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.

2

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.

9

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

10

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.

11

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

14

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

16

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