid distribution is skewed to the right of the eBay distribution(p=.000 for all rounds and p=.000 for the last 5 rounds).
22Kagel and Levin define overbidding in their analysis as b > v. Nevertheless, considering thelatter definition, overbidding in 2Dutch increases marginally from 25% to 28%.
23Only in round 9, the percentage of bids playing b = v is lower in 2Dutch.24For all rounds: p=.5991 (b = v), p=.554 (b = v±1); and for last 5 rounds: p=.7671 and p=.8693,
respectively.25p=.0099 (b = v) and p=.0038 (b = v ± 1).
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0.1
.2.3
.4.5
.6.7
Perc
enta
ge
1 2 3 4 5 6 7 8 9 10Round
b=v, 2Dutch b=v, eBayb=v+/-1 b=v+/-1
(a) Expected Bidding
0.1
.2.3
.4.5
.6.7
Perc
enta
ge
1 2 3 4 5 6 7 8 9 10Round
b<v-1, 2Dutch b<v-1, eBay
(b) Underbidding
0.1
.2.3
.4.5
.6.7
Perc
enta
ge
1 2 3 4 5 6 7 8 9 10Round
b>v+1, 2Dutch b>v+1, eBay
(c) Overbidding
Figure 4: Bidding Dynamics
gain experience and learn this fact.
The evolution of under- and overbidding follow two different trends. In 2Dutch, the
percentage of underbidding decreases significantly (p=.0096), being 10% on average.
Hereby, it seems to set a change in the bidding activity, turning some under- into
overbidding. In eBay, overbidding decreases significantly too, some 10% and drops
to a mere 6% (p=.0713) on average. In contrast, it increases significantly in 2Dutch,
by 10% on average, and it represents almost one third of all bids in the last five
rounds.26 Nevertheless, 40% and 78% of all the overbids are at most within a 5 and
26Although the difference in overbidding between the first and last five rounds cannot be rejected(p=.1191), it can be rejected (p=.0238) using a different interval: for instance, first and last three
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0.0
2.0
4.0
6.0
8Pe
rcen
tage
100 90 80 70 60 50 40 30 20 10 0Remaining Time
(a) All bidders
0.0
2.0
4.0
6.0
8Pe
rcen
tage
100 90 80 70 60 50 40 30 20 10 0Remaining Time
(b) Winner
Figure 5: Time distribution of last bids submitted in eBay auctions
10-point range from the valuation, respectively. Overbidding occurs regularly in small
amounts. As suggested by Kagel and Levin (1993), it is possible that by raising their
bids above their private valuations, bidders naively believe in increasing their winning
probabilities without incurring any losses in return.
Time Distribution and Number of Bids
Figures 5(a) and (b) summarize the time distribution of last bids submitted by each
bidder and by the winner, respectively, in each eBay auction. In 5% of the cases, there
was no bid placed by one bidder.27 but at least one bid was submitted in all eBay
auctions. Figure 5(a) shows three clear timing patterns with respect to the submission
of last bid: the first 15 (left-hand side of graph) and last 10 seconds (right-hand side)
of an auction, and the time in between (middle part). 30% of all last bids were sent
in the first 15 seconds and 17% were close to the private value (b = v ± 1).28 This
evidence shows that several subjects were aware of the benefits of providing the proxy
agent with their reservation price, and letting him bid on their behalf up to their
private value. While several bids, 40%, are evenly spread between the first 15 seconds
and the last 10 seconds before the auction ends, a non-negligible amount of last bids
rounds.27One plausible reason is that in all 21 cases, except one of them, the price set by the contestant’s
first bid was already higher than the bidders’ private value.28It is equal to 9% considering bids exactly equal to the private value (b = v).
17
concentrate very close before the auction terminates. In the last 10 seconds 29% of
last bids are being submitted. Even 22% are found when narrowing down the time
interval just to the last 5 seconds. A clear hint of sniping behavior is that 10% of
all last bids are being sent in those last 5 seconds and after a 30-second period of
no bidding activity on their respective auctions.29 Ariely et al. (2005) report higher
percentages of sniping behavior, between 40 and 80% depending on the treatment.
However, in their experimental setup, the incentive to snipe was stronger,30. Subjects
also increased their experience because they played double the number of rounds than
in each of the two treatments of this experiment.
The time distribution of the winning bids, as shown in Figure 5(b), follows the
same trend as with all last bids. 31% of the winning bids were submitted at the
beginning of the auction, during the first 15 seconds, while another 22% of those
winning bids took place within the last 5 seconds. But winning an auction in the last
seconds bears consequences. Out of the 49 auctions whose winner was determined in
the last moments, 11 auctions (22%) had an inefficient outcome. The winner was not
the subject with the highest private value. This result contrasts strongly with the
time period before the last 5 seconds. In the 171 auctions decided before the last 5
seconds, only 19 auctions (11%) led to an inefficient outcome.
Regarding bidding activity on eBay, more than half of the auctions (65%) received
4 or less bids, 2 bids being the most frequent occurrence with 31%. 35% of the
auctions received 5 or more bids, which is more likely to occur in situations involving
incremental bidding or bidding wars.
In contrast, in 2Dutch auctions subjects hardly made any adjustment to their
bidding decision. In 77% of the cases subjects bid just once. They only modified
their first bid in 17% of the cases. Regarding the bidding method, the majority
(86%) programmed the proxy for stopping the clock at a preselected price. The other
29It increases to 12.89% or 14.08% if the no bidding activity period is 20 or 10 seconds instead.30The authors run auctions in discrete time using bidding periods. First, contestants had always
time to counter-bid in earlier periods but they could not do so in the last and final period of theauction. In one treatment, there was a small probability (20%) of the bid not being submittedcorrectly in the final period.
18
Dominant Overbid. Dom/Over. Underbid. Dom/Under. Other31
2Dutch 43.2 (19) 13.6 (6) 15.9 (7) 4.5 (2) 18.2 (8) 4.5 (2)eBay 25 (11) 0 (0) 6.8 (3) 15.9 (7) 36.4 (16) 15.9 (7)
Note: Absolute number of bidders in parentheses
Table 2: Player Type (in %) according to Bidding Behavior
Rounds 1-5 Rounds 6-10 All Rounds
eBay 81.48 91.67 86.572Dutch 90.65 93.52 92.09
Table 3: Percentage of Efficiency Distribution
bidding method, to bid the price currently displayed on the clock, was used 14% of
the occasions.
Individual Bidding Behavior
Type of bidders are identified according to their main bidding activity throughout
all auctions. In Table 2, bidders are assigned to each category if 80% of their bids
qualify for that condition. Bidders classified as Dominant, Over- or Underbidders are
not counted again in categories Dom/Overbid or Dom/Underbid.32
In 2Dutch, a high number of bidders, almost half of them, play constantly the
dominant strategy. Including those in the categories Dom/Over. and Dom/Under.
increases the percentage to 77.2%. There exists also a small share of participants that
overbid constantly. In contrast, the distribution in eBay looks quite different. The
largest amount of bidders belong to the category Dom/Under. or Dominant. Both
categories account for over 60% of all bidders. No overbidders are found in eBay in
contrast to 2Dutch.
19
.5.6
.7.8
.91
Percentage
1 2 3 4 5 6 7 8 9 10Round
2Dutch eBay
Figure 6: Average Efficiency
Efficiency
The outcome of an auction is efficient when the bidder with the highest valuation wins
the object. Independently of the price paid by the bidder, social welfare is maximized
when this occurs. Social welfare is defined as the sum of bidders’ and auctioneer’s
profit.
Table 3 shows average efficiency levels by auction type, while Figure 6 displays the
evolution of those levels. Overall, 2Dutch achieves the highest levels of efficiency, over
90%, and remains fairly constant. In contrast, eBay performs clearly much better
towards the end. Starting at 81%, it reaches almost 92% in the last five rounds.
Thus, at the start, eBay seems to go through a phase of poor efficiency levels, which
is only ameliorated as experience sets in. The null hypothesis of equal efficiency levels
across treatments can not be rejected (p=.1627) for all rounds. Restricting attention
to the last five rounds shows no significant differences (p=.4393) either. To conclude,
except a slight increase at the beginning in eBay, average efficiency levels do not vary
31One bidder in 2Dutch and two in eBay are assigned to the category Other but satisfied theconditions of both categories Dom/Over. and Dom/Under.
32For instance, a bidder is considered Dom/Overbid. if at least 80% of his bids are equal to thedominant strategy or above his private value.
20
-10
-50
510
Difference
1 2 3 4 5 6 7 8 9 10Round
2Dutch eBay
(a) Selling vs. Expected Price
1520
2530
3540
Earnings
1 2 3 4 5 6 7 8 9 10Round
2Dutch eBay
(b) Earnings
Figure 7: Dynamics of Prices and Earnings
much within this treatment. However, except in one round, efficiency remains equal
or higher in 2Dutch.
Prices and Earnings
In 2Dutch, the expected price is equal to the lower private value of both bidders plus
an increment of 1 point,33. By contrast, any price that does not exceed the lower
private value plus the increment is expected in eBay. Recall that Independently of
the winner’s bid, the selling price is determined by the losing or lower bid.
Figure 7(a) represents average selling price with respect to the expected price.
Values close to (or below) zero represent prices predicted by theory in 2Dutch (eBay).
Comparing prices across treatments, there exists strong evidence that they are differ-
ent in the last 5 rounds (p = .0028).34 Testing the hypothesis that prices are equal
to the prediction shows that eBay’s average prices are not significantly different in
the last 5 rounds (one-tailed Wilcoxon signed-rank test, p = .9983). In 2Dutch, this
hypothesis cannot be rejected either (two-tailed p = .4476). Despite strong evidence
of overbidding, it does not translate directly into higher selling prices.
The dynamic of average earnings is shown in Figure 7(b). While earnings in
33Exceptionally, the expected price is equal to the lower private value, when the higher and lowerprivate values of both bidders are the same.
34The hypothesis cannot be rejected when looking at all rounds (p = .2244) but considering anyother interval up to the last round leads to a rejection at least at a 5% significance level.
21
2Dutch are characterized by a declining trend, those in eBay follow an increasing
pattern. However, the difference in earnings is not significant between the first and
last 5 rounds in either treatment (p = .1305 2Dutch, p = .1823 eBay).35 Despite
different trends, earnings in both auctions are not significantly different from each
other in all rounds or in the last 5 (p = .2786 and p = .6934, respectively).
5 Conclusion
Sniping or last-minute bidding on eBay has been well documented by Ockenfels and
Roth (2006), Roth and Ockenfels (2002) and Bajari and Hortacsu (2003), as well
as laboratory experiments by Ariely et al. (2005). Sniping behavior can arise as a
rational response to incremental bidding or bidding wars. Also as a means to prevent
disclosing private information to other bidders. Nevertheless, due to late bid arrivals,
it can lead to inefficiency and economic losses for the auctioneer.
The second-price Dutch auction posits an alternative mechanism to eBay’s. The
former avoids sniping de facto. Other contestants’ bidding activity cannot be observed
during the course of an auction. Bidding one’s own private value remains the weakly
dominant strategy due to its strategic equivalence with the second-price sealed bid
auction. I conducted a laboratory experiment to test the performance of the second-
price Dutch auction with respect to experimental evidence on second-price sealed bid.
A comparison in terms of efficiency, prices and bidders’ earnings is carried out with a
mechanism similar to eBay’s.
The results show that, on the Dutch format, almost 60% of all bids are close to the
private valuations, the weakly dominant strategy, and 25% are above, which are re-
spectively higher than the 20-30% and lower than the 60-70% observed in experiments
on second-price sealed bid auctions (Kagel and Levin 1993). In eBay’s similar mech-
anism, sniping behavior severely increases the amount of inefficient outcomes. Selling
prices in the Dutch format are significantly higher than those on eBay’s similar auc-
35The difference in 2Dutch becomes significant when comparing the first and last 3 rounds (p =.0619).
22
tion, while there exists no significant differences in bidders’ earnings nor efficiency
levels between both mechanisms.
In the current experimental design, the performance of the second-price Dutch
auction seems promising. Sniping behavior leading to an increase in economic in-
efficiencies can also be replicated with a simple design. Logical extensions of the
actual design include increasing the number of bidders to foster more competition,
and extending the number of auctions for more experienced bidders.
23
References
Ariely, Dan, Axel Ockenfels, and Alvin E. Roth, “An Experimental Analysis
of Ending Rules in Internet Auctions,” RAND Journal of Economics, 2005, 36 (4),
890–907.
Bajari, Patrick and Ali Hortacsu, “The Winner’s Curse, Reserve Prices, and
Endogenous Entry: Empyrical Insights from eBay Auctions,” RAND Journal of
Economics, 2003, 34 (2), 329–355.
and , “Economic Insights from Internet Auctions,” Journal of Economic Liter-
ature, June 2004, 42, 457–486.
Coppinger, Vicki M., Vernon L. Smith, and John A. Titus, “Incentives and
Behavior in English, Dutch and Sealed-Bid Auctions,” Economic Enquiry, 1980, 18
(1), 1–22.
Cox, James C., R. Roberson, and Vernon L. Smith, “Theory and Behavior of
Single Object Auctions,” Research in Experimental Economics, 1982, 1, 61–99.
, Vernon L. Smith, and James M. Walker, “A Test that Discriminates between
Two Models of the Dutch-First Non-Isomorphism,” Journal of Economic Behavior
and Organization, 1983, 4 (2-3), 205–219.
Ely, Jeffrey C. and Tanjim Hossain, “Sniping and Squatting in Auction Markets,”
American Economic Journal: Microeconomics, 2009, 1 (2), 68–94.
Fischbacher, Urs, “zTree: Zurich Toolbox for Ready-Made Economic Experiments,
Experimental Economics,” Experimental Economics, 2007, 10 (2), 171–178.
Gray, Sean and David Reiley, “Measuring the Benefits to Sniping on eBay: Evi-
dence from a Field Experiment,” 2004.
Hossain, Tanjim, “Learning by Bidding,” RAND Journal of Economics, 2008, 39
(2), 509–529.
24
Kagel, John H. and Dan Levin, “Independent Private Value Auctions: Bidder
Behavior in First-, Second- and Third-Price Auctions with Varying Numbers of
Bidders,” Economic Journal, 1993, 103, 868–79.
, Ronald M. Harstad, and Dan Levin, “Information Impact and Allocation
Rules in Auctions with Affiliated Private Values: A Laboratory Study,” Economet-
rica, 1987, 55 (6), 1275–1304.
Katok, Elena and Anthony M. Kwasnica, “Time is Money: The Effect of Clock
Speed on Seller’s Revenue in Dutch Auctions,” Experimental Economics, 2008, 11,
344–357.
Lucking-Reiley, David, “Using Field Experiments to Test Equivalence between
Auction Formats: Magic on the Internet,” American Economic Review, 1999, 89
(5), 1063–1080.
, “Auctions on the Internet: What’s Being Auctioned, and How?,” The Journal of
Industrial Economics, September 2000, 48 (3), 227–252.
Ockenfels, Axel and Alvin E. Roth, “Late and Multiple Bidding in Second Price
Internet Auctions: Theory and Evidence Concerning Different Rules for Ending an
Auction,” Games and Economic Behavior, 2006, 55, 297–320.
Peters, Michael and Sergei Severinov, “Competition among Sellers Who Offer
Auctions instead of Prices,” Journal of Economic Theory, 1997, 75, 141–179.
Rasmusen, Eric B., “Strategic Implications of Uncertainty over One’s Own Private
Value in Auctions,” BE Press Journal, 2006, 6 (1).
Roth, Alvin E. and Axel Ockenfels, “Last-Minute Bidding and the Rules for
Ending Second-Price Auctions: Evidence from eBay and Amazon Auctions on the
Internet,” American Economic Review, 2002, 92 (4), 1093–1103.
25
Vickrey, William, “Counterspeculation, Auctions, and Competititve Sealed Ten-
ders,” Journal of Finance, 1961, 16, 8–37.
Wang, Joseph Tao-Yi, “Is Last Minute Bidding Bad?,” 2006. Humanities and
Social Sciences, Caltech.
26
A Instructions
WELCOME TO THE EXPERIMENT!
The purpose of this experiment is to study the behavior on decision making. Do not
think that it is expected a special behavior from you. However, be aware that your
decisions will affect the money you can earn during the experiment.
These instructions will explain you the rules of the experiment and how to use the
computer interface. Instructions are identical for all participants. The anonymity of
the participants and their decisions is also guaranteed.
The examples in the instructions are exclusively thought to illustrate different
situations and are therefore irrelevant for the experiment itself.
Earnings will be expressed in points which will be exchanged at the end at a rate
of 3e per 100 points.
Please, it is important that you do not talk to nor disturb other participants. If
you need help, raise your hand and wait in silence. Someone will come to you as soon
as possible.
THE EXPERIMENT
During the experiment you will participate in 26 auctions divided into two PHASES.
Each phase consists of 13 auctions. The only difference between both phases are the
auction rules.
In each auction there will be two bidders: one bidder will be yourself and the other
will be another person from this room. In two consecutive auctions you will always be
paired with a DIFFERENT person, that means, between one auction and the next,
the other bidder will be a different person from the previous one.
What is auctioned and how do I calculate my profit?
The object auctioned is fictitious. At the beginning of each auction, you will be
informed of the value the object has for you. This value, called personal value v, will
27
be determined in the interval [1, 100] points, and all integer numbers in the interval
have the same probability.
The personal values for each bidder and for each auctions are generated randomly
and independently from each other.
If your bid is the highest at the end of the auction, you will be therefore the winner
and will have to pay a price p. Your profit or loss will be v−p, depending whether this
quantity is positive, zero or negative. On the other hand, if you are not the winner,
your profit will be zero.
Examples in case of being the winner:
Personal value (v) Price (p) Profit/Loss (v − p)
(a) 60 50 10(b) 50 50 0(c) 40 50 -10
The profit or losses will be added up or deducted from an initial amount we provide
you with at the beginning. This amount is equal to 200 points. The final amount will
paid to you in cash when the experiment is over.
Although it is possible to incur in losses in an auction, there is always the possibility
to bid in such a way to avoid losing money.
If you lose all your points (included the amount provided at the beginning) at
some point during the experiment, you will be asked to abandon the room and the
experiment will be over for you.
At the end of each auction you will receive the following information: the winner
of the auction, the price paid, your profit in the current auction and the accumulated
profit.
PHASE 1
How can I bid in the auction?
To bid in the auction you have to submit two values: your “Bid” and your “Max-
imum Bid”. The meaning of both things will be explained next in more detail.
28
With your “Bid” you indicate the price you are willing to pay for the object in
case you are the winner. It always has to be higher than the price of the highest bid
at that moment.
Example:
BEFORE AFTER
Highest Bid (Price) Bidder Your “Bid” Highest Bid (Price) Bidder(a) 50 Other 60 60 You(b) 50 You 70 70 You
With your “Maximum Bid” you let the computer bid for you so that you remain
having the highest bid. The computer will only outbid the other bidder by one point.
This will only happen in case you are being outbid. The computer will bid on your
behalf up until the value indicated in “Maximum Bid”.
In case the other bidder, trying to outbid you, matches your bid (this happens
when his “Maximum Bid” and your “Maximum Bid” are the same), you will remain
as highest bidder and the price of your bid is equal to your “Maximum Bid”.
The information about your “Maximum Bid” is always PRIVATE and will not
ever be revealed to the other bidder.
If your bid is to be valid, your “Bid” and your “Maximum Bid” have to satisfy
the following:
• Your “Bid” has to be higher than the price of the highest bid.
• Your “Maximum Bid” has to equal or higher than your “Bid”.
• Your “Bid” and your “Maximum Bid” can only be between 1 and 100.
In case your bid does not comply with all conditions above stated, the computer
will show you an error message reminding you what was the problem.
Examples in case no bid has been received yet:
If no bid is received during an auction, there will be no winner and each bidder’s
profit will be zero.
29
BEFORE AFTER
Other BidderYour Your Highest Bid His His Highest Bid“Bid” “Max. Bid” (Price) Bidder “Bid” “Max. Bid” (Price) Bidder
(a) 50 60 50 You 55 55 56 You(b) 50 60 50 You 55 58 59 You(c) 50 60 50 You 55 60 60 You(d) 50 60 50 You 55 65 61 Other
Each auction lasts 100 seconds and will finish when this time is exhausted.
Computer interface
In the figure above you can observe what you will see on the computer screen
during an auction.
On the top part, you can see the actual auction number.
On the left, all information related to the actual auction is displayed: remaining
30
time, highest bid and its bidder. This information is PUBLIC and is exactly the same
for both bidders.
On the right you can see your PRIVATE information: your personal value of the
object and the values of your last bid. This information cannot be seen by the other
bidder.
You can use the bottom part to submit your bid. There are two boxes where you
indicate your “Bid” and your “Maximum Bid”. When you are sure, simply press on
the button “BID” to submit you bid. Recall that you have to provide both values
“Bid” and “Maximum Bid”.
Training auctions
Out of the 13 auctions played in PHASE 1, the first 3 are training auctions, that
means, all possible profits or losses will not count for the final payoff. During these
auctions you should familiarise with the auction mechanism and computer interface.
PHASE 2
How do I bid in this auction?
In this auction there is a clock indicating the selling price of the object being
auctioned. The particularity is that the clock starts at a price equal to 100 points
and descends until a price equal to zero at a rate of one point per second.
You bid by selecting the price that is indicated by the clock at that moment.
The winner of the auction is the one with the highest bid. If you have the highest
bid and have therefore won the auction, you and ONLY you will be informed about
it. For the other bidder, the auction continues normally and the clock continues to
decrease the price. That means, the other bidder cannot know that there is already
a winner.
The price to be paid by the winner is determined by the bid submitted by the
other bidder. The price is equal to the lowest bid plus one point.
31
If both bidders submit the same bid, a lottery will determine the winner and the
price is equal to his bid.
If there is only one bid, its bidder will be the winner and will pay a price equal to
1 point. If there are no bids during an auction, there is no winner.
Your bid can only be a value between 1 and 100.
32
Examples:
Your Bid Other Bidder’s Bid Winner Price
(a) 50 40 You 41(b) 50 60 Other 51(c) 50 50 Lottery: You/Other 50(d) 50 - You 1
The auction finishes when the lowest bid has been submitted or when the clock
reaches zero.
Computer interface
In the figure above you can observe what you will see on the computer screen
during an auction.
On the top part, you can see the actual auction number.
33
On the left, all information related to the actual auction is displayed: the clock
indicating the selling price. This information is PUBLIC and is exactly the same for
both bidders.
On the right you can see your PRIVATE information: your personal value of the
object and the value of your last bid. This information cannot be seen by the other
bidder.
On the bottom part you can submit your bid in two ways:
• On the left, by pressing the button “BID NOW” you will bid the price indicated
by the clock in that moment.
• On the right, you can indicate the computer the price you want to bid. To do
so, you indicate the value in the box and press the button “BID”. The computer
will bid on your behalf when the clock reaches that price. This value has to be
lower or equal to price on the clock. You can always change you bid (even using
the button “BID NOW”) as long as the clock has not reached that value.
At the beginning of each auction, the clock will only start to work, and therefore
decrease the price, after 10 seconds. During this time you also have the possibility to
submit your bid.
Training auctions
Out of the 13 auctions played in PHASE 2, the first 3 are training auctions, that
means, all possible profits or losses will not count for the final payoff. During these
auctions you should familiarise with the auction mechanism and computer interface.
34