The High/Low Divide: Self-Selection by Values inAuction Choice�

Radosveta Ivanova-Stenzely

Helmut Schmidt University HamburgTimothy C. Salmonz

Florida State University

October 2010

Abstract

Most prior theoretical and experimental work involving auction choice has assumedbidders �nd out their value after making a choice of which auction to enter. We examinewhether or not bidders knowing their value prior to making a choice of which amongmultiple alternative auction formats to enter impacts their choice decision and/or theoutcome of the auctions. The results show a strong impact on auction choice. Subjectswith low values choose the �rst price sealed bid auction more often while subjects withhigh values choose the ascending auction more often. The number of bidders in eachauction, revenue, e¢ ciency and average bidder surplus all end up equalized.JEL Codes: C91, D44Key Words: bidder preferences, private values, sealed bid auctions, ascending auc-tions, endogenous entry

1 Introduction

While most theoretical and experimental work on auctions focuses on environments with an

exogenously �xed number of participants, there has recently been increased attention paid

to the importance of the entry decision of bidders. An important element to consider in

the entry decision of a bidder is that in many situations their actual decision is typically

richer than to enter a single auction or not as the bidder can often choose among multiple

possible auctions as well as other ways of acquiring an object. Understanding how individuals

�The authors would like to thank seminar participants at the University of Pittsburgh, the University ofArkansas, Humboldt University, Hamburg University as well as participants at the ESA World meeting inCopenhagen for useful comments and suggestions.

yDepartment of Economics and Social Sciences, Holstenhofweg 85, D-22043 Hamburg, Germany, E-mail:ivanova@hsu-hh.de

zDepartment of Economics, Florida State University, Tallahassee, FL, 32306-2180, tsalmon@fsu.edu.Phone: 850-644-7207 Fax: 850-644-4535.

1

might make decisions in this more complex environment is important to potential auctioneers

interested in raising revenue as revenue is typically increasing in the number of bidders

participating (common values environments being the obvious exception)1 and it may also

be important to those interested in maximizing e¢ ciency.

In the present study we seek to take a step along the path to furthering an understanding

of how bidders choose which among multiple possible auction formats to enter as well as what

impact that ability to choose has upon standard measures of auction performance.2 The

environment we investigate allows bidders a choice between the two most common standard

auction formats used in the �eld; the sealed bid �rst price auction and the ascending (or

English) auction. The reason we are investigating the choice between these mechanisms is in

part because this basic structure should serve as a good vantage point for beginning the study

of these issues. This environment is also �eld relevant in helping to understand something

about how electronic markets may have developed. This environment matches with the

description of the formation of early internet auction markets described in Lucking-Reiley

(1999b) in which sellers would o¤er certain types of trading cards and di¤erent sellers would

be di¤erentiated largely by the mechanism they selected for use. Our study may therefore be

able to provide some understanding for why certain types of mechanisms may have evolved

into use by later online marketplaces.3

A key element of much (though not all) of the existing theoretical and experimental

literature on situations involving choice between auction formats is the use of the assump-

tion that bidders make these decisions without knowing their value for winning until after

the entry decision is made. Under this assumption, Smith and Levin (1996) demonstrate

theoretically that for the empirically relevant speci�cation of risk preferences (i.e. that bid-

ders possess risk preferences consistent with Decreasing Absolute Risk Aversion) the revenue

1A reasonable claim is that most objects being auctioned possess both common and private value com-ponents. Goeree and O¤erman (2003) investigate auctions under these assumptions and demonstrate thatrevenue and e¢ ciency increase with the number of bidders.

2There is a substantial theoretical literature examining the choice of entering an auction or not (e.g.Engelbrecht-Wiggans (1993), Smith and Levin (1996), Smith and Levin (2002), Pevnitskaya (2004) andPalfrey and Pevnitskaya (2008)) as well as additional papers examining a bidder�s decision of which auctionto enter with the auctions di¤erentiated by entry prices ( e.g. Samuelson (1985), Bajari and Hortacsu (2003),Lucking-Reiley (1999a) and Levin and Smith (1994)). These environments though are quite di¤erent fromours and so we will not survey them in depth.

3It is important to note that while Lucking-Reiley (1999b) conducts a �eld study in which bidders choosebetween auction mechanisms, his results are not directly comparable to those presented here. The choicesthere were between a �rst price auction and Dutch auction in one study and then an ascending auction or asecond price auction in a separate study. While the �rst price auctions there yielded more revenue than thelist price of the objects and the ascending yielded less revenue, the designs of those studies do not allow fora fair comparison of those two results. The studies were separate and the number and composition of itemsauctioned were di¤erent between them as was the number and composition of bidders invited to participate.

2

ranking between the �rst price and the ascending auction is indeterminate and depends cru-

cially on several factors including the exact distribution of risk preferences in the population.

Ivanova-Stenzel and Salmon (2008a) (ISS08) investigates this environment experimentally

and �nds that more subjects choose to enter the ascending auction than the sealed bid and

this leads to a negation of the traditional revenue ranking between ascending and sealed bid

auctions, as established in Cox, Roberson, and Smith (1982), in that the revenue raised in

ascending and sealed bid auctions equalized.

While there are certainly arguments for why it is reasonable to model auction choice

under the assumption that values are only learned after entry, the alternative assumption,

i.e. that values are known prior to entry, is also empirically plausible in many situations. The

key di¤erence of strategic importance between these two assumptions is that according to the

latter assumption it is possible that the entry choice could depend on the value the bidder

possesses. This could lead to self-selection e¤ects in which bidders choose di¤erent auction

types depending on their values and that in turn could lead to important e¤ects on revenue

and auction e¢ ciency that may di¤er from the e¤ects found when values are unknown prior

to entry. Menezes and Monteiro (2000) develops a theoretical model of endogenous entry

into auctions subject to entry costs in which bidders observe their value before entry. The

authors derive equilibria based on cut-o¤ strategies for the entry decisions in which bidders

with values above a certain level will choose to enter an auction while those with lower

values choose to stay out of the auction. This represents one form of bidder self-selection

into auctions based on values. In their model though the choice by the bidders is to enter

a particular auction format or not when facing an entry cost rather than choosing between

multiple auction formats. Should we observe self-selection in our environment in which

bidders can choose among multiple formats it will necessarily be of a di¤erent sort.4

Our results will show that the knowledge of own value does in�uence entry choice signi�-

cantly. Bidders with lower values prefer to enter sealed bid �rst price auctions while bidders

with higher values prefer to choose ascending auctions. The observed self-selection bias

creates a high/low divide among bidders between auction formats. The ultimate e¤ect on

revenue generation is that there is no statistically signi�cant di¤erence between the revenue

in the two auction formats (just as in ISS08 where subjects learned of their value after their

4A common suggestion we have received is that we could have had subjects choose to enter an auction ornot, rather than choose between actions, and then compared the mechanisms indirectly. The key design detailto that version though is how one structures the outside option. Di¤erent outside options could certainlyimpact the results and calibrating it accurately would be di¢ cult. In our view the most �eld relevant outsideoption is the ability to obtain the item elsewhere and this drove our design choice to have the subjects choosebetween competing auctions.

3

entry choice). Further, we �nd a similar result in regard to auction e¢ ciency and bidder

earnings. We also �nd that the entry behavior we observe is due to the subjects using cut-o¤

strategies in choosing between auctions and we �nd that the strategies in use constitute a

near best response to the observed decisions by others. Thus this high/low divide appears to

be a straightforward product of bidders responding to the pecuniary incentives of entering

the two formats. Given that we �nd the format of the auction having strong impacts on

the type of bidders participating in an auction, this demonstrates that auctioneers should

be strongly concerned about how entry decisions of potential bidders may be impacted by

the institution chosen by the auctioneer. In the conclusion we will discuss in greater detail

how our results may extend to more complicated environments.

The remainder of the paper is organized as follows: Section 2 will present an overview

of the experiment conducted for this study. Section 3 contains an analysis of the data

developed through a series of results. In Section 4 we discuss our �ndings and Section 5

provides concluding remarks.

2 Experimental Design

The experiment consists of two phases. The �rst phase we will refer to as the Learning

Phase as in this phase subjects participate in several rounds of ascending auctions5 (will

be abbreviated henceforth as the �A�auction) and sealed bid �rst price auctions (will be

abbreviated henceforth as the �SB�auction) with di¤ering but exogenously �xed n�s. This

allows subjects to develop some experience with both auction formats and to give them some

idea of how pro�t levels might vary with n. In the second phase, which we will refer to as the

Auction Choice Phase, subjects repeatedly choose between participating in either a sealed

bid auction or an ascending auction. The subjects know their value prior to choosing but

the number of competitors is endogenously determined and unknown at the time of choosing

(though the number of competitors is known at the time of bidding).

We conducted �ve sessions with 12 subjects per session. In the Learning Phase, subjects

participate in twelve rounds of �xed n auctions and subjects do receive real earnings from

these rounds. In each round they are informed of their value for winning the auction which

is drawn independently for each subject from a uniform distribution over the integers in the

5The ascending auctions we used were clock auctions in which the price would start at 0 and increaseby 1 ECU every second up to a maximum of 150. Each subject had a button on their screen to exit theauction and the auction ended when only 1 bidder remained with that bidder paying the price at which thelast bidder dropped out.

4

range [0; 100]: All values are denoted in a �ctitious currency termed ECU for Experimental

Currency Unit. The subjects then participate in both a SB and A auction using the same

value. They �rst submit a bid in the SB auction and then immediately participate in the

A auction and only after the A auction is completed will they be informed of the results

from both auctions. These twelve rounds consist of two blocks of six period cycles in which

the subjects participate in three rounds with n = 2 auctions and then three with n = 4: At

the end of the Learning Phase the subjects receive feedback telling them the session-wide

average pro�t in each auction format and for each n: They also receive information on their

total pro�t up to this time.

The Auction Choice Phase consists of 30 rounds in which subjects choose in which auction

to participate. Subjects are told their value for winning an object in that round prior to

choosing an auction format.6 To maximize the number of auction choice periods, we do

not have the subjects play the auctions in each round. Instead, each set of auctions is

only conducted with a 20% probability. This allows us to obtain more observations on the

auction choice behavior of the subjects which is important because this represents a non-

trivial coordination problem that could take a while to equilibrate. We use in each period

the exact same value draws and con�guration of the bidder groups from the experiment in

Ivanova-Stenzel and Salmon (2008a). Furthermore, we pair each session with a session from

Ivanova-Stenzel and Salmon (2008a), and conduct the auctions in the same rounds as in

the sessions from ISS08. This amounts to simply using a pre-drawn set of random draws

to determine which rounds will be chosen so our explanation to the subjects that any given

round will be conducted with a 20% probability is still valid. By using the same draws across

experiments, we ensure comparability across the data sets of the two experiments.

In each round after subjects have made their entry choice, they are told the number of

people choosing both formats and whether the auctions are going to be conducted or not.

If the auctions are conducted that round, the subjects are informed about the number of

bidders in their auction before the bidding. At the end of each round they are told whether

or not they won that round, the price paid by the winner and how much pro�t they made.7

For the Auction Choice Phase, we split each session of twelve subjects into separate groups

of six. We will refer to these groups as G1 and G2 inside of a session. These groupings are

held constant throughout the rest of the session, yielding two independent observations per

6 In the experiments from Ivanova-Stenzel and Salmon (2008a), subjects were not told of their valuebefore choosing which auction format to enter. It was, however, made clear to them that they would receivethe same value regardless of which format they chose.

7Transated instructions are in an appendix while the originals in German are available upon request.

5

session, one for each group. The choice of the size of the groups is important. Having six in

the pool allows for auction sizes to vary in what is a key region for this issue. Auctioneers

should be mostly concerned about choosing the right mechanism to maximize revenue in

the small n range8. The reason is that in this range a marginal bidder contributes the most

gain in revenue. Once n becomes large, the marginal increase in revenue from an additional

bidder is small relative to the total revenue received. Further, in many environments the

performance of auction mechanisms tends to converge as n increases. Consequently, if an

auctioneer knows he or she will get 8 or more bidders, the choice of an auction mechanism is

much less important than if the number of prospective bidders is in the 2-6 range. Further,

having an even number in the prospective bidder pools allows for the possibility that bidders

can easily split evenly into stable con�gurations between auctions should that be their natural

preference without the additional coordination problems of doing so through the use of mixed

strategies had the pool size been odd.

Because we know from prior work, Ivanova-Stenzel and Salmon (2004) and Ivanova-

Stenzel and Salmon (2008b), that subjects generally prefer the ascending auction, we de-

signed our main treatment with a feature to minimize the rent seeking strategy of attempting

to be the one person in the pool to choose the sealed bid. We wanted to guarantee that an

auction would be competitive if someone chose it. We achieve this by taking two of our six

group members in each round and placing one in the SB and the other in the A auction by

default, allowing the other four to choose. This means that in this treatment, two bidders

are forced into an auction format (henceforth will be referred to as the FB-treatment) while

the other four are allowed to choose, and any of those four choosing to enter into an auc-

tion knew that they would face at least one other bidder. This design choice is somewhat

controversial and to test its e¤ects we conducted an additional treatment, NFB (no forced

bidders) where the auction format was freely chosen by all six bidders.

Most participants were students of economics and business administration of Humboldt

University Berlin. The software for the experiments was programmed using z-Tree (Fis-

chbacher (2007)). Earnings from the experiment were translated into Euros at the exchange

rate of 1 ECU = e 0.10. Subjects�total earnings including e3.00 participation fee ranged

from e9.20 to e37.30 with an average of e22.20 in sessions that lasted approximately two

hours each.8In an extensive review on online auctions Ockenfels, Reiley, and Sadrieh (2006) reports average number

of bidders not higher than 5.0.

6

Number of Bidders Average Value� Max Value�

Treatment-Session-Group SB A SB A SB AFB-S1-G1 2.83 3.17 43.44 55.00 58.83 81.23FB-S1-G2 3.10 2.90 35.17 51.09 56.67 74.22FB-S2-G1 3.27 2.73 39.76 58.71 58.54 70.69FB-S2-G2 2.70 3.30 38.78 57.23 54.71 75.04FB-S3-G1 2.77 3.23 41.09 52.45 56.74 70.69FB-S3-G2 2.83 3.17 35.55 61.92 45.68 75.89FB-S4-G1 2.97 3.03 37.69 56.49 47.54 77.31FB-S4-G2 2.87 3.13 39.14 54.58 53.92 67.07All (FB) 2.92 3.08 38.77 55.93 66.41 75.12NFB�S5-G1 3.07 2.93 41.63 55.78 60.03 81.20NFB�S5-G2 3.33 2.67 45.89 52.99 73.00 68.83All (NFB) 3.20 2.80 43.85 54.45 66.41 75.12All (FB&NFB) 2.97 3.02 40.27 55.56 56.89 74.23ISS08 2.44 3.56 47.72 47.71 58.77 66.60�� Average and Max value calculations exclude values of forced bidders from consideration.

Table 1: Summary of key descriptive statistics considering all rounds. The Averagecolumn is done o¤ of individual values. It is not an average of the group level averages.

3 Results

3.1 Auction Outcomes and Bidder Behavior

An overview of the data can be found in tables 1 and 2 which present descriptive statistics

on the key variables of interest. Table 1 contains the key variables that one can compute

taking into account all of the choice rounds and it presents the averages broken out by the 8

independent groups from the FB-treatment in which two bidders were forced into an auction

format each round and 2 independent groups in the supplementary NFB-treatment in which

there were no forced bidders. Table 2 contains the key variables that one can compute from

the rounds in which auctions were actually conducted. We also include in both tables the

average of the same statistics from ISS08 for use as a benchmark comparison.

Result 1: The number of bidders participating in each auction format is not statistically

di¤erent and there is no time trend over the course of the experiment.

There is already strong evidence for this result in the simple descriptive statistics. The

average number of bidders in the SB and A auctions in the full sample are 2.97 and 3.02,

respectively, and in the rounds in which auctions were conducted the averages are 2.87 and

3.12, respectively. Additional evidence can be found in the top panel of �gure 1 which shows

7

Auction Num of Avg� Max� Revenue Winner Bidder E¤Treatment Format Bidders Value Value Surplus�� Surplus���

FB SB 3.00 38.97 59.84 46.48 17.21 10.45 0.99A 3.00 53.13 78.51 50.17 24.31 9.99 1.00

NFB SB 2.20 39.00 55.89 44.22 11.56 7.13 1.00A 3.80 56.18 84.90 66.40 13.90 4.36 0.93

All (FB&NFB) SB 2.87 38.98 58.98 46.15 16.38 9.96 0.99A 3.12 53.94 79.87 52.79 22.63 9.08 0.99

ISS08 SB 2.63 44.12 54.26 51.95 11.94 5.96 0.99A 3.38 47.63 67.31 54.90 20.73 6.48 0.99

�� Average and Max value calculations exclude values of forced bidders from consideration.��� Average surplus earned by the auction winner in each period���� Winner Surplus divided by the number of bidders in each auction

Table 2: Summary of key descriptive statistics considering only rounds in which auctionswere conducted.

the density plot of the distribution of auction sizes in the two formats (for the FB data)

and then table 3 presents panel regressions in which the dependent variable is variously

the di¤erence between number of bidders, revenue, e¢ ciency and surplus in the A and SB

formats. The distribution plots show quite clearly that the distribution of auction sizes is

virtually identical between the two formats. For statistical evidence we have provided several

speci�cations for the regressions on the number of bidders in the auctions aimed at allowing

us to make clear inference on several di¤erent questions. The �rst two speci�cations contain

a constant and a dummy variable for the last 10 rounds of the experiment with the di¤erence

being that the �rst uses data from only the sessions with forced bidders (FB) while the second

uses data only from the session with no forced bidders (NFB). The lack of signi�cance of any

of the coe¢ cients in these regressions provides clear support for there being no di¤erence in

the number of bidders in the two formats and that this relationship does not change over

time. The third speci�cation uses both sets of data and includes interaction variables to help

us determine if there were any di¤erences in this result between the FB and NFB treatments.

Again, no variables are signi�cant indicating that this treatment di¤erence had no e¤ect on

the results.

The fourth speci�cation is not necessary to support this result but it is necessary for

allowing proper interpretation of later results regarding the conducted auctions. This spec-

i�cation includes data from both treatments but only from rounds in which auctions were

conducted. The time variables are left out of this regression due to the low number of obser-

vations but we have included the interaction variables to determine if there is a di¤erence due

8

Figure 1: Density plots of number of bidders in auctions and revenue in each auctionformat using data from the FB treatment.

to the FB/NFB treatment. The results clearly indicate that there is no di¤erence between

treatments and even in this subset there is no di¤erence in the size of auctions between

formats. It is important to verify that the auction size equivalence holds in this subset of

the data prior to presenting the following results because had this not been the case it would

have required a substantially di¤erent interpretation of the results.

Result 2: The revenue and the e¢ ciency generated by each auction format is not signi�-

cantly di¤erent.

Again, the data in table 2 suggests rather strongly that there will be no di¤erences in the

revenue raised by both formats and a graphical view of the revenue distributions from both

formats using data from the FB treatment is seen in the lower panel of �gure 1. A statistical

con�rmation of the result regarding revenue can be found in the �fth column of table 3.

While we do not provide a histogram on e¢ ciency, the statistical veri�cation is found in the

sixth column of table 3. For both we present a panel regression with the revenue or e¢ ciency

di¤erential (A-SB) as the dependent variable using random e¤ects speci�cation at the group

level. This speci�cation uses data from both treatments and a dummy variable to determine

if there is a di¤erence between the two. We �nd that in both cases neither the constant nor

the dummy variable is signi�cant indicating that in neither data set do we see statistically

9

Number of Bidders Revenue E¢ ciency SurplusAR / FB AR/ NFB AR / All CA / All CA / All CA / All CA / All

Constant 0.013 -0.500 -0.500 1.600 26.60 0.036 -0.953(0.166) (0.397) (0.346) (0.998) (16.381) (0.051) (11.767)

Last 10 Periods 0.463 0.300 0.300(0.288) (0.687) (0.600)

FB Treatment - - 0.513 -1.478 -21.20 -0.025 -0.148(0.387) (1.111) (18.177) (0.056) (13.098)

FB* Last10 - - 0.163(0.670)

Obs (Groups) 240 (8) 60 (2) 300 (10) 62 (10) 62 (10) 62 (10) 62 (10)R2 0.011 0.003 0.019 0.076 0.046 0.003 <0.001Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1

Dependent variables are di¤erence between noted statistic in ascending and sealed bid auctions.

AR=All Rounds, CA=Rounds with Conducted Auctions, FB/NFB=Treatment with Forced Bidders or Not

Table 3: Random E¤ects Panel regressions examining paired di¤erences in number ofbidders, revenue and surplus between formats.

signi�cant revenue or e¢ ciency di¤erences between formats and this is again unchanged by

the treatment choice. Of course if we examine outcomes in the learning phase we do �nd

a substantial di¤erence in revenue in the two bidder auctions as expected (33.52 in the A

and 51.38 in the SB) with the di¤erence narrowing substantially in the four bidder auctions

(71.04 in the A and 73.97 in the SB). E¢ ciency averages out to be about the same in all cases

(2 bidder auctions A:0.99 SB:0.98, 4 bidder auctions A:0.99 SB:0.99). This means that the

revenue similarity result is likely a consequence of something in the way bidders are choosing

between auctions rather than a consequence of bidders bidding in the SB auction according

to the standard risk neutral prediction.

There are two issues to note with these e¢ ciency and revenue results. First, the e¢ ciency

measurement here is not social e¢ ciency but rather auction e¢ ciency. We are measuring

whether the bidder winning the object has the highest value among those in that auction.

We are not measuring social e¢ ciency which would measure whether the two bidders with

the highest values in the pool of six win the two items. The measures are di¤erent because

the two highest value bidders could (and as we will see are likely) to be in the same auction.

It isn�t clear what the latter measure would mean so we have not provided it. In regard to

the revenue similarity result, one might argue that the lack of di¤erence we �nd is due to a

sample size issue rather than being a true lack of di¤erence. While simple calculations show

that it might require more than 30 additional sessions of data to generate a signi�cant result

10

given the current means and standard deviations of the data, it is always a possibility and

one we do not discount. The true important aspect of the result though is not actually the

notion that the two revenue levels are equivalent but rather that the revenue from the A is

not less than the SB. Since if there is any di¤erence it would be that the revenue in the A is

greater than the SB, it should be quite clear that the standard result of revenue dominance

of the SB does not hold.

Result 3: The average bidder surplus earned by bidders in both formats is not signi�cantly

di¤erent.

Evaluating average or expected bidder earnings is slightly di¢ cult in these experiments

since the number of participants is not held constant, even though the numbers turn out to

be approximately the same. Comparing raw earnings can still be somewhat misleading. In

table 2 we present two measures of surplus with one being the average surplus earned by

the auction winner in each period and a second we refer to as bidder surplus in which we

divide that by the number of bidders in each auction to obtain a rough measure of expected

or average earnings. The statistical evidence for this result can be found in the last column

of table 3. The speci�cation used is the same as in the previous cases and again we �nd all

variables to be insigni�cant.

Result 4: Bidders self select into auctions based upon their value but not based upon their

risk aversion or general degree of overbidding as measured by behavior in Phase 1.

By examining the di¤erences in the distributions of values of bidders participating in both

formats we begin to see some very interesting consequences of the endogenous auction choice

mechanism. As is shown in tables 1 and 2 there appear to be substantial di¤erences in the

average value of the bidders in the A and SB auctions and this in turn leads to a substantial

di¤erence in the average of the maximum value of a bidder in A and SB auctions as well.

These comparisons become even more interesting when these averages are compared to those

found in the ISS08 data. In the ISS08 data, average values in the A and SB auctions were

the same but there is almost the exact same di¤erence in magnitude between the maximum

values in the two formats in the ISS08 data as in the current data. In ISS08 this di¤erential is

due to the fact that A auctions have more bidders in them on average and so with more value

draws the �rst order statistic rises. In the current data, the di¤erence can not be attributed

to the properties of order statistics because the two formats attract the same number of

bidders. This suggests instead that there is self-selection occurring among the bidders. A

more detailed graphical depiction of the outcome of this self-selection is contained in �gure 2

11

0 10 20 30 40 50 60 70 80 90 100Value

0.000

0.005

0.010

0.015

0.000

0.005

0.010

0.015

0.000

0.005

0.010

0.015

No Choice

Chose Sealed Bid

Chose Ascending

Figure 2: Distribution plots of the values of bidders choosing Asc vs. SB as well as valuedistribution of bidders with no choice.

which shows histograms and distribution plots of bidder values from the FB-sessions among

those who chose the A, chose the SB and had no choice. The panel for the �No Choice�group

shows a uniform distribution as would be expected since bidders were randomly assigned to

be in that group. The panel for those who chose the A has a distribution which slopes slightly

up while the SB panel has a de�nite downward slope. These distributions are consistent with

self-selection occurring among the bidders in which bidders with high values tend to choose

the A format more often while those with lower values chose the SB more often.

Statistical veri�cation of the self-selection result and more generally an analysis of what

drives bidder auction choice decisions is found in table 4 which presents several di¤erent

speci�cations of random e¤ects Logit regressions with the dependent variable being Auction

Choice which takes the value of 1 to denote the choice of A and 0 to denote the choice of SB.9

In all speci�cations we use a non-parametric risk aversion measure or a generic measure of

how aggressive a bidder is in SB auctions which is just the coe¢ cient on the variable for the

bidder�s value in a regression of the form bit = �i+ �ivit:We conduct the regression for each

treatment and then for both data sets combined to examine whether there are any di¤erences

in auction choice behavior derived from the treatment. The �rst point to make is that in this

latter speci�cation all of the interaction terms are insigni�cant indicating once again that

9Instances in which bidders had no choice were not considered in the regression.

12

the treatment had no observable impact on behavior. In regard to the self-selection issues,

the results show that a bidder�s value has a positive and highly signi�cant impact on his

likelihood of choosing the A while the risk/overbidding measure is insigni�cant.10 We also

again �nd no time trend as we included a dummy variable for the last 10 periods and an

interaction between that dummy variable and the bidder�s value but both are insigni�cant.

We �nd a small but signi�cant e¤ect in the FB treatment showing that bidders are less likely

to choose the A auction the higher was the di¤erential between the number in that format

and the number in the SB in the previous round which is a perfectly sensible result showing

that on the margin subjects move away from over-crowded auctions.11

By examining the choice behavior on individual level we can see more clues about the

nature of the behavior as well as even stronger evidence of the self-selection by value. Out

of 60 subjects, 48 chose the A during the round in which they had their highest value for the

session. The overall average of the highest value each subject received in the experiment was

94.3. The average highest value at which subjects chose the SB was only 70.0 while it was

91.1 for the A. Further, only 19 subjects chose the A at their lowest value and the average

of the lowest values at which subjects chose each auction are 12.5 for the SB and 25.13 for

the A while the overall average lowest value each subject received was 4.5. Combining these

two reveals a pattern which suggests that subjects followed a form of a cut-o¤ strategy. At

values below some critical value, x; bidders choose only the SB and at values above some

critical value, y; bidders choose only the A while for intermediate values they choose both.

There is de�nitely heterogeneity in the values of x and y between bidders and it is typically

the case that x 6= y:12 The next subsection will attempt to determine why bidders might

follow such cut-o¤ strategies in their choice behavior.

10We have also conducted all regression speci�cations using the estimated CRRA risk aversion parameterfor each individual based on their phase 1 bids. Given the fact that the two measures are perfectly correlatedit should be clear that the results are identical between the two speci�cations.11This e¤ect does bring to light the possibility that there is serial correlation in the choices of the subjects.

We have checked the robustness of our results with several speci�cations to correct for the serial correlationincluding regressions with a lag of the dependent variable as well as FGLS speci�cations in which the errorstructure is modeled explicitly as an AR1 process. While the lagged term is generally signi�cant in theseregressions neither the sign nor signi�cance of the coe¢ cient on bidder value ever changes and typically thesigni�cance of the other variables remains the same as well. We chose to present the simpler regressionspeci�cation but details on the other results are available from the authors upon request.12If one examines the choice patterns at the individual level while many exhibit this pattern, not all of

the bidders appear to follow cut-o¤ strategies like this one. There are some who choose with a strong biastowards one mechanism or the other, typically in favor of the A, and a few others who choose according tosome unknown criteria.

13

FB Treatment NFB Treatment All DataValue 0.028��� 0.019��� 0.019���

(0.004) (0.006) (0.006)

Risk Aversion 0.327 1.626 1.331(1.213) (3.284) (2.556)

Num in A-SB t� 1 -0.066� -0.047 -0.046(0.037) (0.051) (0.050)

Last 10 Periods 0.324 0.213 0.215(0.319) (0.528) (0.520)

Last 10 * Value 0.003 0.001 0.001(0.006) (0.010) (0.010)

FB Treatment 0.558(2.306)

FB * Value 0.010(0.007)

FB * Risk Aversion -0.983(2.867)

FB * Num in A-SB t� 1 -0.022(0.062)

FB * Last10 0.118(0.611)

FB * Last10 * Value 0.003(0.011)

Constant -1.592 -2.431 -2.183(0.991) (2.624) (2.051)

Obs (Groups) 928 (48) 348 (12) 1276 (60)LL -551.39 -200.59 -752.69

Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1

Table 4: Random e¤ects logit panel regressions of auction choice where 1=A and 0=SB.

14

3.2 What can account for the observed high/low divide?

To help interpret the self-selection result we need to calculate the expected utility of bidders

for choosing either auction format. Since they know their value at the time of making their

auction choice we must calculate these expected utilities conditional upon their value. To

model the bidding behavior we will use bid functions that are an empirical best response

to the observed behavior. For the A, we can use the standard bid function, b�(vi) = vi; as

it is invariant to the value distribution13 but the bid function for the SB is not and so we

numerically calculate the optimal bid function given the observed value distributions.

To account for the fact that our subjects bid more aggressively in the SB than predicted

by the risk neutral equilibrium we will calculate our results for a range of risk aversion

parameters using a standard CRRA utility function; u(x) = x�. The empirical best response

bid function for the SB is calculated separately for each level of risk aversion and is based

on �nding the bid which would maximize the bidder�s expected utility assuming they face

n � 1 other bids drawn from the empirical distribution of bids in auctions of size n: While

the assumption that risk aversion is driving the bidding behavior is controversial,14 we adopt

this speci�cation purely for convenience and later we will discuss how incorporating other

explanations for overbidding in the SB auction will a¤ect our conclusions.

Full details on how we perform the expected utility calculations can be found in the

appendix but it is important to point out that in performing these calculations we are

attempting to make the minimal assumptions on the bidding behavior possible to allow the

calculations. The way to interpret this procedure is that we are calculating the expected

utility for a bidder with a particular degree of risk aversion bidding according to a best

response to the empirical distributions from the experiment. Since we do not know the

utility functions of the subjects we can not say these calculations represent their utility. Our

intention with these calculations though is to get an idea for how a rational bidder in the

experiment might choose between formats given the behavior of others.

The results from these calculations are summarized in �gure 3 which shows the expected

utility graphs in both auction formats for ten di¤erent levels of risk aversion ranging from

extreme risk aversion, � = :1; to risk neutrality, � = 1. There is a clear and consistent

pattern across all levels of risk aversion. In each case, the expected utility of the �rst price

auction is above that of the ascending for all values below 80. At values above 80, the

13Truthful bidding also largely matches observed individual behavior.14See for example Cox, Roberson, and Smith (1982), Harrison (1989) and many subsequent reply comments

over the years in the AER as well as Crawford and Iriberri (2007), Filiz-Ozbay and Ozbay (2007) andEngelbrecht-Wiggans and Katok (2007) for more recent examinations of this issue.

15

Figure 3: Expected utility of ascending and sealed bid auctions for varying levels of riskaversion.

expected utility of the ascending comes to dominate the �rst price and the less risk averse

is the individual the later this domination occurs.

Figure 3 explains why rational subjects may well have made their entry decisions accord-

ing to a decision rule similar to the one we described above with cut-o¤ values, x and y; for

being willing to start choosing the A and stop choosing the SB. These calculations suggest

that the optimal such strategy would be x = y 2 [80; 100]: As explained earlier, on averagewe �nd x = 25:13 and y = 70:0: The upper cut-o¤ for no longer choosing the SB is lower

than expected but approximately in the range predicted. The lower cut-o¤ for beginning

to choose the A is much lower than predicted. There are some simple and parsimonious al-

terations to our underlying choice model which could help explain both of these deviations.

First, if we assume that subjects best respond in a probabilistic manner by choosing the

auction format expected to yield greater expected utility with a higher probability based on

the relative di¤erential in expected utilities then we would no longer expect to empirically

observe x = y. Since �gure 3 shows that the expected utility of the SB is only slightly

16

greater than the A at low values, one would expect that probabilistic choice would lead to a

number of �errors�in this range. At higher values where we see greater conformity with the

deterministic predictions, we see that expected utilities diverge.

There are also reasonable alterations to the model which would explain why we observe

that on average y = 70 as opposed to being closer to 90. First, there are relatively few

auctions conducted in the second phase and so bidders might not have enough experience

with the change in the value distribution to allow them to adjust their bidding behavior. If

one calculates a version of �gure 3 using the standard risk averse bid functions for the uniform

distribution (and therefore without the correction for the skewed value distributions), the

change in the �gure is that the SB auction becomes less attractive and so the cross-over

points move a bit to the left in a manner more consistent with the data.

Another alternative would be to assume that bidders experience some form of regret as

described in Filiz-Ozbay and Ozbay (2007) and Engelbrecht-Wiggans and Katok (2007) and

this, rather than or in addition to risk aversion, explains their overbidding in the SB auction.

If we examine the � = 1 cell in �gure 3, then the e¤ect of adding this regret element will

be to leave the expected utility of the A auction unchanged but drop the expected utility

in the SB auction due to the increase in bidding and to the utility decrease from the regret

concern itself. This would again lower the expected utility of the SB and shift the cross-over

point to the left to be more consistent with the self-selection �ndings.15 This analysis allows

us to generate one �nal observation which summarizes the explanation of the self-selection

result and the overall action choice behavior:

Observation 1: The observed self-selection behavior is qualitatively consistent with a subject

probabilistically best responding to the expected utilities of participating in the two formats

assuming either that the subject is risk averse or that they expect to su¤er from ex-post regret

from losing an auction they could have pro�tably won.

4 Conclusion

This study empirically investigates, for the �rst time, the impact of bidder�s knowing their

values on entry decisions in auctions. It provides clear evidence that the knowledge of own

15There is a third explanation of overbidding contained in a previously cited paper, Crawford and Iriberri(2007), that one could also consider useful to explain this phenomenon but it is not applicable in thisenvironment. That paper proposes level�k strategic reasoning as an explanation for overbidding and showsthat it can lead to bids above the risk neutral level but this result does not hold for uniform value distributions.Since we see the overbidding in Phase I in which the values are uniformly distributed, this explanation willnot successfully rationalize our data. Thus, we do not consider how it might a¤ect our predictions.

17

value does in�uence auction choice as bidders choose di¤erent auction formats depending

on whether they have a low or high value. Examining this self-selection result in regard to

the argument put forth in Klemperer (2002) leads to an interesting similarity. In Klemperer

(2002), the author proposes that bidders who are disadvantaged in the sense that their values

are drawn from a dominated value distribution would be discouraged from entering into an

ascending auction and would prefer a sealed bid auction wherein they might still have a

chance of winning. We �nd that even when subjects are ex ante identical, i.e. have their

values drawn from equivalent value distributions, subjects with low values self-select into the

sealed bid auction. We show that this behavior can be explained as a near best response to

the choice and bidding behavior of others.

While investigations of the revenue generation of sealed bid and ascending auctions with

�xed numbers of bidders going back to Cox, Roberson, and Smith (1982) have shown that

the sealed bid auction has a clear revenue advantage, the current results show that this

conventional wisdom fails once entry choice is allowed. Both here and in ISS08 we �nd that

when endogenous entry is allowed revenue rises enough in the ascending auction relative to

the sealed bid to remove the revenue advantage of the sealed bid auction. The intriguing

aspect of the revenue result is that it occurs for very di¤erent reasons in the two studies

based on how bidders select into the two formats. If the entry choices are made behind the

veil of ignorance regarding the bidder�s value (as in ISS0816), revenue is equalized by virtue

of more bidders entering the ascending auction as this delivers higher order statistics for

the values of bidders in the ascending than the sealed bid auctions. If bidders know their

values when deciding which auction to enter (as in this study), the number of bidders in

both formats ends up being on average the same but the sealed bid auctions attract bidders

with lower values. Despite the aggressive bidding of those entering the sealed bid auctions,

the fact that the bidders in the ascending auction have higher values leads to the revenue

again being approximately the same between both formats. The two auction formats also

generate e¢ ciency levels and bidder earnings that are roughly equivalent across mechanisms.

While we do �nd that the revenue between the two formats becomes equalized regardless

of when bidders learn their value, we do not intend this to be taken as a global claim that

revenue is always equalized when endogenous entry choice is allowed. As discussed in the

introduction, while there is no clear theoretical prediction regarding revenue generation in

this environment which accounts for the bidding behavior in the sealed bid auction, were

one to be generated it would almost certainly depend on the exact distribution of risk/regret

16In a related experiment design, Engelbrecht-Wiggans and Katok (2005), �nd the same result as welldemonstrating the robustness of the result to di¤erent con�gurations.

18

preferences of bidders in the auction, the value distribution and so forth. We have certainly

not provided either theoretical or empirical evidence for a global claim about how this revenue

comparison would hold for general value or preference parameter distributions.

We have also yet to investigate environments with more choices between auction formats

and when there might be multiples of the same format leading to situations in which there

are more sealed bid auctions than ascending or vice versa. We can not make strong claims

about revenue comparisons in these situations though expanding to environments like this is

certainly important for future research. Depending on the number of bidders and the number

and con�guration of auctions, a di¤erent result on revenue generation may well be found but

our results do have important insights for what should be expected in these more complex

environments. In environments in which bidders learn their values prior to entry one should

still expect that the bidders will self-select into di¤erent auction formats with regard to their

value for winning. Our prior results indicate that when bidders are ignorant of their value,

one should expect to observe higher numbers of bidders entering into ascending auctions.

While the composition of options might change in these richer environments, the nature

of the strategic di¤erences between ascending and sealed bid auctions will not change and

so the strategic drivers of these selection behaviors observed in these simple environments

should still drive behavior in the richer ones.

Another important implication of these results which should translate into richer envi-

ronments is that the revenue superiority of the sealed bid auction should not be assumed.

Both here and in ISS08 it is shown that endogenous entry ends up equalizing revenue be-

tween formats but as the number and composition of auctions change, that equality could

well no longer hold. In environments in which the value selection pressures are strong or

larger numbers are attracted to ascending auctions, the ascending auction may become rev-

enue dominant. In environments in which the opposite pressures exist, then the sealed bid

auction will likely retain its revenue dominance. Understanding what environmental factors

will lead to which outcome will require careful future work in theoretical modeling as well

as additional empirical investigation.

In order to have a more complete picture of how self-selection by bidders may have driven

the adoption of di¤erent auction formats in di¤erent markets and environments, we must also

eventually move away from exogenously �xed auction formats and allow human auctioneers

to choose which auction formats to use when selling to human bidders and competing with

other human auctioneers. While this is certainly the ultimate goal of this line of research, it

is one that must be worked toward incrementally so that we begin to build up a thorough

19

understanding of the pieces of the dynamics in such markets before attempting to investigate

the more complex interactions all at once. The results presented here represent an important

step towards understanding the dynamics of behavior when endogenous auction choice is

considered but it is certainly not the �nal step.

APPENDIX A: Computation of Expected UtilitiesFor the analysis in this paper we needed to calculate the expected utility and expected

surplus contingent on an observed value since this was known prior to entering into anauction. Since value distributions were not uniform in each institution, this must be takeninto account in the calculations.The equation for calculating expected utility in �rst price auctions is shown in equation

1. To calculate the expected utility in �rst price auctions, we �rst have to sum the expectedutilities of ending up in auctions of sizes 1� 5 and multiply each by the probability of thatauction size occurring. This probability, represented by g(n) will be the empirical frequencyof each auction size. There is an important detail for the FB sessions which is that it wasimpossible for a bidder making a choice to enter a SB auction and have it be a 1 bidderauction. Thus when we wish to compare auctions from the point of view of analyzing achoice by a bidder we will begin the sum at n = 2: For an auction of each size, we simplyhave to calculate the expected utility which is their utility if they win (i.e. v � b(v; �) )multiplied by the probability of winning. For this we are assuming this bidder is biddingaccording to an empirical best response bid function. This empirical best response bidfunction is calculated separately for each level of risk aversion and is based on �nding thebid which would maximize the bidder�s expected utility assuming they face n� 1 other bidsdrawn from the empirical distribution of auctions of size n:While this may seem restrictive,since we calculate this for all � 2 (0; 1] in increments of .01 (though only increments of .1are displayed in the paper) we are able to get a good overall sense of the expected utilitycalculation for any way a subject might bid. We calculate the probability of any bid winningusing a kernel estimate of the distribution of bids based on the empirical bid distributionfrom all auctions conducted of each size which means we are taking no stand in regard tothe process generating the competing bids. Thus, for any bid x we use the kernel densityestimate of the probability that the bidder draws n � 1 opponent bids from the empiricaldistribution that are less than x: This is given by W (x; n)n�1:

EUSB(v; �) =5Xn=1

�(v � bBR(v; �))�W (bBR(v; �); n)n�1

�g(n) (1)

To calculate the expected utilities in the A auction, we must follow a similar approach.Again we sum the expected utility of participating in an auction of size n over all possibleauction sizes and multiply by the empirical fraction of auctions of each size, h(n): Sincebidders in A auctions do bid for the most part as theory predicts, there is no controversyin using their value as their predicted bid but since the distribution of values is no longeruniform there is an additional complication in the calculation. We must add over all thepossible states of the world in which this bidder wins the auction (i.e. when the highest ofthe other n� 2 values are lower) and to �nd the probability of each of these other values is

20

the second highest we must use the CDF J(v; n) and PDF j(v; n) based o¤ of kernel densityestimates from the actual bids instead of the theoretical analogs. This calculation is givenby equation 2.

EUA(v; �) =

5Xn=1

" vXp=0

(v � p)�(n� 1)j(p; n)J(p; n)n�2!#

h(n) (2)

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Cox, J. C., B. Roberson, and V. L. Smith (1982). Theory and Behavior of Single ObjectAuctions. In Research in Experimental Economics, Volume 2, pp. 1�43. JAI Press Inc.

Crawford, V. P. and N. Iriberri (2007). Level-k auctions: Can a nonequilibrium modelof strategic thinking explain the winner�s curse and overbidding in private-value auctions?Econometrica 75 (6), 1721�1770.

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Engelbrecht-Wiggans, R. and E. Katok (2005). Experiments on Auction Valuation andEndogenous Entry. In J. Morgan (Ed.), Experimental and Behavior Economics, Advancesin Applied Microeconomics, Volume 13, pp. 171�196. Elsevier.

Engelbrecht-Wiggans, R. and E. Katok (2007). Regret in Auctions: Theory and Evidence.Economic Theory 33, 81�107.

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21

Ivanova-Stenzel, R. and T. C. Salmon (2008b). Robustness of Bidder Preferences AmongAuction Institutions. Economic Inquiry 46 (3), 355�368.

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22

APPENDIX B: Translated InstructionsPlease, read these instructions carefully. They are identical for all participants.During the experiment you will take part in several auctions. In each auction the bidder

groups are formed randomly. The number of bidders in all auctions is not indentical. At thebeginning of each auction you are informed, how many bidders (incl. you) will participatein this auction.In every auction a �ctitious commodity is for sale which you can resell to the experi-

menters. In every auction the private reselling value v of each bidder is independently drawnfrom the interval 0� v �100 ECU (Experimental Currency Unit), with every integer num-ber between 0 and 100 being equally likely. You are informed only about your own privatevalue. You will not get to know the private value of the other bidders. Note that the valuesof the other bidders are drawn from this same range in an independent manner from yourdraw which means that the value you receive gives you no information on the values drawnby other bidders. There are two di¤erent auction types.

Type 1-Auction:The bidders submit simultaneously their bids, i.e., o¤er a (single) price at which they

are willing to buy the commodity. Every integer between 0 and 150 is permitted as a bid.The bidder with the highest bid within the group buys the commodity. He pays his own bidand receives his reselling value. The other bidders do not pay anything and do not receiveanything. If more bidders have submitted the highest bid, the buyer is chosen randomlywith each bidder having the same probability of winning.To make it clear how this format works, we will show you the details from four sample

auctions representing possible sizes of auctions you could participate in over the course ofthe experiment. In the �rst sample, there are 5 bidders with the values listed in the row ofthe table labeled �Value�. In the next row we have listed bids these players might make.Notice that bidder 1 had the highest bid which means that they win and their payo¤ is listedin the bottom row. All others players have a payo¤ of 0.

Bidder 1 Bidder 2 Bidder 3 Bidder 4 Bidder 5Value (v) 76 52 88 34 15Bid 65 48 64 34 12Payo¤ 11 0 0 0 0

In the second example, there are 4 bidders with di¤erent values from before. In this casebidder 2 submitted the highest bid and their payo¤ is the di¤erence between their value andtheir bid.

Bidder 1 Bidder 2 Bidder 3 Bidder 4Value (v) 5 65 32 18Bid 5 45 30 6Payo¤ 0 20 0 0

In the third example, there are 3 bidders, again with new values. In this case bidders 1and 3 submitted the highest bid. Bidder 3 is chosen randomly among the two as the buyerand their payo¤ is the di¤erence between their value and their bid.

23

Bidder 1 Bidder 2 Bidder 3Value (v) 70 60 85Bid 60 50 60Payo¤ 0 0 25

The last example is a 2 bidder auction, notice that bidder 1 wins.

Bidder 1 Bidder 2Value (v) 87 43Bid 54 12Payo¤ 33 0

These examples for auctions of type 1 were intended to illustrate the range of auctionsizes you might be in over the course of the experiment as well as how the values are drawnand how bids determine the outcome of the auction. The bids in the tables are in no wayintended to be taken as suggested bids as they were randomly generated purely to demonstratethe rules.

Type 2-Auction:The bidding proceeds as follows: A clock starts with price equal to 0 ECU and goes up

one ECU per second until 150 ECU. If the clock displays a price a bidder does not want topay for the good, he can leave the auction by clicking the "OK"-button. The last remainingbidder in the auction becomes the buyer, receives the commodity, and pays the price at whichthe last but one bidder left the auction. The bidders who have already left the auction do notpay anything and do not receive anything. If all last remaining bidders leave the auction atthe same time, the buyer is chosen randomly with each bidder having the same probabilityof winning. If the clock reaches 150 ECU with more than 1 bidder remaining in the buyeragain is chosen randomly among the bidders who didn�t leave the auction. The price thebuyer has to pay for the good is equal to 150 ECU.To make it clear how this format works, we will again show you the details from four

sample auctions. In the �rst sample, there are 5 bidders with the values listed in the rowof the table labeled �Value�. In these tables the bid row indicates the point at which thebidder withdrew from the auction. In this case bidder 1 never withdraws from the auctionwhile bidder 4 is the second to last to withdraw at a price of 76. Bidder 1 wins the auction.He pays the price of 76 where bidder 4 withdrew.

Bidder 1 Bidder 2 Bidder 3 Bidder 4 Bidder 5Value (v) 99 85 62 75 4Bid 72 50 76 2Payo¤ 23 0 0 0 0

In the second example, there are 4 bidders. Bidder 3 is the second to last to drop outleaving bidder 4 in the auction alone. Thus bidder 4 wins at the price where bidder 3 droppedout.

24

Bidder 1 Bidder 2 Bidder 3 Bidder 4Value (v) 13 34 83 55Bid 25 19 45Payo¤ 0 0 0 10

In the third example there are three bidders. Bidder 1 withdraws �rst. Bidders 2 and 3withdraw at the same time at price of 40. The buyer is chosen randomly. Bidder 2 wins atthe price where all last remaining bidders dropped out.

Bidder 1 Bidder 2 Bidder 3Value (v) 23 48 53Bid 12 40 40Payo¤ 0 8 0

The last example is a 2 bidder auction. Here bidder 2 drops out at a price of 39, leavingbidder 1 as the winner paying a price of 39.

Bidder 1 Bidder 2Value (v) 76 24Bid 39Payo¤ 37 0

These examples for auctions of type 2 were again intended to illustrate the range ofauction sizes you might be in over the course of the experiment as well as how the valuesare drawn and how bids determine the outcome of the auction. The bids in the tables arein no way intended to be taken as suggested bids as they were randomly generated purely todemonstrate the rules.

Today�s experiment will consist of two phases.

Phase 1:In the �rst phase you will participate in a series of both type 1 and type 2 auctions. In

each round of this phase, you will be informed of your value for this round and of the numberof bidders you are bidding against. Auction groups are randomly determined (each round)so the auction group you are participating in will likely change from round to round.In every round, after being informed of your value, you will �rst submit your bid for a

type 1 auction. Before learning the outcome of the type 1 auction, you will participate in atype 2 auction using the same value and competing against the same other bidders. At theend of the round, you will be informed of the outcome of both auctions including whether ornot you were the buyer, about the price, which has to be paid by the buyer, your own privatevalue, buyer�s private value and bid, how much pro�t you have earned in each auction andyour total pro�t in this auction round (sum of the pro�ts for both auctions in this round).The next round would then begin in which you would receive a new value, be assigned intoa new auction group and again participate in both a type 1 and type 2 auctions.There will be a total of 12 rounds in this phase, which consists of two cycles of 6 bidding

rounds. In the �rst three rounds of each cycle, each auction you participate in will consist of

25

2 bidders, yourself and one co-bidder. In the last three rounds, each auction will consist of 4bidders, yourself and 3 other bidders. At the beginning of each round you will be informedof the number of bidders you are bidding against in this round.At the conclusion of this phase of the experiment you will be informed about the average

buyer�s pro�t per auction type and number of bidders and your total pro�t up to this time.

Phase 2:The instructions for this phase will be distributed after the �rst phase is completed.

You make all your decisions on the PC. Any decision you make is anonymous and cannotbe related to you personally by your co-bidders.The valid exchange rate from ECU to EURO is: 1 ECU = e 0.10. You receive a show

up fee of e 3.00. If you make losses, these will be balanced with your present pro�t (resp.show up fee).If you have any questions, please, raise your hand. We will then clarify your problems

privately.

Additional Instructions (Phase 2):We will now begin phase 2 of the experiment. This phase will consist of 30 rounds.At the beginning, all participants will be randomly divided into two groups of 6 bidders.

In each round, you and the other bidders in your group will each have the option of choosingto participate in either a type 1 or 2 auction. Thus, the number of bidders in each auctiontype is variable and depends on how many bidders have chosen each auction type.

The next two paragraphs apply only to the FB-treatment:[In order to have at least one bidder per auction type, two participants of each group

will be automatically assigned to one of the two auction types. This means that based uponyour choice of which format to participate in and the choices of the other participants inyour group, you could be in auctions with 2, 3, 4 or 5 bidders. Note that 2 is the minimumbecause even if you are the only one to choose to enter into an auction, there was already oneother bidder automatically placed in that format. The identity of the players who will not beasked to choose the auction type will be changed in each round, so that each participant willnot be allowed to choose the auction type 10 times during the 30 rounds. At the beginningof each round you are informed if you can choose the auction type. If you are automaticallyassigned to an auction type you are also informed in which auction type you are going toparticipate in this round.The previous phase was intended to give you experience with both auction types as well

as with auctions with di¤erent numbers of bidders. While all of those auctions consisted ofeither 2 or 4 bidders, there is no reason that this must be true in this phase. Again, dependingon the choices of yourself and others you could be participating in auctions of 2, 3, 4 or 5bidders. Also note that should you be randomly assigned to an auction type that no one elsechooses to participate in, in that case and that case only, you would be in an auction byyourself allowing you to win at a price of 0. In any round in which you are making a choice,there is no chance for you to be in an auction by yourself. ]

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The next paragraph applies only to the NFB-treatment:[The previous phase was intended to give you experience with both auction types as well

as with auctions with di¤erent numbers of bidders. While all of those auctions consisted ofeither 2 or 4 bidders, there is no reason that this must be true in this phase. Depending onthe choices of yourself and others you could be participating in auctions of 1, 2, 3, 4, 5 or6 bidders. Also note that should you be the only one bidder in an auction, in that case andthat case only, you would win the auction at a price of 0. ]

Your reselling value v is drawn as in the �rst phase at the beginning of each round. Youare informed about your own private value before you make your auction type choice.After all participants have made their choice a chance move determines whether this

auction round will be actually played (with probability 20%). You are informed if theauction will be conducted or not. You are also informed how many bidders will participatein each auction type. If the auction round will be carried out, you will participate in theauction type you have chosen in the same way as in the �rst phase.At the end of each actually played auction round you are informed whether or not you

are the buyer, about the price, which has to be paid by the buyer, and how much you haveearned in this auction. You are informed again about your own private value in this auction.At the end of this phase you will be informed about your total pro�t in this phase.If you have any questions, please, raise your hand. We will then clarify your problems

privately.

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