Experimental Business Research II springer 2005 phần 5 pot

I
NTERNET
II
C
T
O
N
G
E
S
TI
ON
95
A
C
KN
O
WLED
G
MEN
T
T
he National Science Foundation funded this work under grant IIS-9986651. We are
a
lso
g
rateful for the research assistance of Alessandra Cassar, Garrett Milam, Ralf
H
epp, an
d
Ka

i
Pommeren
k
e, an
d
t
h
e programm
i
ng support o
f
Ne
il
Macnea
l
e, Jerem
y
Avnet an
d
N
i
ta
i
Farmer. We
b
ene
fi
te
d

f
rom comments
b
y co
ll
eagues
i
nc
l
u
di
ng
J
oshua Aizenman, Eileen Brooks, Ra
j
an Lukose, Nirvikar Sin
g
h, and Donald Wittman
,
a
n
d

b
y HKUST con
f
erence part
i
c
i

pants, espec
i
a
ll
y Yan C
h
en, Rac
h
e
l
Croson an
d
Er
i
c Jo
h
nson. S
i
gn
ifi
cant
i
mprovements to t
h
e
fi
na
l
vers
i

on are
d
ue to t
h
e comments
o
f an anon
y
mous referee
.
N
O
TE
S
1
T
h
e s
i
mu
l
at
i
ons reporte
d

i
n Maurer an
d
Hu

b
erman (2001) suggest an a
l
ternat
i
ve
h
ypot
h
es
i
s: pro
fi
ts
i
ncrease
i
n no
i
se amp
li
tu
d
e t
i
mes (
s
−
1
/

1
2
)
, w
h
ere
s

i
s t
h
e
f
ract
i
on o
f
p
l
ayers
i
n auto mo
d
e. It s
h
ou
ld

b
e

noted that their bot al
g
orithm supplemented Rule R with a Reload option.
2
Indeed, a referee of our grant proposal argued that it was redundant to use human subjects. He thought
it obvious that the bots would
p
erform better
.
3
T
hi
s var
i
a
bl
e
i
s generate
d

b
y summ
i
ng up t
h
e t
i
mes
f

or success
f
u
l
(t
h
e
d
own
l
oa
d
too
k

l
ess t
h
an or
exactl
y
ten seconds) and unsuccessful (failed download attempt, i.e., no download within ten seconds)
download attem
p
ts that were completed within the last ten seconds
.
The result is then divided b
y
the
number of download attempts to lead to the average delay (

AD
(
(
)
. T
h
e var
i
a
bl
e
i
s cont
i
nuous
l
y up
d
ate
d
.
T
i
mes
f
or
d
own
l
oa

d
attempts t
h
at
h
ave
b
een a
b
orte
d
(
b
y t
h
e p
l
ayer
hi
tt
i
ng t
h
e “STOP” or t
h
e
“RELOAD” button) are disre
g
arded
.

R
EFEREN
C
E
S
Anderson, S., Goeree, J. and Holt, C., (Au
g
ust 1998). “The All-Pa
y
Auction: Equilibrium with Bounded
R
ationality.
”
J
ournal o
f
Political Economy
,
106(4), 828–8
5
3
.
C
ox J. C. and Friedman, D. (October 2002). “A Tractable Model of Reciprocity and Fairness,” UCSC
Manuscr
i
pt.
F
eller, William, (1968). An Introduction to Probabilit
y

Theor
y
and Its Applications, Vol 2. NY: Wile
y
.
F
riedman, Eric, Mikhael Shor, Scott Schenker, and Barr
y
Sopher, (November 30, 2002). “An Experiment
on Learn
i
ng w
i
t
h
L
i
m
i
te
d
In
f
ormat
i
on: Nonconvergence, Exper
i
mentat
i
on Casca

d
es, an
d
t
h
eA
d
vantage
o
f
Be
i
ng S
l
ow.” Games an
d
Economic Be
h
avio
r
(forthcoming).
r
E
conomist ma
g
azine, “Robo-traders,” Nov. 30, 2002, p. 6
5
.
Gardner, Roy, Ostrom, Elinor and Walker, James, (June 1992). “Covenants With and Without a Sword:
Self-Governance is Possible.”

A
merican Political
S
cience Re
v
ie
w
, 86
(
2
)
, 404–417
.
H
e
h
en
k
amp, Bur
kh
ar
d
, Le
i
n
i
nger, Wo
lf
gang, an
d

Possa
j
enn
ik
ov, A
l
ex, (Decem
b
er 2001). “Evo
l
ut
i
onary
Rent Seekin
g
.” CESifo Workin
g
Paper
6
20.
M
aurer, Sebastian and Bernardo Huberman, (2001). “Restart Strate
g
ies and Internet Con
g
estion.”
J
ourna
l
of Economic Dynamics & Control

25, 641–654.
l
Oc
h
s, Jac
k
, (May, 1990). “T
h
e Coor
di
nat
i
on Pro
bl
em
i
n Decentra
li
ze
d
Mar
k
ets: An Exper
i
ment.” T
h
e
Quarterly Journal o
f
Economic

s
, 10
5
(2),
5
4
5
–
55
9.
Rapoport, A., Seale, D. A., Erev, I., & Sundali, J. A., (1998). “Equilibrium Play in Large Market Entry
Games.”
M
ana
g
ement Scienc
e
,
44
,
119–141.
Rapoport, A., Ste
i
n, W., Parco, J. an
d
Sea
l
e, D., (Ju
ly
2003). “Equ

ilib
r
i
um P
l
a
y

i
n S
i
n
gl
e Server Queues
wi
t
h
En
d
o
g
enous
ly
Determ
i
ne
d
Arr
i
va

l
T
i
mes.” Un
i
vers
i
t
y
o
f
Ar
i
zona Manuscr
i
pt.
Seale, D., Parco, J., Stein, W. and Rapoport, A., (Januar
y
2003). “Joinin
g
a Queue or Sta
y
in
g
Out: Effects
of
In
f
ormat
i

on Structure an
d
Serv
i
ce T
i
me on Large Group Coor
di
nat
i
on.” Un
i
vers
i
ty o
f
Ar
i
zona
M
anuscr
i
pt.
Stahl, D. O. and Wilson, P., (199
5
). “On Pla
y
ers’ Models of Other Pla
y
ers – Theor

y
and Experimental
E
vidence.
”
G
ames and Economic Beha
v
ior
,
1
0, 213–2
5
4
.
96 Ex
p
erimental Business Research Vol. I
I
A
PPENDIX A. TE
C
HNI
C
AL DETAIL
S.
A.1. Latency and Noise.
F
ollowin
g

the nois
y
M/M/1 queuin
g
model of Maurer
and Huberman (2001), latenc
y
for a download request initiated at time
t
i
s
λ
()
λ
[ ()]
()
S
[ (
(
(
(

+
1
(
A1
)
i
f the denominator is
p

ositive, and otherwise is
λ
max
λ
λ
>
0. To un
p
ack the ex
p
ressio
n
(A1), note t
h
at t
h
e su
b
scr
i
pte
d

“
+
” re
f
ers to t
h
e pos

i
t
i
ve part,
i
.e.,
[
x
]
+
= max
{
x
,
0}
.
T
he
p
aramete
r

C
is the capacity chosen for that period; more precisely, to remain
C
c
onsistent with conventions in the literature,
C
represents full capacity minus 1. The
C

paramete
r
S
is the time scale, or constant of proportionality, and
S
U
(
t
)
i
s usage, t
h
e
n
umber of downloads initiated but not
y
et completed at time
t
.
The ex
p
erimen
t
truncates the latenc
y
computed from (A1) to the interval [0.2, 10.0] seconds. The
l
ower truncat
i
on earns t

h
e 10 po
i
nt rewar
d

b
ut t
h
e upper truncat
i
on a
t

λ
max
λ
λ
=
1
0
s
econds does not
.
T
h
e
r
a
n

do
m n
o
i
se

e
(
t
) is Normall
y
distributed with volatilit
y

σ
and unconditional
σ
m
ean 0. T
h
e no
i
se
i
s mean revert
i
ng
i
n cont
i

nuous t
i
me an
d

f
o
ll
ows t
h
e Ornste
i
n-
U
hlenbeck
p
rocess with
p
ersistence
p
arameter
τ
>
0 (see Feller,
p
. 336). That is,
e
(0)
=
0 and,

g
iven the previous value
x
=
e
(
t
−
h
)
drawn at time
t
−
h
>
0, the
a
l
gor
i
t
h
m
d
raws a un
i
t Norma
l
ran
d

om var
i
ate
z
an
d
sets
e
(
t
)
=
x
exp
(
−
τ
h
)
+
zh
[ exp( )]/( ).
h
τ
h
)]/(
h
τ
τ
h

Thus the conditional mean of noise is t
y
picall
y
differen
t
from zero; it is the most recentl
y
observed value
x
s
hrunk towards zero via a
n
e
xponent
i
a
l
term t
h
at
d
epen
d
s on t
h
e t
i
me
l

ag
h
si
nce t
h
e o
b
ser
v
at
i
on
w
as ma
d
e
a
n
d

a

s
hrink r
ate

τ
>
0. In the no-
p

ersistence (i.e., no mean reversion or shrink-
i
n
g
) limit
τ
→
0, we have Brownian motion with conditional variance
σ
2
h
, an
d
e
(
t
)
=
x
+
zh
.
In t
h
e
l
ong run
li
m
i

t as
h
→
∞

w
e reco
v
er t
h
e uncon
di
t
i
ona
l
varianc
e
σ
2
/(2
τ
). The appropriate measure of noise amplitude in our setting there-
τ
fore is its s
q
uare roo
t

στ

/.
τ
τ
τ
I
n our exper
i
ments we use
d
two
l
eve
l
s eac
h

f
o
r

σ
and
σ
τ
. Rescaling time in
τ
s
econds instead of milliseconds, the levels are 2.
5
and 1.

5
for
σ
, and 0.2 and 0.02
σ
f
o
r
τ
. Figure A1 shows typical realizations of the noise factor [1
τ
+
e
(
t
)]
+
f
o
r
t
h
e
two com
bi
nat
i
ons use
d
most

f
requent
l
y,
l
ow amp
li
tu
d
e (
l
ow
σ
,
hi
g
h
τ
) an
d

hi
g
h
amplitude (hi
g
h
σ
, low
σ

τ
)
.
A.2. E
ffi
c
i
enc
y
, no no
i
se case.
S
oc
i
a
l

v
a
l
ue
V
is the average net benefit
V
π
=
r
−
λ

c
p
er download times the total number of downloads
n
≈
UT
/
T
T
λ
, where
λ
λ
is the avera
g
e
l
atency,
T
is the length of a period and
T
U
is the average number of users attempting
U
t
o
d
o
w
n

l
oa
d
. Assume t
h
at
σ
=
0 (no
i
se amp
li
tu
d
e
i
s zero) so
b
y (A1) t
h
e averag
e
latenc
y
is
λ
=
S
/(1
S

S
+
C
−
U
)
. Assume also that the ex
p
ression fo
r

n
is exact
.
Then
th
e
fi
rst or
d
er con
di
t
i
on (ta
ki
ng t
h
e
d

er
i
vat
i
ve o
f

V
=
π
n
wi
t
h
respect to
U
an
d
fi
n
di
ng t
h
e root) y
i
e
ld
s
U
*

= 0.5
(
1
+
C
−
cS
/
S
S
r
)
. T
h
us
λ
*
λ
=
2
S
/(1
SS
+
C
+ c
S
/r
)
, an

d
s
o
m
aximized social value is
V
*
=
0.2
5
S
−
1
Tr
(1
+
C
−
c
S/r
)
2
.
I
NTERNET
II
C
T
O
N

G
E
S
TI
ON
97
0
.
2
0
.
4
0
.
6
0.
8
1
1.
2
1
.
4
1
.
6
Ti
m
e
H

i
g
h volatilit
y
L
ow volatilit
y
F
i
g
ure A1. Noise (exp 10/3/03, periods 1 and 4)
.
To obtain the u
pp
er bound on social value consistent with Nash e
q
uilibrium,
suppose t
h
at more t
h
an 10 secon
d
s rema
i
n, t
h
e p
l
ayer current

l
y
i
s
idl
e an
d
t
h
e
e
xpected latenc
y
for the current download is
λ
. The zero-profit latency is derived
λ
f
rom 0
=
π
=
r
−
λ
c.
N
o
w
λ

=
r
/
rr
c

a
n
d

t
h
e

assoc
i
ated
n
u
m
be
r
o
f
use
r
s
i
s

U
**
=
2
U
*
=
C
+

1

−
c
S
/r
.
Hence t
h
e m
i
n
i
mum num
b
er o
f
users cons
i
stent

wi
t
h
NE
i
s
U
M
N
E
=
U
*
*
−
1
=
C
−
c
S/r
.
The associated latenc
y
is
λ
MNE
λ
λ
=

rS
/(
S
S
r
+
cS
)
, and the associated
p
rofit
p
er download is
π
MNE
=
r
2
/
(
r
+
cS
)
, inde
p
endent o
f

C

.
The maximum number
of

d
o
w
n
l
oa
d
s
i
s
N
MNE
=
TU
MNE
U
U
/
E
λ
MNE
λ
λ
=
T
(

TT
r
+
c
S
)(
r
C
−
cS
)/(
r
2
S
)
. Hence t
h
e upper
bound on NE total
p
rofit is
V
MNE
=
N
MNE
π
MNE
=
T

(
TT
r
C
−
c
S
)/
S
, and the maximum N
E
e
fficiency is
V
MNE
VV
/
E
V
*
=
(
C
−
c
S/r
)/(1
+
C
−

cS/
r
)
2
=
4
U
MNE
/(1
E
+

U
MNE
)
2
≡
Y
. Since
d
U
MNE
/d
E
C
=
1
,

i

t
f
o
ll
ows t
h
at
d
Y
/d
Y
Y
C
<

0

iff

d
Y
/d
YY
U
MNE
<

0

iff

1
<
U
MNE
=
C
−
c
S
/
r
.
I
t is eas
y
to verif
y
tha
t

Y
is 0(1/
Y
C
)
.
A
.3 Bot algor
i
thm

.
In
b
r
i
e
f
, t
h
e
b
ot a
l
gor
i
t
h
m uses Ru
l
e R w
i
t
h
a ran
d
om t
h
res
h
o

ld
ε
drawn independently from the uniform distribution on [0, 1.0] sec. The value of
ε
λ
is the mean reported in the histogram window, i.e., the average for download
λ
requests comp
l
ete
d

i
n t
h
e
l
ast 10 secon
d
s. Between
d
own
l
oa
d
attempts t
h
e a
l
gor-

i
thm waits a random time drawn independentl
y
from the uniform distribution on
[
.2
5
, .7
5
] sec
.
I
n
d
eta
il,

b
ots
b
ase t
h
e
i
r
d
ec
i
s
i

on on w
h
et
h
er to
i
n
i
t
i
ate a
d
own
l
oa
d
on two
factors. One of these determinants is the variable “avera
g
e dela
y
”
3
(
AD
(
(
)
. The secon
d

f
actor is a confi
g
urable randoml
y
drawn threshold value. In each period, bots (and
rea
l
p
l
ayers
i
n automat
i
c mo
d
e)
h
ave t
h
ree
b
e
h
av
i
or sett
i
ngs t
h

at can
b
e set
b
y t
h
e
e
xperimenter. If the
y
aren’t defined for a
g
iven period, then the previous settin
g
s are
98 Ex
p
erimental Business Research Vol. I
I
u
se
d
, an
d

if
t
h
ey are never set, t
h

en t
h
e
d
e
f
au
l
t sett
i
ngs are use
d
. An examp
l
e (us
i
ng
t
h
e
d
e
f
au
l
t sett
i
n
g
s)

i
s
AutoBe
h
av
i
or P
l
ayer 1: M
i
nT
h
res
h
o
ld
4000, Ran
d
omW
id
t
h
1000, Pre
di
ctTren
d
Di
sa
bl
e

d
Th
e
d
e
fi
n
i
t
i
ons are:
1) MinThreshold (
MT
): The lowest
p
ossible threshold value in milliseconds. If the
a
verage
d
e
l
ay
i
s
b
e
l
ow t
hi
s m

i
n
i
mum t
h
res
h
o
ld
, t
h
en t
h
ere
i
s 100% certa
i
nty
t
h
at t
h
e ro
b
ot (or p
l
a
y
er
i

n Auto mo
d
e) w
ill
attempt a
d
own
l
oa
d

if
not a
l
rea
dy
d
ownloadin
g
. The default settin
g
is 4000
(
=
4 seconds)
.
2)
Ran
d
om W

id
t
h

(
R
W
)
: T
h
e ran
d
om
d
raw
i
nterva
l
w
id
t
h

i
n m
illi
secon
d
s. T
hi

s
is
t
h
e max
i
mum ran
d
om
v
a
l
ue t
h
at can
b
e a
dd
e
d
to t
h
e m
i
n
i
mum t
h
res
h

o
ld

v
a
l
ue
to determine the actual threshold value instance. That is,
MT
+
RW
=
Max
T
h
res
h
o
ld
Va
l
u
e
.
3
)
Pre
di
ct Tren
d

(
PT
)
: T
h
e
d
e
f
au
l
t sett
i
ng
i
s D
i
sa
bl
e
d
. However, w
h
en Ena
bl
e
d
, t
h

e
f
ollowin
g
linear trend prediction al
g
orithm is used:
MT
2
T
T
=
MT
+
AD
2
−
AD
.
A
n
ew M
i
n
i
mum T
h
res
h
o

ld

(
MT
2
TT
)
i
s ca
l
cu
l
ate
d
an
d
use
d

i
nstea
d
o
f
t
h
e or
i
g
i

na
l
M
i
n
i
mum T
h
res
h
o
ld
va
l
ue
(
M
T
). The average delay (
AD
(
(
)

f
rom exact
l
y 2 sec-
onds ago (
AD

(
(
2
)
is used to determine the new Minimum Threshold value.
A
b
ot w
ill
attempt a
d
own
l
oa
d
w
h
en
AD
≤
T
=
M
T
+
R
D. A ne
w
t
h

res
h
o
ld

v
a
l
u
e
(
T
) will be drawn
(
RD
from a uniform distribution on [0,
RW
]
) after each download
a
ttempt
b
y t
h
e ro
b
ot. Anot
h
er
i

mportant
f
eature o
f
t
h
e ro
b
ot
b
e
h
av
i
or
i
s t
h
at a ro
b
ot
w
ill
never a
b
ort a
d
own
l
oa

d
attempt.
To avoid artificial s
y
nchronization of robot download attempts, the robots check
on
AD
e
v
er
y
x
seconds, where
x
x
is a uniformly distributed random variable on
x
[.05, .15] seconds. Also, there is a delay (randomly picked from the uniform dis-
tribution on [.1
5
, .4
5
] seconds) after a download (successful or unsuccessful) has
b
een comp
l
ete
d
an
d

b
e
f
ore t
h
e ro
b
ot
i
s perm
i
tte
d
to
d
own
l
oa
d
aga
i
n. Bot
h

d
e
l
ays
a

re
d
rawn
i
n
d
epen
d
ent
ly

f
rom eac
h
ot
h
er an
d

f
or eac
h
ro
b
ot a
f
ter eac
h

d

own
l
oa
d
a
ttem
p
t. The absolute maximum time a robot could wait after a download attem
p
t
en
d
s an
d

b
e
f
ore
i
n
i
t
i
at
i
ng a new
d
own
l

oa
d
(g
i
ven t
h
a
t

AD
i
s su
ffi
c
i
ent
l
y
l
ow)
i
s t
h
us
450
m
s
+
1
50

ms
=

600
ms
.
APPENDIX B: STARCATCHER INSTRUCTIONS
UCSC 2/200
3
I
.
G
ENERAL
You are a
b
out to part
i
c
i
pate
i
n an exper
i
ment
i
n t
h
e econom
i
cs o

f

i
nter
d
epen
d
ent
d
ec
i
s
i
on-ma
ki
n
g
. T
h
e Nat
i
ona
l
Sc
i
ence Foun
d
at
i
on an

d
ot
h
er
f
oun
d
at
i
ons
h
ave
I
NTERNET
II
C
T
O
N
G
E
S
TI
ON
99
p
rov
id
e
d

t
h
e
f
un
di
ng
f
or t
hi
s pro
j
ect. I
f
you
f
o
ll
ow t
h
ese
i
nstruct
i
ons care
f
u
ll
y an
d

m
a
k
e goo
d

d
ec
i
s
i
ons, you can earn a CONSIDERABLE AMOUNT OF MONEY,
which will be PAID TO YOU IN CASH at the end of the ex
p
eriment.
Your computer screen w
ill

di
sp
l
ay use
f
u
l

i
n
f
ormat

i
on regar
di
ng your payo
ff
s an
d
r
ecent networ
k
congest
i
on. Remem
b
er t
h
at t
h
e
i
n
f
ormat
i
on on your computer screen
i
s PRIVATE. In order to insure best results for
y
ourself and accurate data for the
e

xper
i
menters, p
l
ease
d
o not commun
i
cate w
i
t
h
t
h
e ot
h
er part
i
c
i
pants at any po
i
nt
d
ur
i
ng t
h
e exper
i

ment. I
f
you
h
ave any quest
i
ons, or nee
d
ass
i
stance o
f
any
ki
n
d
,
r
aise
y
our hand and somebod
y
will come to
y
ou.
I
n t
h
e exper
i

ment you w
ill

i
nteract w
i
t
h
a group o
f
ot
h
er part
i
c
i
pants over a
n
um
b
er o
f
per
i
o
d
s. Eac
h
per
i

o
d
w
ill

l
ast severa
l
m
i
nutes. In eac
h
per
i
o
d
you earn
“p
oints” which are converted into cash at a
p
re-announced rate that is written on
t
h
e
b
oar
d
. You earn po
i
nts

b
y
d
own
l
oa
di
ng stars. Eac
h
star success
f
u
ll
y
d
own-
l
oa
d
e
d
g
i
ves you 10 po
i
nts,
b
ut wa
i
t

i
ng
f
or a star to
d
own
l
oa
d

i
ncurs a cost. Every
s
econd that it takes to download the star will cost
y
ou 2 points. For example, if
y
ou start a
d
own
l
oa
d
an
d

i
t comp
l
etes

i
n 2 secon
d
s, your
d
e
l
ay cost
i
s 4 = 2 po
i
nt
s
per secon
d
t
i
mes 2 secon
d
s. T
h
ere
f
ore
i
n t
hi
s examp
l
e you wou

ld
earn 10
−

4
=
6

p
oints.
Down
l
oa
d

d
e
l
ays range up to 10 secon
d
s,
d
epen
di
ng on t
h
e num
b
er o
f

ot
h
er
part
i
c
i
pants try
i
ng to
d
own
l
oa
d
at t
h
e same t
i
me an
d

b
ac
k
groun
d
congest
i
on. T

h
e
d
ela
y
cost can exceed the value of the download, so
y
ou can lose mone
y
when
t
h
e networ
k

i
s congeste
d
. I
f
t
h
e
d
own
l
oa
d
ta
k

es 9 secon
d
s you wou
ld
earn 10
−
2*9
=
−
8
po
i
nts, a negat
i
ve payo
ff
s
i
nce t
h
e
d
e
l
ay cost (18)
i
s
l
arger t
h

an t
h
e va
l
ue
of a star (10). Of course
y
ou can wait till the con
g
estion clears: that wa
y

y
ou don’t
m
a
k
e money,
b
ut ne
i
t
h
er w
ill
you
l
ose any. Do
i
ng not

hi
ng earns you zero,
b
ut a
l
so
c
osts zero.
I
I. A
C
TI
O
N
S
You have four action buttons: DOWNLOAD, RELOAD, STOP or GO TO AUTO-
MATIC. C
li
c
ki
ng t
h
e DOWNLOAD
b
utton starts to
d
own
l
oa
d

a star, an
d
a
l
so starts
to accumu
l
ate
d
e
l
ay costs, unt
il
e
i
t
h
er:
–
T
h
e star appears on your screen, so you earn 10 po
i
nts m
i
nus t
h
e
d
e

l
ay cost; or
–
T
h
e star
d
oes not appear w
i
t
hi
n 10 secon
d
s, so you
l
ose 20 po
i
nts; or
–
You click the STOP button before 10 seconds elapse, so
y
ou lose twice the
num
b
er o
f
secon
d
s e
l

apse
d
; or
–
You c
li
c
k
t
h
e RELOAD
b
utton. T
hi
s
i
s
lik
e
hi
tt
i
ng STOP an
d
DOWNLOAD
immediatel
y
after
.
W

h
en you c
li
c
k
GO TO AUTOMATIC a computer a
l
gor
i
t
h
m
d
ec
id
es
f
or you w
h
en
to download. There sometimes are computer pla
y
ers (in addition to
y
our fellow
h
umans) w
h
o are a
l

ways
i
n AUTOMATIC. T
h
e a
l
gor
i
t
h
m ma
i
n
l
y
l
oo
k
s at t
h
e
l
eve
l
o
f
recent congest
i
on an
d

d
own
l
oa
d
s w
h
en
i
t
i
s not too
l
arge.
100 Ex
p
erimental Business Research Vol. I
I
I
II.
SC
REEN INF
O
RMATI
O
N
Your screen g
i
ves you use

f
u
l

i
n
f
ormat
i
on to
h
e
l
p you c
h
oose your act
i
on. T
h
e ma
i
n
window reports con
g
estion on the network (how man
y
people were downloadin
g
) in
t

h
e
l
ast 10 secon
d
s. T
h
e
h
or
i
zonta
l
ax
i
s s
h
ows t
h
e
d
e
l
ay t
i
me (
f
rom 0 to 10 secon
d
s)

a
n
d
t
h
e
h
e
i
g
h
t o
f
eac
h
vert
i
ca
l

b
ar represent t
h
e num
b
er o
f
success
f
u

l

d
own
l
oa
d
s.
For example, in the 10 seconds slice of histor
y
shown in Fi
g
ure 1, one successful hit
too
k
one secon
d,
4 success
f
u
l

hi
ts too
k
two secon
d
s
,
10 too

k
t
h
ree secon
d
s
,
10 too
k
f
our secon
d
s
,
4 too
k

fi
ve secon
d
s
,
etc. T
h
e co
l
or o
f
t
h

e
b
ar
i
n
di
cates w
h
et
h
er t
h
e
pa
y
off from the download was positive (
g
reen) or ne
g
ative (red). The Black bar
o
n t
h
e r
i
g
h
t
i
n

di
cates t
h
e num
b
er o
f
peop
l
e w
h
o wa
i
te
d
unsuccess
f
u
ll
y
f
or a star.
Th
eB
l
ue
b
ar (not s
h
own

i
n p
i
cture)
i
n
di
cates t
h
e num
b
er o
f
peop
l
e w
h
o
hi
t Stop
o
r Reload
.
I
NTERNET
II
C
T
O
N

G
E
S
TI
ON
101
J
ust
b
e
l
ow t
h
e grap
h
s
h
ow
i
ng recent tra
ffi
c
i
s a
h
or
i
zonta
l
status

b
ar. T
hi
s “status
bar” has the same horizontal time scale as the
g
raph above but shows the time of
YOUR CURRENT download. When
y
ou click the “DOWNLOAD” button, a verti-
c
a
l

b
ar w
ill
appear
i
n t
h
e
f
ar
l
e
f
t s
id
e o

f
t
hi
s status
b
ar. T
h
e
h
e
i
g
h
t o
f
t
hi
s
b
ar
represents the net pa
y
off of a successful download if it finished at that tim
e
.
As
y
o
u
wait for the download, this bar moves from left to ri

g
ht and shrinks as
y
our dela
y
c
osts accumu
l
ate. I
f
t
h
e
d
own
l
oa
d
ta
k
es so
l
ong t
h
at t
h
e
d
e
l

ay cost excee
d
s t
h
e 10 pt.
v
alue of the star, this bar drops below the middle line, indicatin
g
a ne
g
ative pa
y
off.
N
OTE: Pushin
g
the STOP button at an
y
point will
g
ive
y
ou a lower pa
y
off than
t
h
e
b
ar

i
n
di
cates
b
y 10 po
i
nts s
i
nce you w
ill
not get t
h
e va
l
ue o
f
t
h
e star
b
ut st
ill
pay
the dela
y
cost.
I
n the window “Current Information”
y

ou will find out how much time passed on
your
l
ast
d
own
l
oa
d
attempt (De
l
ay), w
h
at your earn
i
ngs were
f
or t
h
e
l
ast
d
own
l
oa
d
a
ttempt (Points), the number of
y

our successful downloads in this period (Success-
ful Downloads),
y
our total amount of points for this period (Point), the time left
i
n t
h
e current per
i
o
d
(T
i
me Le
f
t), an
d
t
h
e t
i
me nee
d
e
d

f
or a
d
own

l
oa
d

i
n t
h
e
l
ast
10 seconds, avera
g
ed across all pla
y
ers (Group Avera
g
e Dela
y
).
After the end of the first period two windows will appear on the ri
g
ht side of
your screen. T
h
e top one
di
sp
l
ays
i

n
f
ormat
i
on a
b
out your act
i
v
i
ty
i
n t
h
e prev
i
ous
p
eriods: number of attem
p
ted downloads (Tries), number of successful downloads
(Hits), points (Winnin
g
s),
y
our avera
g
e points per tr
y
(Avera

g
e), and a runnin
g
total
o
f
your payo
ff
s
f
or a
ll
per
i
o
d
s (Tota
l
). T
h
e
b
ottom w
i
n
d
ow s
h
ows t
h

e same stat
i
st
i
cs
for the entire
g
roup. These windows will sta
y
on
y
our screen and will be updated at
the end of each
p
eriod
.
I
V. P
A
YMEN
T
Th
e computer a
dd
s up your payo
ff
s over a
ll
per
i

o
d
s
i
n t
h
e exper
i
ment. T
h
e
l
ast
v
alue in the ‘Total’ column in the ‘Your Performance’ window determines
y
our
102 Ex
p
erimental Business Research Vol. I
I
pa
y
ment at t
h
e en
d
o
f
t

h
e exper
i
ment. T
h
e mone
y

y
ou w
ill
rece
i
ve
f
or eac
h
po
i
n
t
will be announced and written on the board. After the ex
p
eriment, the conductor will
c
a
ll
you up
i
n

di
v
id
ua
ll
y to ca
l
cu
l
ate your net earn
i
ngs. You w
ill
s
i
gn a rece
i
pt an
d
receive
y
our cash pa
y
ment of $5 for showin
g
up, plus
y
our net earnin
g
s.

V
. FREQUENTLY ASKED QUESTIONS
Q:
W
hat happens if m
y
net earnin
g
s are ne
g
ative? Do I have to pa
y

y
ou
?
A:
No. To ma
k
e sure t
h
at t
hi
s never
h
appens, you w
ill

b
e as

k
e
d
to
l
eave t
h
e
e
xper
i
ment
if

y
our tota
l
earn
i
n
g
s start to
b
ecome ne
g
at
i
ve. In t
h
at case

y
ou
would receive onl
y
the $5 show up fee.
Q:
Is t
hi
s some
ki
n
d
o
f
psyc
h
o
l
ogy exper
i
ment w
i
t
h
an agen
d
a you
h
aven’t to
ld

us?
A:
No. It
i
s an econom
i
cs exper
i
ment. I
f
we
d
o an
y
t
hi
n
g

d
ecept
i
ve, or
d
on’t pa
y
y
ou cash as described, then
y
ou can complain to the campus Human Sub

j
ects
C
omm
i
ttee an
d

w
e
will

b
e
i
n ser
i
ous trou
bl
e. T
h
ese
i
nstruct
i
ons are on t
h
e
l
e

v
e
l
an
d
our
i
nterest
i
s
i
n see
i
n
g

h
ow peop
l
e ma
k
e
d
ec
i
s
i
ons
i
n certa

i
n s
i
tuat
i
ons.
Q:
I
f I push STOP or RELOAD before a download is finished I
g
et a ne
g
ativ
e
p
ayo
ff
? W
h
y?
A:
Once
y
ou start a
d
own
l
oa
d
,

d
e
l
a
y
costs
b
e
gi
n to accumu
l
ate. T
h
ese costs are
deducted from
y
our total points even if
y
ou stop to download b
y
clickin
g
STOP
or REL
O
AD
.
Q
: How
i

s con
g
est
i
on
d
eterm
i
ne
d
?
A:
Con
g
estion is determined mainl
y
b
y
the number of download requests b
y

y
ou
an
d
ot
h
er part
i
c

i
pants (
h
umans an
d
computer p
l
ayers). But t
h
ere
i
s a
l
so a
r
an
d
om component so somet
i
mes t
h
ere
i
s more or
l
ess
b
ac
kg
roun

d
con
g
est
i
on.
E
XPERIMENTAL
EE
E
L
V
IDEN
CE
O
N
THE
E
E
NDOGENOUS
E
E
E
S
NTRY
EE
OF
B
F
IDDER

S
103
103
Chapter
5
EXPERIMENTAL EVIDEN
C
E
O
N THE END
OG
EN
OUS
ENTRY
O
F BIDDER
S
IN INTERNET A
UC
TI
O
N
S
Dav
id
H. Re
il
ey
1
University o

f
Arizon
a
A
bstrac
t
T
his paper tests the empirical predictions of recent theories of the endo
g
enous entr
y
of

bidd
ers
i
n auct
i
ons. Data come
f
rom a
fi
e
ld
exper
i
ment,
i
nvo
l

v
i
ng sea
l
e
d
-
bid
a
uct
i
ons
f
or co
ll
ect
ibl
e tra
di
n
g
car
d
s over t
h
e Internet. Man
i
pu
l
at

i
n
g
t
h
e reserve
prices in the auctions as an experimental treatment variable
g
enerates several results.
F
i
rst, o
b
serve
d
part
i
c
i
pat
i
on
b
e
h
av
i
or
i
n

di
cates t
h
at
bidd
ers cons
id
er t
h
e
i
r
bid
su
b
-
mi
ss
i
on to
b
e cost
ly
, an
d
t
h
at
bidd
er part

i
c
i
pat
i
on
i
s
i
n
d
ee
d
an en
d
o
g
enous
d
ec
i
s
i
on.
Second, the participation is more consistent with a mixed-strate
gy
entr
y
equilibrium
t

h
an w
i
t
h
a
d
eterm
i
n
i
st
i
c equ
ilib
r
i
um. T
hi
r
d
, t
h
e
d
ata re
j
ect t
h
e pre

di
ct
i
on t
h
at t
h
e
pro
fi
t-max
i
m
i
z
i
n
g
reserve pr
i
ce
i
s
g
reater t
h
an or equa
l
to t
h

e auct
i
oneer’s sa
l
va
g
e
v
alue for the
g
ood, showin
g
instead that a zero reserve price provides hi
g
her
e
xpecte
d
pro
fi
ts
i
n t
hi
s case.
1
. INTR
O
DU
C

TI
O
N
T
he earliest theoretical models of auctions assumed a fixed number N of
p
arti-
c
ipating bidders, with the number commonly known to the auctioneer and the
part
i
c
i
pat
i
n
g

bidd
ers. More recent mo
d
e
l
s
h
ave re
l
axe
d
t

hi
s assumpt
i
on, cons
id
er-
i
n
g
the possibilit
y
of costl
y
bidder participation, so that the actual number of
participating bidders is an endogenous variable in the model. In this paper, I use a
fi
e
ld
exper
i
ment, auct
i
on
i
n
g
severa
l

h

un
d
re
d
co
ll
ect
ibl
e tra
di
n
g
car
d
s
i
n an ex
i
st
i
n
g
m
arket on the Internet, to test the assum
p
tions and the
p
redictions of models of
a
uctions with endogenous entry

.
I
concentrate on t
h
ree emp
i
r
i
ca
l
quest
i
ons
i
n t
hi
s paper. F
i
rst, can an exper
i
-
m
ent turn up evidence of endo
g
enous entr
y
behavior in a real-world market?
T
he answer to this question appears to be yes. Second, given the existence of
e

n
d
o
g
enous entr
y
,
d
oes t
h
e entr
y
equ
ilib
r
i
um appear to
b
e
b
etter mo
d
e
l
e
d
as stoc
h
ast
i

c,
o
r as deterministic? Evidence from the ex
p
eriment indicates that the stochastic
e
quilibrium concept is a better model of behavior. Third, is it possible to verify the
t
h
eor
y
o
f
McA
f
ee, Quan, an
d
V
i
ncent (2002,
h
ence
f
ort
h
, MQV), t
h
at even w
i
t

h
e
ndo
g
enous bidder entr
y
, the optimal reserve price for the auctioneer to set is at least
©
200
5
Sprin
g
er
.
P
r
inted

i
n the
N
etherlands.
A. Rapoport and
R
.

d
Zwick (
e
(

(
ds.
)
,

E
x
p
erimental Business Researc
h
,
Vol. II
,
1
03
–121
.
104 Ex
p
erimental Business Research Vol. II
a
s
g
reat as the auctioneer’s salva
g
e value? The answer to this question is “no,” as a
reserve price of zero appears to provide hi
g
her expected profits than a reserve price
a

t t
h
e auct
i
oneer’s sa
l
vage va
l
ue.
The field-experiment methodolo
gy
of this stud
y
, that of auctionin
g
real
g
oods in
a
preexistin
g
market, represents a h
y
brid between traditional laborator
y
experiments
a
n
d
tra

di
t
i
ona
l

fi
e
ld
researc
h
w
hi
c
h
ta
k
es t
h
e
d
ata as g
i
ven. It s
h
ares w
i
t
h

l
a
b
oratory
e
xperiments the important advanta
g
e of allowin
g
the researcher to control certain
v
ariables of interest, rather than leavin
g
the researcher sub
j
ect to the va
g
aries of the
a
ctua
l
mar
k
etp
l
ace. (T
h
e
k
ey exper

i
menta
l
treatment
i
n t
hi
s paper
i
s t
h
e man
i
pu
l
a-
tion of the reserve
p
rice across auctions, to observe how
p
artici
p
ants react in their
e
ntr
y
and biddin
g
decisions.) It shares with traditional field research the advanta
g

e
o
f
stu
d
y
i
ng agents’
b
e
h
av
i
or
i
n a rea
l
-wor
ld
env
i
ronment, rat
h
er t
h
an
i
n a more
a
rtificial laborator

y
settin
g
.
Althou
g
h the experimental literature on auctions is vast,
2

a
lm
ost

a
ll
o
f
t
h
ese
stu
di
es
h
ave
i
mpose
d
an exogenous num
b

er o
f

bidd
ers (
d
eterm
i
ne
d

b
y t
h
e exper
i
-
m
enter). Three exceptions are Smith and Levin (2001), Palfre
y
and Pevnitska
y
a
(2003), and Cox, Dinkin, and Swarthout (2001). Smith and Levin (2001) and Palfre
y
a
n
d
Pevn
i

ts
k
aya (2003)
d
es
i
gn t
h
e
i
r exper
i
ments to
d
eterm
i
ne w
h
et
h
er t
h
e entry
e
quilibrium which obtains is deterministic or stochastic, a question I also investi
g
ate
i
n this
p

a
p
er. Cox, Dinkin, and Swarthout (2001) show that when
p
artici
p
ation in a
c
ommon-va
l
ue auct
i
on
i
s cost
l
y, w
i
nner’s-curse e
ff
ects are attenuate
d
.
I
n the em
p
irical literature on auctions in the field,
3
one recent stud
y

consider
s
e
ndo
g
enous entr
y
. Ba
j
ari and Hortacsu (2003) note that in eBa
y
auctions for coin
proo
f
sets, t
h
e num
b
er o
f
o
b
serve
d

bidd
ers
i
s pos
i

t
i
ve
l
y corre
l
ate
d
w
i
t
h
t
h
e
b
oo
k
v
alue of the item and ne
g
ativel
y
correlated with the minimum bid for the item. From
this the
y
infer that biddin
g
is costl
y

, and the
y
therefore provide a structural eco-
n
ometr
i
c mo
d
e
l
o
f

biddi
ng t
h
at
i
nc
l
u
d
es an en
d
ogenous entry
d
ec
i
s
i

on. T
h
e present
paper adds to the empirical and experimental literatures on the endo
g
enous entr
y
of
bidders b
y
conductin
g
a controlled experiment to
g
ather evidence on the t
y
pe of
e
n
d
ogenous entry
f
oun
d

i
n a rea
l
-wor
ld

mar
k
et.
The paper is or
g
anized as follows. The next section describes the relevant
a
spects of endo
g
enous-entr
y
auction theor
y
, focusin
g
on the testable implications.
Th
e t
hi
r
d
sect
i
on
d
escr
ib
es t
h
e mar

k
etp
l
ace w
h
ere t
h
e exper
i
ments too
k
p
l
ace, w
i
t
h
tw
i
n su
b
sect
i
ons exp
l
a
i
n
i
ng t

h
e respect
i
ve
d
es
i
gns o
f
t
h
e two sets o
f
exper
i
ments.
T
he fourth section
p
resents the results, and a fifth section concludes.
2. THEORETICAL BACKGROUND
R
ecently, there have been a number of important extensions to Vickrey’s (19
6
1)
or
i
g
i
na

l
mo
d
e
l
o
f
auct
i
ons w
i
t
h
a
fi
xe
d
,
k
nown num
b
er o
f

bidd
ers. T
h
e ear
li
est

e
xamples of endo
g
enous-entr
y
biddin
g
models include Samuelson (198
5
),
Enge
lb
rec
h
t-W
i
ggans (1987), an
d
McA
f
ee an
d
McM
ill
an (1987). In t
h
ese mo
d
e
l

s,
bidd
ers
h
ave some cost to part
i
c
i
pat
i
ng (e
i
t
h
er t
h
e researc
h
requ
i
re
d
to
l
earn one’s
v
alue for the
g
ood, or the effort required to decide on a bid and submit it). This
E

XPERIMENTAL
EE
E
L
V
IDEN
CE
O
N
THE
E
E
NDOGENOUS
E
E
E
S
NTRY
EE
OF
B
F
IDDER
S
10
5
c
ost causes some potential bidders to sta
y
out of the auction entirel

y
, and can cause
o
ther effects as well. For example, Samuelson (198
5
) and En
g
elbrecht-Wi
gg
ans
(1987), ma
ki
ng
diff
erent mo
d
e
lli
ng assumpt
i
ons,
b
ot
h

fi
n
d
t
h

at en
d
ogenous entry
d
rives down the auctioneer’s o
p
timal reserve
p
rice relative to a model of costless
e
ntr
y
. One of the
g
oals of the present paper is to demonstrate the existence of entr
y
c
osts
i
n a rea
l
-
w
or
ld
auct
i
on mar
k
et

.
M
cAfee and McMillan (1987) model bidder entr
y
as a pure-strate
gy
, as
y
mmetric
Nash equilibrium. In these models, exactl
y
n bidders enter the auction (out of a
tota
l
o
f
N
>
n potent
i
a
l

bidd
ers), an
d
n
i
s
d

eterm
i
ne
d
en
d
ogenous
l
y
f
rom t
h
e ot
h
er
parameters of the model (the auction format, the de
g
ree of affiliation of bidder
v
alues, the cost of entr
y
, and so on). Alternativel
y
, others have modeled a mixed-
strategy, symmetr
i
c entry equ
ilib
r
i

um (Enge
lb
rec
h
t-W
i
ggans (1987), Lev
i
n an
d
Smith (1994), MQV). In the mixed-strate
gy
models, bidders each enter with probabil-
it
y
ρ
, where
ρ
is determined endogenously.
ρ
4
L
ev
i
n an
d
Sm
i
t
h

(1994) po
i
nt out t
h
at t
h
e
diff
erence
b
etween pure-strategy
(deterministic) models and mixed-strate
gy
(stochastic) ones has implications for
social welfare: if entr
y
is stochastic, then expected social surplus is decreasin
g
in the
n
um
b
er N o
f
potent
i
a
l

bidd

ers. T
h
e reason
i
s t
h
at t
h
e var
i
ance o
f
t
h
e num
b
er n o
f
a
ctual entrants is increasin
g
in N, and such variance is costl
y
. In common-value
a
uctions, then, it turns out that auctioneers can increase both social welfare and their
own pro
fi
ts
b

y us
i
ng reserve pr
i
ces to
di
scourage entry
.
I
n a se
p
arate
p
a
p
er, Smith and Levin (2001)
p
erform an ex
p
eriment in which
the
y
attempt to determine whether entr
y
b
y
bidders is stochastic or deterministic:
t
h
ey

fi
n
d
ev
id
ence
i
n
f
avor o
f
t
h
e
i
r stoc
h
ast
i
c
h
ypot
h
es
i
s. However, t
h
e exper
i
menta

l
procedure doesn’t actuall
y
involve an
y
auctions; rather, it assi
g
ns simulated auction
pa
y
offs b
y
a lotter
y
procedure
.
5
Palfre
y
and Pevnitska
y
a (2003) modif
y
this experi-
m
enta
l

d
es

i
gn to con
d
uct a
fi
rst-pr
i
ce sea
l
e
d
-
bid
auct
i
on a
f
ter t
h
e entry
d
ec
i
s
i
on.
T
he
y
observe that the same bidders tend to enter repeated auctions, indicatin

g
a
pure- rather than mixed-strate
gy
equlibrium. Pevnitska
y
a (2004) provides a theoret-
i
ca
l
mo
d
e
l
o
f

h
eterogenous
l
y r
i
s
k
-averse
bidd
ers to exp
l
a
i

n t
hi
s o
b
servat
i
on. W
h
en
some bidders are more risk-averse than others, and all bidders know this fact, the
m
ore risk-averse bidders sta
y
out of the auction deterministicall
y
in order to collect
a

fi
xe
d
payo
ff
. On
l
y t
h
e re
l
at

i
ve
l
y
l
ess r
i
s
k
-averse
bidd
ers enter t
h
e auct
i
on, a
l
so
d
eterm
i
n
i
st
i
ca
ll
y.
6
M

i
xe
d
-strategy equ
ilib
r
i
um
di
sappears
i
n
f
avor o
f
a pure-strategy
e
quilibrium the more risk-averse bidders sta
y
out of the auction in favor of a fixed
payo
ff
, w
hil
e re
l
at
i
ve
l

y
l
ess r
i
s
k
-averse
bidd
ers enter t
h
e auct
i
on. In t
hi
s paper, I
a
ttempt to prov
id
e ev
id
ence on t
h
e quest
i
on o
f
stoc
h
ast
i

c versus
d
eterm
i
n
i
st
i
c entry
eq
uilibria in a field environment
.
M
QV exam
i
ne t
h
e e
ff
ects o
f
reserve pr
i
ces w
h
ere va
l
uat
i
ons are w

h
ere
bidd
er
e
ntry
i
s en
d
ogenous an
d

bidd
er va
l
uat
i
ons may
b
e e
i
t
h
er a
ffili
ate
d
. In t
h
e

i
r mo
d
e
l
,
the auctioneer chooses a reserve price and announces her auction, to
g
ether with the
l
eve
l
o
f

h
er reserve pr
i
ce, to N potent
i
a
l

bidd
ers. B
idd
ers t
h
en
d

ec
id
e w
h
et
h
er or not
to
i
ncur t
h
e part
i
c
i
pat
i
on costs, ma
ki
ng a stoc
h
ast
i
c (m
i
xe
d
-strategy) entry
d
ec

i
s
i
on.
Next the participatin
g
bidders find out their private information about the value of
106 Ex
p
erimental Business Research Vol. II
the
g
ood, the
y
submit their bids, and finall
y
the auctioneer awards the
g
ood to the
h
i
g
hest bidder. If no bidder chooses to enter and to bid at least the reserve price, then
t
h
e auct
i
oneer
k
eeps t

h
e goo
d

f
or
h
erse
lf
an
d
earns some outs
id
e opt
i
on ut
ili
ty, or
“
salva
g
e value.” The main prediction of MQV is that the optimal reserve price is at
l
east as hi
g
h as the salva
g
e value of the
g
ood. This is a testable prediction; raisin

g
t
h
e reserve pr
i
ce
f
rom some
l
ower va
l
ue to t
h
e expecte
d
sa
l
vage va
l
ue o
f
t
h
e goo
d
should raise re
v
enues for the auctioneer.
To summarize, this
p

a
p
er will attem
p
t to answer three main
q
uestions. First, are
e
ntry costs re
l
evant
i
n t
h
e Internet auct
i
on mar
k
et w
h
ere I ran my exper
i
ments?
Second, is the entr
y
equilibrium a deterministic or a stochastic one? Third, is the
optimal reserve price at least as hi
g
h as the auctioneer’s salva
g

e value? Note that the
fi
rst quest
i
on
i
s a
b
out an assumpt
i
on o
f
en
d
ogenous-entry, t
h
e secon
d
attempts
to distin
g
uish between two rival theories, and the third is a test of the empirical
p
rediction of a s
p
ecific model.
3
. EXPERIMENTAL DESIGN
For t
hi

s exper
i
ment, I auct
i
one
d
tra
di
ng car
d
s v
i
a
fi
rst-pr
i
ce, sea
l
e
d
-
bid
auct
i
ons,
v
ar
y
in
g

the reserve prices across treatments. The data in this paper are the same as
i
n Luckin
g
-Reile
y
(1999). The experiments took place in 199
5
in a pre-eBa
y
online
m
ar
k
et
f
or co
ll
ect
ibl
e car
d
s
f
rom Ma
g
ic: t
h
e Gat
h

erin
g
,
a game w
hi
c
h

h
as en
j
oye
d
g
reat success since its launch in Au
g
ust 1993. In the
g
ame, pla
y
ers assume the roles
of duelin
g
wizards, each with their own libraries of ma
g
ic spells (represented b
y
d
ec
k

s o
f
car
d
s) t
h
at may potent
i
a
ll
y
b
e use
d
aga
i
nst opponents. Car
d
s are so
ld

i
n
random assortments,
j
ust like baseball cards, at retail stores ran
g
in
g
from small

g
ame and hobb
y
shops to lar
g
e chain retailers. The
g
ames’s maker, Wizards of the
C
oast (now a
di
v
i
s
i
on o
f
Has
b
ro)
h
as
d
eve
l
ope
d
an
d
pr

i
nte
d
t
h
ousan
d
s o
f

di
st
i
nct
c
ard t
y
pes, each of which pla
y
s a sli
g
htl
y
different role in the
g
ame.
As discussed in Luckin
g
-Reile
y

(1999), soon after the introduction o
f
Magic
,
p
l
ayers an
d
co
ll
ectors
i
ntereste
d

i
n
b
uy
i
ng, se
lli
ng, an
d
tra
di
ng game car
d
s
b

egan to
u
se the Internet to find each other and carr
y
out transactions. In a Usenet news
g
roup
d
edicated to this purpose, traders used a variet
y
of tradin
g
institutions, includin
g
n
egot
i
ate
d
tra
d
es o
f
one car
d

f
or anot
h
er, sa

l
es at poste
d
pr
i
ces, an
d
auct
i
ons o
f
v
ar
i
ous
f
ormats, typ
i
ca
ll
y
l
ast
i
ng mu
l
t
i
p
l

e
d
ays.
Scarcit
y
was one ma
j
or determinant of transaction prices for cards, as some cards
were pr
i
nte
d

i
n re
l
at
i
ve
l
y
l
ow quant
i
t
i
es, an
d
some car
d

s
h
a
d
gone out o
f
pr
i
nt. T
h
e
m
ost common
i
n-pr
i
nt car
d
s were not wort
h
tra
di
ng over t
h
e Internet; t
h
e
i
r va
l

ues
were pennies or less. Cards desi
g
nated “uncommon” but not “rare” traded for prices
o
f
ten cents to two
d
o
ll
ars. Car
d
s
d
es
i
gnate
d
“rare”
b
ut st
ill

i
n pr
i
nt typ
i
ca
ll

y range
d
i
n pr
i
ce
f
rom one to
fif
teen
d
o
ll
ars. Out-o
f
-pr
i
nt car
d
s,
d
epen
di
ng on t
h
e
i
r
i
n

i
t
i
a
l
scarcit
y
and on other attributes, traded for as much as three hundred dollars. In this
researc
h
pro
j
ect, I
d
ea
l
t on
l
y
i
n out-o
f
-pr
i
nt car
d
s
.
I
n a

ddi
t
i
on to
d
ata generate
d

i
n my own auct
i
ons, I a
l
so ma
k
e use o
f
contem-
poraneous market data from the weekl
y
Cloister price list in this marketplace.
E
XPERIMENTAL
EE
E
L
V
IDEN
CE
O

N
THE
E
E
NDOGENOUS
E
E
E
S
NTRY
EE
OF
B
F
IDDER
S
10
7
Cl
o
i
ster was a car
d
tra
d
er w
h
o wrote a computer program t
h
at automat

i
ca
ll
y searc
h
e
d
t
h
e mar
k
etp
l
ace newsgroup
f
or eac
h

i
nstance o
f
eac
h
car
d
name (w
i
t
h
some to

l
erance
f
or misspellin
g
s) and
g
athered data on the prices posted next to each card name in
t
h
e newsgroup messages. It t
h
en compute
d
stat
i
st
i
cs
f
or eac
h
car
d
, an
d
automat
i
ca
ll

y
a
rc
hi
ve
d
t
h
ese
d
ata on t
h
e Internet as a pu
bli
c serv
i
ce
f
or ot
h
er
i
ntereste
d
tra
d
ers.
Each card’s re
p
orted list

p
rice is a trimmed mean over hundreds or thousands of
diff
erent o
b
servat
i
ons on t
h
e newsgroup. Desp
i
te some pro
bl
ems w
i
t
h
t
h
ese
d
ata,
di
scusse
d

i
n Luc
ki
ng-Re

il
ey (1999) many car
d
tra
d
ers a
d
opte
d
t
h
e C
l
o
i
ster pr
i
ce
li
st
a
s a standard measure of card market value, so I adopt it as a useful measure in m
y
o
wn ana
l
ys
i
s
.

T
hi
s mar
k
etp
l
ace represente
d
an exc
i
t
i
ng opportun
i
ty to run auct
i
on
fi
e
ld
exper
i
-
m
ents. For the ex
p
eriments, I
p
urchased several thousand dollars’ worth of cards
(a

l
so v
i
a t
h
e Internet), an
d
auct
i
one
d
t
h
em o
ff
w
hil
e systemat
i
ca
ll
y man
i
pu
l
at
i
ng t
h
e

reserve pr
i
ces
i
n or
d
er to o
b
serve t
h
e
i
r e
ff
ects on
bidd
er part
i
c
i
pat
i
on an
d

biddi
ng
behavior. Because in an
y

g
iven week there were dozens of auctioneers holdin
g
M
ag
i
c auct
i
ons on t
h
e Internet, as an exper
i
menter I was a
bl
e to
b
e a “sma
ll
p
l
ayer”
w
h
o
did
not s
i
gn
ifi
cant

l
y pertur
b
t
h
e overa
ll
mar
k
et.
I
emplo
y
ed two distinct experimental desi
g
ns to collect the data. The first desi
g
n
e
xam
i
nes t
h
e e
ff
ects o
f
a
bi
nary var

i
a
bl
e: w
h
et
h
er or not m
i
n
i
mum
bid
s were use
d
.
B
y auct
i
on
i
ng t
h
e same car
d
s tw
i
ce, once w
i
t

h
an
d
once w
i
t
h
out m
i
n
i
mum
bid
s,
i
t
e
xploits within-card variation to find the effects of the treatment variable on biddin
g
a
n
d
entry
b
e
h
av
i
or. T
h

e secon
d

d
es
i
gn
i
nvest
i
gates t
h
e e
ff
ects o
f
a cont
i
nuous var
i
-
abl
e: t
h
e reserve pr
i
ce
l
eve
l

(expresse
d
as a
f
ract
i
on o
f
t
h
e C
l
o
i
ster re
f
erence pr
i
ce).
T
he between-card variation
p
rovides information that can be used to test the MQV
pre
di
ct
i
on a
b
out t

h
e opt
i
ma
l
reserve pr
i
ce
l
eve
l
.
3.1. Within-Card Experiment
s
Th
e
fi
rst part o
f
t
h
e
d
ata co
ll
ect
i
on cons
i
ste

d
o
f
two pa
i
rs o
f
auct
i
ons. Eac
h
o
f
t
h
e
f
our auctions was a sealed-bid, first-
p
rice auction of several dozen
M
a
gic
ca
r
ds
a
uct
i
one

d
o
ff

i
n
di
v
id
ua
ll
y. T
hi
s s
i
mu
l
taneous auct
i
on o
f
many
diff
erent goo
d
s at
o
nce, a
l
t

h
ou
gh
not common
i
n ot
h
er econom
i
c env
i
ronments,
7
i
s t
h
e norm
f
or auct
i
on
s
o
f
M
a
gic
cards on the Internet. Runnin
g
auctions in this simultaneous-auction forma

t
t
h
us ma
d
e t
h
e exper
i
ment as rea
li
st
i
c an
d
natura
l
as poss
ibl
e
f
or t
h
e
bidd
ers, w
h
o see
many ot
h

er s
i
m
il
ar auct
i
ons
i
n t
h
e Internet mar
k
etp
l
ace
f
or car
d
s.
E
ach auction lasted for one week, from the time the auction was announced to
t
h
e
d
ea
dli
ne
b
y w

hi
c
h
a
ll

bid
s
h
a
d
to
b
e rece
i
ve
d
. I announce
d
eac
h
auct
i
on
to potent
i
a
l

bidd

ers v
i
a two c
h
anne
l
s. F
i
rst, I poste
d
t
h
ree announcements to t
h
e
a
ppropriate Internet news
g
roup. For each auction, I posted a total of three news-
g
roup messages space
d
even
l
y over t
h
e course o
f
t
h

e wee
k
o
f
t
h
e auct
i
on. Secon
d
,
I
so
li
c
i
te
d
some
bidd
ers
di
rect
l
y v
i
a ema
il
messages to t
h

e
i
r persona
l
e
l
ectron
i
c
mailboxes. M
y
mailin
g
list for direct solicitation was comprised of people who had
al
rea
d
y
d
emonstrate
d
t
h
e
i
r
i
nterest
i
n auct

i
ons
f
or Magic car
d
s
b
y part
i
c
i
pat
i
on
in
prev
i
ous ones.
108 Ex
p
erimental Business Research Vol. II
The
p
aired-auction ex
p
eriment
p
roceeded as follows. First, I held an absolute
a
uction (no minimum bid) for 86 different cards (one of each card in the Anti

q
uities
e
xpans
i
on set). T
h
e su
bj
ect
li
ne o
f
t
h
e announcement rea
d
“Re
il
ey’s Auct
i
on #4:
ANTIQUITIES,
5
Cent Minimum, Free Shippin
g
!” so that potential bidders mi
g
ht
be attracted b

y
the unusuall
y
low minimum bid per card, essentiall
y
zero. (A
5
-cent
mi
n
i
mum
i
s e
ff
ect
i
ve
l
y no m
i
n
i
mum, s
i
nce t
h
e auct
i
on ru

l
es a
l
so requ
i
re
d
a
ll

bid
s to
be in inte
g
er multiples of a nickel.) After the one-week deadline for submittin
g
bids
h
ad passed, I computed the hi
g
hest bid on each card. To each bidder who had won
one or more car
d
s, I ma
il
e
d
(e
l
ectron

i
ca
ll
y) a
bill

f
or t
h
e tota
l
amount owe
d
.
8
A
f
te
r
receivin
g
a winner’s pa
y
ment via check or mone
y
order, I mailed them their cards.
Almost no one defaulted on their winnin
g
bids.
9

I
a
l
so ma
il
e
d
a
li
st o
f
t
h
e w
i
nn
i
ng
bid
s to eac
h

bidd
er w
h
o
h
a
d
part

i
c
i
pate
d

i
n t
h
e
a
uction, whether or not the
y
had won cards. This represented an effort to maintain
my
reputation as a credible auctioneer, demonstratin
g
m
y
truthfulness to those who
h
a
d
part
i
c
i
pate
d
. I

did
not,
h
owever, g
i
ve t
h
e
bidd
ers any exp
li
c
i
t
i
n
f
ormat
i
on a
b
out
the number of
p
eo
p
le who had
p
artici
p

ated in the auction, or about the number of
p
eo
p
le who had received email invitations to
p
artici
p
ate.
A
f
ter one a
ddi
t
i
ona
l
wee
k
o
f

b
u
ff
er t
i
me a
f
ter t

h
e en
d
o
f
t
h
e
fi
rst auct
i
on
,
I
ran the second auction in the paired experiment, this time with reasonabl
y
hi
g
h
m
inimum bid levels on each of the same 86 cards as before. The minimum bid levels
were
d
eterm
i
ne
d

b
y consu

l
t
i
ng t
h
e stan
d
ar
d
(tr
i
mme
d
-mean) C
l
o
i
ster pr
i
ce
li
st o
f
M
agic cards cited above of this paper, and settin
g
the minimum bid level for each
c
ard e
q

ual to 90% of the value of that card from the
p
rice list.
T
hi
s contrast
i
n m
i
n
i
mum
bid

l
eve
l
s (zero versus 90% o
f
t
h
e C
l
o
i
ster pr
i
ce
li
st)

was the onl
y
economicall
y
si
g
nificant difference between the two auctions.
1
0
B
y
keepin
g
all other conditions identical between the two auctions, I attempted to
i
so
l
ate t
h
e e
ff
ects o
f
m
i
n
i
mum
bid
s on potent

i
a
l

bidd
ers’
b
e
h
av
i
or. One con
di
t
i
on
that could not be kept identical, unfortunatel
y
, was the time period durin
g
which the
a
uction took
p
lace. Because the two auctions took
p
lace two weeks a
p
art, there were
potent

i
a
l

diff
erences
b
etween t
h
e auct
i
ons t
h
at m
i
g
h
t
h
ave a
ff
ecte
d

bidd
er
b
e
h
av

i
or.
First, the demands for the cards (or the supplies b
y
other auctioneers) mi
g
ht have
chan
g
ed s
y
stematicall
y
over time, which is a realistic possibilit
y
in such a fast-
c
h
ang
i
ng mar
k
et as t
hi
s one
.
11
Secon
d
, s

i
nce t
h
e auct
i
ons s
h
are
d
many o
f
t
h
e same
bidd
ers, t
h
e resu
l
ts o
f
t
h
e
fi
rst auct
i
on may
h
ave a

ff
ecte
d
t
h
e
d
eman
d

f
or t
h
e car
d
s
sold in the second auction
.
12
To contro
l

f
or suc
h
potent
i
a
l
var

i
at
i
ons
i
n con
di
t
i
ons over t
i
me, I s
i
mu
l
taneous
l
y
ran t
h
e same exper
i
ment
i
n reverse or
d
er, us
i
ng a
diff

erent samp
l
e o
f
car
d
s. T
hi
s
second pair of auctions each featured the 78 cards in the Arabian Ni
g
hts expansion
set, w
i
t
h
m
i
n
i
mum
bid
s present
i
n t
h
e
fi
rst auct
i

on
b
ut a
b
sent
i
n t
h
e secon
d
. Just as
b
e
f
ore, m
i
n
i
mum
bid
s were set at n
i
nety percent o
f
t
h
e mar
k
et pr
i

ce
l
eve
l

f
rom t
h
e
C
loister price list. The first auction in this pair be
g
an three da
y
s after the start of
t
h
e
fi
rst auct
i
on
i
n t
h
e prev
i
ous pa
i
r, so t

h
at t
h
e auct
i
ons
i
n t
h
e two exper
i
ments
over
l
appe
d

i
n t
i
me
b
ut were o
ff
set
b
y t
h
ree
d

ays. A
l
so, I use
d
a
l
arger ma
ili
ng
li
st
for m
y
email announcement in this pair of auctions (232 people) than I had for the
E
XPERIMENTAL
EE
E
L
V
IDEN
CE
O
N
THE
E
E
NDOGENOUS
E
E

E
S
NTRY
EE
OF
B
F
IDDER
S
109
previous pair of auctions (
5
0 people), with the first mailin
g
list bein
g
a subset of the
second mailin
g
list. Otherwise, all other conditions were identical between the two
pa
i
rs o
f
auct
i
ons.
13
Table 1 shows a set of summar
y

statistics for each of the four auctions in th
e
within-card ex
p
eriments
.
14
The auctions are displa
y
ed in two pairs: first Auctions
AA and AR, for the 8
6
Antiquities cards, and then Auctions BA and BR, for the 78
Arabian Ni
g
hts cards
.
15
Auctions AA and BA were with no minimum bids, while
Auctions AR and BR had sizable minimums (e
q
ual to 90% of the market
p
rice).
T
h
e ta
bl
e conta
i

ns qu
i
te a
bi
t o
f

d
escr
i
pt
i
ve
i
n
f
ormat
i
on a
b
out t
h
e auct
i
ons,
i
ncludin
g
the number of participatin
g

bidders, the number of bids received, and
the total pa
y
ments received from winnin
g
bidders. Note two ke
y
points. First
,
“
rea
l
money” was
i
nvo
l
ve
d

i
n t
h
e auct
i
on transact
i
ons. O
f
t
h

e 73
diff
erent
bill
s I
sent to winnin
g
bidders over the course of the experiment, the median pa
y
ment
a
mount for each auction was between $10 and $24. A few individual pa
y
ments even
e
xceeded
$
100
.
Second, in each auction there are multi
p
le winners. The number of winners in
e
ach auction ran
g
es from 6 to 27, and the fraction of bidders who win at least one
c
ard is between 40 percent and 8
6
percent. In each auction, the median number of

c
ards won b
y
each winner is between 2 and 3.
5
, while the maximum number of
c
ards won b
y
a sin
g
le bidder ran
g
es from 12 to 26. Except in Auction AR, no winner
won more t
h
an 29 percent o
f
t
h
e car
d
s so
ld

i
n any s
i
ng
l

e auct
i
on. (In Auct
i
on AR,
participation was ver
y
low: onl
y
7 people submitted bids,
6
of whom won at least
o
ne card, and 39 of the cards went unsold.) The bi
gg
est spender in an
y
of the
a
uctions won cards totalling
$
316.50 of the total revenue of
$
774.75 in Auction BA,
g
eneratin
g
41 percent of the revenue despite winnin
g
no more than 1

5
percent of the
c
ards – evidentl
y
, she was particularl
y
interested in hi
g
h-value cards. Thus, it is not
t
h
e case t
h
at some peop
l
e are t
h
e
hi
g
h
est
bidd
ers on a
ll
car
d
s
i

n an auct
i
on, w
hi
c
h
su
gg
ests that a
g
iven bidder’s valuations for different cards are at least somewha
t
i
ndependent. This
g
ives some
j
ustification for reportin
g
re
g
ression results in which
e
ac
h

i
n
di
v

id
ua
l
car
d

bid

i
s assume
d
to
b
e an
i
n
d
epen
d
ent o
b
servat
i
on.
3.2. Between-Car
d
Experiment
s
A secon
d

set o
f
exper
i
ments was
d
es
i
gne
d
to exam
i
ne t
h
e e
ff
ects o
f
c
h
anges
i
n t
h
e
le
v
e
l
of the reserve price, rather than merely changes in the

l
ex
i
stenc
e
of reserve
pr
i
ces. F
i
ve
fi
rst-pr
i
ce, sea
l
e
d
-
bid
auct
i
ons too
k
p
l
ace, eac
h
w
i

t
h
a one-wee
k
t
i
me
f
rame
f
or t
h
e su
b
m
i
ss
i
on o
f

bid
s. Eac
h
was a s
i
mu
l
taneous auct
i

on o
f
many
diff
erent
i
tems,
this time with no overla
p
of items between auctions. Each card in the first fou
r
a
uct
i
ons (R1 t
h
roug
h
R4)
h
a
d
a poste
d
reserve pr
i
ce. T
h
e
fif

t
h
auct
i
on (R0) use
d
a
z
ero reserve pr
i
ce on every car
d
,
i
n or
d
er to prov
id
e a
b
as
i
s
f
or compar
i
son.
16

J

ust as
before, I announced each auction via three posts to the relevant news
g
roup, as well
a
s
vi
a ema
il
to a
li
st o
f

bidd
ers.
1
7
I
n t
h
e
fi
rst
f
our auct
i
ons, I auct
i
one

d
99
diff
erent car
d
s eac
h
t
i
me, sett
i
ng a
reserve
p
rice for each card as a
p
articular fraction of the current Cloister
p
rice of tha
t
110 Ex
p
erimental Business Research Vol. II
Table 1. Summary statistics
f
or within-card experiments
.
Auctio
n
AA Auctio

n
A
R
Auctio
n B
A Auctio
n B
R
Minimum bids?
N
o Yes
N
oYe
s
Card set Antiquities Antiquities Arabian Ni
g
hts Arabian Ni
g
hts
S
tart date Fri, 24 Feb Fri, 10 Mar Tue, 14 Mar Tue, 28 Feb
End date Fri, 3 Mar Fri, 17 Mar Tue, 21 Mar Tue, 7 Mar
Number of items for auction 86 86 78 7
8
Number of items sold 86 47 78 74
R
evenue from twice-sold cards $189.90 $234.75 $758.25 $783.80
T
otal auction revenue $292.40 $234.75 $774.75 $783.80
T

otal number of bids
5
6
5
71 1
5
83 238
T
otal number of bidders 19 7 63 4
2
from email invitations 12
5
44 3
5
from news
g
roup announcements 7 2 19 7
Number of email invitations sent
5
2
5
0 232 234
Number of winners 1
5
62
5
27
W
inner/bidder ratio 78.9% 8
5

.7% 40.3% 64.3
%
Cards
p
er winner
:
Max 2
5
26 12 1
8
as share of total 29.1%
55
.3% 1
5
.4% 24.3
%
Min 1 1 1 1
Mean
5
.7 7.8 3.1 2.
7
Median 3 3.
5
2
2
P
a
y
ment per winner:
Max $70.00 $129.40 $316.50 $128.0

0
as share of total 23.9%
55
.1% 40.9% 16.3
%
Min $3.00 $0.70 $1.05 $2.55
Mean $19.49 $39.13 $30.99 $29.0
3
Median $10.50 $23.68 $13.15 $13.00
E
XPERIMENTAL
EE
E
L
V
IDEN
CE
O
N
THE
E
E
NDOGENOUS
E
E
E
S
NTRY
EE
OF

B
F
IDDER
S
111
T
able 2 Bids recei
v
ed in the
w
ithin-card auctions
.
Auction AA Auction AR Auction BA Auction BR
Auction AR Auction BA
Minimum bids? No Yes No Yes
No Yes No
Card set Antiquities Antiquities Arabian Nights Arabian Nights
Antiquities Antiquities Arabian Nights
Number of bidders 19 7 62 42
19 7 62
Number of items for auction 86 86 78 78
86 86 78
Number of bids
p
er bidder
:
Mean 29.7 10.1 25.5 5.7
29.7 10.1 25.5
Median 13.0 4.0 14.0 4.0
13.0 4.0 14.0

Max 86.0 29.0 78.0 30.0
86.0 29.0 78.0
Min 1.0 1.0 1.0 1.0
1.0 1.0 1.0
c
ar
d
. In eac
h
o
f
t
h
e
fi
rst two auct
i
ons
,
n
i
ne car
d
s were auct
i
one
d
at a m
i
n

i
mum
bid
o
f 10
p
ercent of the Cloister
p
rice, nine at 20
p
ercent, nine at 30
p
ercent, and so on,
up
to a maximum of 110
p
ercent of the Cloister
p
rice. For each reserve-
p
rice level,
I
c
h
ose an assortment o
f

diff
erent car
d

s w
i
t
h
w
id
e
l
y
diff
erent C
l
o
i
ster pr
i
ces, an
d
scattered the
g
roup randoml
y
across the complete list of cards. After an anal
y
sis of
the data from those auctions, I chose to collect more data both at very low and at
v
ery
hi
g

h
reserve pr
i
ce
l
eve
l
s. T
h
ere
f
ore, t
h
e t
hi
r
d
an
d

f
ourt
h
auct
i
ons were
d
es
i
gne

d
to have e
q
ual numbers of cards auctioned at reserve levels of 10, 20, 30, 40,
5
0, 100,
110, 120, 130, 140, and 1
5
0
p
ercent of the Cloister
p
rice.
18
T
hi
s var
i
at
i
on
i
n reserve pr
i
ce
l
eve
l
s was
d

es
i
gne
d
to
i
nvest
i
gate
h
ow
b
ot
h

bidd
er
behavior and expected auction revenue would react to chan
g
es in the reserve price,
a
nd to calculate the optimal reserve price level. Normalizing by the Cloister price,
s
i
nce t
hi
s
i
s a stan
d

ar
d
re
f
erence pr
i
ce compute
d

i
n t
h
e same way
f
or a
ll
Magi
c
c
ards, makes cross-card com
p
arisons feasible. Besides the exce
p
tions noted above, all
e
x
p
erimental
p
rotocols and bidder instructions were ke

p
t identical to those used in
t
h
e auct
i
ons w
i
t
h
reserve pr
i
ces
i
n t
h
e exper
i
menta
l

d
es
i
gn
d
escr
ib
e
d

i
n sect
i
on 3.1.
Summar
y
statistics for the between-card auctions are
g
iven in Table 3. In auc-
tions R1 to R4, reserve prices ranged from 0% to 1
5
0% of each individual card’s
Cl
o
i
ster va
l
ue, an
d
t
h
e average reserve pr
i
ce
l
eve
l
var
i

e
d
s
li
g
h
t
l
y
f
rom auct
i
on to
a
uction, from 60% to 8
5
%. In auction R0, of course, the avera
g
e reserve price level
was zero.
As can
b
e seen
i
n t
h
e ta
bl
e
,

eac
h
auct
i
on
h
a
d

d
ozens o
f

bidd
ers an
d

h
un
d
re
d
s
of bids on individual cards. The number of people receivin
g
email invitations to
112 Ex
p
erimental Business Research Vol. II
Table 3. Summary statistics

f
or the between-card experiments
.
Auction R1 Auction R2 Auction R3 Auction R4 Auction R0
Card set Artifacts Black White Blue Red/Green
Start date Tue, 3 Oct Fri, 6 Oct Fri, 20 Oct Mon, 23 Oct Tue, 31 Oct
End date Tue, 10 Oct Fri, 13 Oct Fri, 27 Oct Mon, 30 Oct Tue, 6 Nov
N
um
b
er o
f

i
tems
f
or auct
i
o
n
99 99 99 99 86
N
umber of items sol
d
98 92 77 78 86
M
ean reser
v
e le
v

e
l
60% 60% 85% 81% 0%
Tota
l n
u
m
be
r
o
f
b
i
ds
798 652 366 401 1069
Tota
l n
u
m
be
r
o
f
b
i
dde
r
s
5
7

55
46 38 42
Number of email invitations sent
5
32
5
23
5
12 489 47
2
Total Cloister value
34
5
.83 271.
55
28
5
.87 224.89 327.0
5
T
ota
l
auct
i
on revenu
e
338.4
5
282.6
5

260.9
5
21
9
.25 316.7
0
R
evenue p
l
us sa
l
vag
e
343.94 283.6
5
26
9
.48 224.52 316.7
0
E
XPERIMENTAL
EE
E
L
V
IDEN
CE
O
N
THE

E
E
NDOGENOUS
E
E
E
S
NTRY
EE
OF
B
F
IDDER
S
113
participate declined with each successive auction, but onl
y
due to recipients askin
g
to be removed from m
y
mailin
g
list, so the chan
g
es in the mailin
g
list should
n
ot

h
ave a
ff
ecte
d
t
h
e num
b
er o
f
potent
i
a
l
part
i
c
i
pants. Note t
h
at t
h
e
d
ata
f
rom t
h
e

between-card auctions is not directl
y
comparable to that from the within-card auc-
tions, because the size and composition of the pool of participatin
g
bidders chan
g
ed
c
ons
id
era
bl
y
d
ur
i
ng t
h
e
i
nterven
i
ng s
i
x mont
h
s. Very
f
ew

bidd
ers over
l
appe
d
between the two ex
p
eriments; most of the bidders in the between-card ex
p
eriment
were new recruits
.
T
h
e ta
bl
e a
l
so
di
sp
l
ays aggregate stat
i
st
i
cs on revenue,
i
nc
l

u
di
ng t
h
e tota
l
C
l
o
i
ste
r
v
alue of all the cards in each auction, the total revenue earned on cards which were
sold, and a
g
rand-total revenue fi
g
ure which also includes the salva
g
e value of the
u
nso
ld
car
d
s. T
h
e auct
i

on revenue
i
n eac
h
case was reasona
bl
y c
l
ose to t
h
e tota
l
C
loister value of the cards; in Auction R2 I earned revenue
g
reater than the total
C
loister value, while in the three others I earned sli
g
htl
y
less.
4. RESULTS
I
now present t
h
e resu
l
ts
f

rom t
h
e exper
i
ment, separate
l
y
f
or eac
h
o
f
t
h
e t
h
ree
e
mpirical questions outlined above. Are entr
y
costs relevant? Is the entr
y
equilibrium
stochastic or deterministic? Do the auctioneer’s
p
rofits im
p
rove as he raises the
reserve pr
i

ce to
b
e at
l
east as
hi
g
h
as
hi
s sa
l
vage va
l
ue?
4
.1 Entry costs are re
l
evan
t
T
he within-card experiments demonstrate that endo
g
enous bidder entr
y
appears
to be the ri
g
ht model for this market. Statistics on the number of card bids per
part

i
c
i
pat
i
ng
bidd
er are s
h
own
i
n Ta
bl
e 2. As expecte
d
,
i
n
di
v
id
ua
l

bidd
ers ten
d
to
submit fewer bids in the presence of minimums than the
y

do in the absence of
m
inimums. This does not in itself demonstrate the existence of biddin
g
costs; a
bidd
er w
h
o contemp
l
ates
h
ow muc
h
to
bid
an
d
t
h
en
d
ec
id
es t
h
at t
h
e reserve pr
i

ce
e
xceeds his maximum willin
g
ness could still be counted as havin
g
“participated,”
because the decision cost would alread
y
have been incurred even thou
g
h the reserve
pr
i
ce prevents me
f
rom o
b
serv
i
ng a
l
ow
bid
. In t
h
e auct
i
ons w
i

t
h
m
i
n
i
mums, no
s
i
ng
l
e
bidd
er su
b
m
i
tte
d

bid
s on even
h
a
lf
o
f
t
h
e car

d
s; t
h
e max
i
mum num
b
er o
f
bids b
y
a sin
g
le bidder was 30. B
y
contrast, there were bidders in both of the
n
o-m
i
n
i
mum auct
i
ons w
h
o su
b
m
i
tte

d

i
n
di
v
id
ua
l

bid
s on every s
i
ng
l
e car
d
.
I
nterest
i
ng
l
y, re
l
at
i
ve
l
y

f
ew
bidd
ers
f
o
ll
owe
d
t
hi
s strategy o
f

biddi
ng on every
sin
g
le card in the absolute (no-minimum) auctions. Onl
y
one out of 19 bidders bid
o
n every single item in Auction AA, and only six of
6
2 bidders bid on every single
i
tem
i
n Auct
i

on BA. T
h
ese stat
i
st
i
cs
i
n
di
cate t
h
at t
h
e cost o
f
su
b
m
i
tt
i
ng a
bid
(t
h
e
participation cost) is hi
g
h enou

g
h to affect bidder behavior, and thus this experi-
m
enta
l
env
i
ronment
i
s appropr
i
ate
f
or exp
l
or
i
ng en
d
ogenous-entry
biddi
ng mo
d
e
l
s
suc
h
as MQV. I
f

t
h
ere were no cost to su
b
m
i
tt
i
ng a
bid
, t
h
en one wou
ld
expect to
see all of the participatin
g
bidders submittin
g
bids on ever
y
card (as low as a nickel,
114 Ex
p
erimental Business Research Vol. II
sa
y
), since ever
y
card does have some positive resale value even to people who

g
et
n
o consumption utilit
y
from it.
19
I conclude that bidders deem the probabilit
y
of
g
ett
i
ng a
b
arga
i
n (an
d
t
h
us a resa
l
e pro
fi
t) on suc
h
a car
d

i
s
l
ow enoug
h
t
h
at t
h
e
e
xpected profit from biddin
g
does not alwa
y
s outwei
g
h the cost of havin
g
to decide
o
n a bid amount and to t
y
pe the approximatel
y
ten characters required to submit
a
not
h
er car

d

bid
. In
d
ee
d
, t
h
e me
di
an num
b
er o
f
car
d

bid
s su
b
m
i
tte
d

b
y a s
i
ng

le
bidder was onl
y
13 (of a possible 87) in Auction AA, and 14 (of a possible 78) in
Auction BA, even thou
g
h these auctions had no minimum bids.
T
h
us,
bidd
ers
d
o appear to ma
k
e a part
i
c
i
pat
i
on
d
ec
i
s
i
on cons
i
stent w

i
t
h
t
h
e
e
xistence of small entr
y
costs; the number of participatin
g
bidders in each auction
i
s not exo
g
enous. The classical theor
y
makes some accurate predictions about the
eff
ects o
f
reserve pr
i
ces, as s
h
own ear
li
er,
d
esp

i
te t
hi
s v
i
o
l
at
i
on o
f

i
ts assumpt
i
ons.
4
.2. Is t
h
e entry e
q
ui
l
i
b
rium stoc
h
astic or
d
eterministic?

Given the existence of endo
g
enous entr
y
, I now ask: is the entr
y
equilibrium
d
eterministic or stochastic? Ver
y
few bidders bid on a card both times it was
off
ere
d
,
d
esp
i
te t
h
e
f
act t
h
at t
h
e same peop
l
e were
i

nv
i
te
d
eac
h
t
i
me. N
i
neteen an
d
seven bidders, respectivel
y
, bid in the two Antiquities auctions, but onl
y
4 people
o
verlapped between the two auctions. In the Arabian Ni
g
hts auctions, there were
42 and
6
2 bidders, but only 17 of the bidders overlapped between the two. Thus,
i
n each pair of auctions, there were a proportionall
y
lar
g
e number people who

e
ntered the first auction but not the second, and other
p
eo
p
le who entered the second
a
uct
i
on
b
ut not t
h
e
fi
rst. T
hi
s argues
i
n
f
avor o
f
a stoc
h
ast
i
c equ
ilib
r

i
um, as t
h
e most
n
atural kind of deterministic e
q
uilibrium is one in which the same bidders enter
e
ach time
.
Two o
bj
ect
i
ons m
i
g
h
t
b
e ra
i
se
d
to t
h
e resu
l
t

j
ust presente
d
. F
i
rst,
i
t m
i
g
h
t
b
e t
h
e
c
ase that
p
eo
p
le enter one auction but not the other because the latter auctio
n
h
as reserve prices which are hi
g
her than the
y
are willin
g

to pa
y
. However, this
screen
i
ng-out exp
l
anat
i
on cannot account
f
or t
h
e
bidd
ers w
h
o
bid

i
n t
h
e presence o
f
reserve
p
rices but fail to bid in the absence of reserve
p
rices; there were 3 such

bidders in the Antiquities auctions, and 2
5
such bidders in the Arabian Ni
g
hts
a
uct
i
ons. T
h
e secon
d
potent
i
a
l
o
bj
ect
i
on
i
s t
h
at
bidd
ers may
h
ave
bid

i
n t
h
e c
h
rono-
l
og
i
ca
ll
y
fi
rst auct
i
on,
b
ut not t
h
e secon
d
,
i
n a pa
i
r
b
ecause t
h

ey
h
a
d
a
l
rea
d
y
b
oug
h
t
the cards b
y
the time the second auction occurred. This complaint potentiall
y
affect
s
the 25 Arabian Nights bidders just cited, who bid in Auction BR but not in Auction
B
A. In
d
ee
d
, t
h
ree o
f
t

h
ese
bidd
ers eac
h
p
l
ace
d
a
bid
on a s
i
ng
l
e car
d

i
n Auct
i
on BR
a
nd won it, so there would be no reason to ex
p
ect them to bid in the second auction.
H
owever, none o
f
t

h
e rema
i
n
i
ng 22
bidd
ers won a
ll
t
h
e car
d
s t
h
ey
bid
on
i
n Auct
i
on
B
R: ten
did
not w
i
n any car
d
s at a

ll
, w
hil
e t
h
e rema
i
n
i
ng twe
l
ve won an average o
f
5
0 percent of the cards the
y
bid on. It is still possible that these bidders mana
g
ed to
purc
h
ase t
h
e rest o
f
t
h
e car
d
s t

h
ey were
i
ntereste
d

i
n
f
rom someone e
l
se
d
ur
i
ng t
h
e
wee
k
t
h
at passe
d

b
etween my two auct
i
ons,
b

ut I can at
l
east say t
h
at t
h
ey
did
not
bu
y
them from me. Thus, the evidence is fairl
y
stron
g
that bidders in these auctions
E
XPERIMENTAL
EE
E
L
V
IDEN
CE
O
N
THE
E
E
NDOGENOUS

E
E
E
S
NTRY
EE
OF
B
F
IDDER
S
11
5
m
ade stochastic entr
y
decisions: faced with the same auction opportunit
y
, the same
person mi
g
ht sometimes enter and sometimes fail to enter. This contrasts with the
resu
l
ts o
f
Pa
lf
rey an
d

Pevn
i
ts
k
aya (2003), w
h
o
fi
n
d
ev
id
ence t
h
at t
h
e
l
ess r
i
s
k
-averse
bidders consistentl
y
tend to enter while the more risk-averse bidders consistentl
y
tend not to enter
.
T

h
e stoc
h
ast
i
c entry
d
ec
i
s
i
on m
i
g
h
t not
b
e
d
ue to consc
i
ous ran
d
om
i
zat
i
on
b
y

a
bidder tr
y
in
g
to follow a “mixed strate
gy
” in the textbook sense. Perhaps bidders
e
nter “randoml
y
” because of other thin
g
s happenin
g
in their lives: a colle
g
e student
h
a
d
too muc
h

h
omewor
k
one wee
k
, or a computer programmer

h
a
d
a
f
am
il
y emer-
g
enc
y
. Lots of random events could cause bidders to show up to one auction but
n
ot another. However, in terms of auction desi
g
n and welfare considerations, what
m
atters
i
s w
h
et
h
er t
h
e entry
d
ec
i
s

i
ons
i
n a rea
l
-wor
ld
auct
i
on are
d
eterm
i
n
i
st
i
ca
ll
y
predictable b
y
the auctioneer and b
y
the rival bidders. M
y
evidence shows that at
l
east in this market, bidder entr
y

decisions are stochastic, so the model of Levin and
Sm
i
t
h
(1994)
h
as emp
i
r
i
ca
l
re
l
evance.
4
.3. Optima
l
Reserve Price wit
h
En
d
ogenous Entr
y
R
ecall that the main prediction of the MQV paper is that raisin
g
the reserve price
f

rom some low value to the salva
g
e value of the
g
ood will increase expected auction
pro
fi
ts, even
i
n an en
d
ogenous-entry context. In or
d
er to un
d
erstan
d
t
h
e e
ff
ect o
f
t
h
e
reserve
p
rice on ex
p

ected revenues, I turn to the between-card ex
p
erimental data.
R
ecall that these data provide samples of auction revenues at differin
g
reserve price
l
eve
l
s (norma
li
ze
d

b
y C
l
o
i
ster pr
i
ce
f
or eac
h
car
d
).
Table 4 summarizes the results of the experiment separatel

y
for each reserve-
p
rice decile, from reserve
p
rices of 0% of the Cloister
p
rice to reserve
p
rices of
150% of the Cloister price. The table displays the total number of cards I auctioned
a
t each reserve
p
rice, the number of those which went unsold, and the mean an
d
standard deviation of the revenues at each reserve
p
rice level. The revenues are also
n
orma
li
ze
d

b
y t
h
e C
l

o
i
ster pr
i
ce o
f
eac
h
car
d
, an
d
an unso
ld
car
d
counts as an
o
bservation of zero revenue. The data are displa
y
ed
g
raphicall
y
in Fi
g
ure 1, with the
m
ean revenues plotted a
g

ainst the reserve prices. The error bars show one standard
e
rror
i
n eac
h

di
rect
i
on (w
h
ere t
h
e stan
d
ar
d
error equa
l
s t
h
e stan
d
ar
d

d
ev
i

at
i
on
i
n
revenues
f
or t
h
at reserve pr
i
ce
l
eve
l

di
v
id
e
d

b
y t
h
e square root o
f
t
h
e num

b
er o
f
o
bservations at that reserve price level). We see that the revenues are quite hi
g
h
a
t a reserve pr
i
ce o
f
zero, t
h
en
d
rop o
ff
s
h
arp
l
y at a reserve pr
i
ce o
f
10% o
f
C
loister price. Revenues seem to rise again, generally, between 50% and 100%

o
f the Cloister price, then fall a
g
ain at hi
g
her reserve price levels. There are surpris-
i
ngly high revenues observed at 140% to 150% of the Cloister price, albeit with
hi
g
h
stan
d
ar
d
errors.
To test the MQV prediction also requires an estimate of the salva
g
e value for the
u
nso
ld
car
d
s. I as
k
e
d
my
l

oca
l
car
d

d
ea
l
er w
h
at
h
e wou
ld
pay me
f
or my unso
ld
c
ar
d
s;
h
e respon
d
e
d
w
i
t

h
an o
ff
er t
h
at was 20 percent o
f
t
h
e
i
r C
l
o
i
ster pr
i
ce. He
f
urther indicated that 20% of Cloister price would be his avera
g
e offer price for
116 Ex
p
erimental Business Research Vol. II
Table 4. Cards and revenues at each reserve
p
rice. (Reserve
p
rices and revenue

s
normalized by the Cloister price o
f
each card).
Reserve price Total cards Unsold cards Mean revenue Std dev o
f
revenue
0
.0 9
6
0 1.192 1.071
0
.1 33 0 0.847 0.
5
49
0
.2 36 2 0.8
5
70.
5
94
0
.3 34 0 0.823 0.
5
99
0
.4 27 2 0.77
5
0.
5

00
0
.5 32 2 0.
9
45 0.517
0
.6 20 1 0.
9
77 0.480
0
.7 16 0 0.96
5
0.2
5
9
0
.8 23 1 1.093 0.4
6
9
0
.9 31 4 0.983 0.
5
00
1
.0 3
5
6 1.0
55
0.674
1

.
132 4 1
.
113 0
.
491
1
.2 1
5
7
0
.
80
4
0
.
86
1
1
.
3
21 1
00
.7
60 0
.772
1
.4 17 6 0.
9
67 0.867

1
.5 14 5 1.104 0.8
9
3
c
ar
d
s o
f
t
hi
s qua
li
ty an
d
quant
i
ty, so I a
d
opt a sa
l
vage va
l
ue o
f
20% percent o
f
t
h
e

Cl
o
i
ster pr
i
ce
f
or eac
h
car
d.
20
N
ow the question is whether a reserve price equal to the salva
g
e value
y
ields
e
xpecte
d
pro
fi
ts at
l
east as
hi
g
h
as a reserve pr

i
ce
l
ess t
h
an t
h
e sa
l
vage va
l
ue (0% or
10%) o
f
sa
l
vage va
l
ue. T
h
e po
i
nt est
i
mates o
f
revenues certa
i
n
l

y
i
n
di
cate t
h
at t
h
e
opposite is the case. In order to perform a formal h
y
pothesis test, first I calculate
e
xpecte
d
pro
fi
ts rat
h
er t
h
an expecte
d
revenues. For t
h
e 0% reserve pr
i
ce, a
ll
car

d
s
so
ld
, so pro
fi
ts rema
i
n t
h
e same as revenues: 1.192. For t
h
e 20% reserve pr
i
ce, two
c
ards went unsold; when I count salva
g
e profits of 20% of Cloister price for each of
E
XPERIMENTAL
EE
E
L
V
IDEN
CE
O
N
THE

E
E
NDOGENOUS
E
E
E
S
NTRY
EE
OF
B
F
IDDER
S
11
7
F
igure 1. Mean Revenue as a Function o
f
Reserve Pric
e
these cards, the estimate of expected profit rises sli
g
htl
y
, from 0.8
5
7 to 0.870. Usin
g
the calculated standard deviations, I conduct a test of the null hypothesis of equality

b
etween expecte
d
pro
fi
ts at 0% reserve pr
i
ce an
d
expecte
d
pro
fi
ts at 20% reserve
price. The resultin
g
standard normal test statistic is 2.18, with a p-value of 0.029.
T
hus, I reject the null hypothesis of equality at the
5
% level of significance, and
c
onc
l
u
d
e t
h
at expecte
d

pro
fi
ts are actua
ll
y
h
ig
h
e
r
for a zero reserve price than they
r
a
re for a reserve price equal to the salva
g
e value.
2
1
This is a violation of the theoretical
p
rediction, an exam
p
le of a case in which
t
h
e auct
i
oneer
d
oes

b
etter to
h
o
ld
an auct
i
on w
i
t
h
a zero reserve pr
i
ce t
h
an to
set the reserve price equal to the salva
g
e value. One possible explanation is that an
a
uction with no reserve price generates more enthusiasm among bidders, causing
hi
g
h
er
l
eve
l
s o
f

part
i
c
i
pat
i
on. In ot
h
er wor
d
s, mo
d
est m
i
n
i
mum
bid
s may e
li
m
i
nate
some hi
g
h valuation-bidders, who would have bid hi
g
h if the
y
had participated,

but decide not to participate unless their attention is attracted by an auction with
z
ero m
i
n
i
mum
bid
s. A
l
t
h
oug
h
a
f
ew
i
tems may en
d
up
b
e
i
ng so
ld
at very
l
ow
prices, the

y
mi
g
ht serve as “loss leaders,” similar to the
g
oods advertised at deep
d
iscounts by supermarkets, enabling the auctioneer to collect higher revenues over-
all
. T
hi
s propose
d
e
ff
ect
i
nvo
l
ves
i
ncrease
d
entry t
h
roug
h
attract
i
ng

bidd
ers’ atten-
tio
n, with the absolute auction as a t
y
pe of promotion, rather than assumin
g
the
bidders will make a careful calculation of the costs versus the benefits of bidding.
Note
i
n Ta
bl
e 4 t
h
at t
h
e tota
l
num
b
er o
f

bidd
ers
i
n Auct
i
on R0

i
s actua
ll
y
l
ower
than in the other auctions, which mi
g
ht seem to be evidence a
g
ainst this effect,
a
lthough I should also note that the number of cards in auction R0 is also lower
t
h
an
i
n t
h
e auct
i
ons w
i
t
h
reserve pr
i
ces. One caveat a
b
out t

hi
s
fi
n
di
ng
i
s t
h
at most o
f
the zero-reserve-price cards were sold in the same auction (R0). Althou
g
h I did
0
0
.
2
0.
4
0
.
6
0
.
8
1
1
.2
1.4

0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.
9
1 1.1 1.2 1.3 1.4 1.5
Reserve Price
(
Fraction of Cloister Price
)
M
ean Revenue
(
Fraction of Cloister Price
)
118 Ex
p
erimental Business Research Vol. II
a
ttempt to keep all other variables constant across auctions, the anomal
y
mi
g
ht be
d
ue to some uncontrolled factor which was different between R0 and the earlier
a
uct
i
ons
.
5

. CONCLUSIONS
T
his stud
y
presents the results of controlled experimental auctions performed in
a

fi
e
ld
env
i
ronment. By auct
i
on
i
ng rea
l
goo
d
s
i
n a preex
i
st
i
ng, natura
l
auct
i

on
m
arket, I have obtained data in a manner that is intermediate between laborator
y
e
xperiments and traditional studies of field data. Some variables were unfortunatel
y
u
no
b
serva
bl
e an
d
uncontro
ll
e
d
–
f
or examp
l
e, I cou
ld
not ass
i
gn “va
l
uat
i

ons”
f
or
e
ach
g
ood to each bidder, as a laborator
y
experimentalist mi
g
ht. On the other hand,
I
have the opportunit
y
to hold constant most of the relevant variables in the environ
-
m
ent, an
d
to man
i
pu
l
ate t
h
e treatment var
i
a
bl
e, w

hi
c
h

i
n t
hi
s case was t
h
e ex
i
st-
e
nce and level of reserve prices. B
y

g
ivin
g
up the abilit
y
to observe and manipulate
some of variables that laborator
y
experimenters can control, I
g
ained a realistic
e
nv
i

ronment. T
h
e part
i
c
i
pants
h
a
d
prev
i
ous exper
i
ence
biddi
ng
f
or t
h
e types o
f
rea
l
g
oods I auctioned, and the auctions took place in an Internet-based market where
bidder entr
y
decisions seemed potentiall
y

important.
T
h
e
fi
rst resu
l
t
i
s t
h
at entry costs are an
i
mportant
f
eature o
f
t
hi
s rea
l
-wor
ld
a
uction markets, thus confirmin
g
the central assumption of endo
g
enous-entr
y

auc-
tion theor
y
. The costs in the Ma
gic
-
card market are probabl
y
not nearl
y
as dramatic
a
s t
h
ose postu
l
ate
d

i
n ot
h
er mar
k
ets (
f
or examp
l
e,
i

n t
h
e mar
k
et
f
or o
ff
s
h
ore o
il
ri
g
hts the bidders t
y
picall
y
hire
g
eolo
g
ists to perform extensive anal
y
sis of the
potential for oil in a
g
iven tract). Here, the cost of acquirin
g
information about

i
n
di
v
id
ua
l
car
d
s
i
s qu
i
te sma
ll
,
b
ut even t
h
e cost o
f
typ
i
ng
i
n a
bid
amount appears
to have observable effects
.

Second, when the same cards were auctioned twice in rapid succession, ver
y
diff
erent sets o
f
peop
l
e
d
ec
id
e
d
to su
b
m
i
t
bid
s,
d
esp
i
te t
h
e
f
act t
h
at t

h
e same superse
t
o
f
p
eo
p
le were invited to
p
artici
p
ate both times. This can be inter
p
reted as evid-
ence in favor of the stochastic (mixed strate
gy
) entr
y
equilibrium model, where the
num
b
er o
f
part
i
c
i
pat
i

ng
bidd
ers var
i
es unpre
di
cta
bl
y.
Third, I found that, contrar
y
to the theor
y
of McAfee, Quan, and Vincent (2002),
a
zero reserve price can earn hi
g
her expected profits than a reserve price equal to the
a
uct
i
oneer’s sa
l
vage va
l
ue. Per
h
aps an a
b
so

l
ute auct
i
on attracts s
i
gn
ifi
cant
l
y more
b
idder attention than an auction with even modest reserve prices, causin
g
more
a
dditional entr
y
than mi
g
ht be su
gg
ested b
y
a model of rationall
y
calculated bidder
entry
d
ec
i

s
i
ons. It w
ill

b
e
i
nterest
i
ng to see w
h
et
h
er t
hi
s
fi
n
di
ng can
b
e rep
li
cate
d

i
n
o

ther auction markets
.
NO
TE
S
1
D
epartment of Economics, the Universit
y
of Arizona. I wish to thank Mike Urbancic, Marius Hauser,
and Mary Lucking for their research assistance, and Skaff Elias for product information about Ma
gi
c
:
t
h
e Gat
h
erin
g
.
I wou
ld

lik
e to t
h
an
k
J.S. But

l
er
,
Rac
h
e
l
Croson
,
G
l
enn E
lli
son
,
E
l
ton H
i
ns
h
aw
,
Dan
E
XPERIMENTAL
EE
E
L
V

IDEN
CE
O
N
THE
E
E
NDOGENOUS
E
E
E
S
NTRY
EE
OF
B
F
IDDER
S
119
Lev
i
n, K
i
p K
i
ng, Preston McA
f
ee, Ro
b

Porter, an
d
Jenn
if
er Re
i
nganum
f
or a
d
v
i
ce an
d
construct
i
ve
c
riticism
.
2
S
ee Ka
g
el (199
5
) for a review of auction experiments.
3
S
ee Hendricks and Paarsch (199

5
) for a review of empirical work on auctions.
4
T
h
ese mo
d
e
l
s
fi
n
d
s
i
mp
l
e, s
y
mmetr
i
c so
l
ut
i
ons
by
assum
i
n

g
t
h
at
bidd
ers
d
ec
id
e w
h
et
h
er to part
i
c
i
pate
b
e
f
ore t
h
e
y

l
earn t
h
e

i
r va
l
uat
i
ons. In m
y
auct
i
ons,
i
t
i
s reasona
bl
e to assume t
h
at part
i
c
i
pants
h
a
d
i
nformation about their valuations before makin
g
the entr
y

decision, so the entr
y
outcome mi
g
ht b
e
as
y
mmetric. An example of such an as
y
mmetric model is
g
iven b
y
Samuelson (198
5
), where onl
y
th
ose
bidd
ers w
i
t
h

hi
g
h
va

l
uat
i
ons part
i
c
i
pate
i
n t
h
e auct
i
on, an
d
t
h
e entry equ
ilib
r
i
um
i
s
i
n pure
s
trate
g
ies

.
5
S
ub
j
ects made the decision whether or not to incur the cost c to enter. After the entr
y
outcome was
observed, each of the n entrants had a 1/n chance of winnin
g
the pa
y
off for that round of th
e
e
xper
i
ment.
6
A
n
i
nterest
i
ng
i
mp
li
cat
i

on o
f
Pevn
i
ts
k
aya’s mo
d
e
l

i
s t
h
at an auct
i
oneer can actua
ll
y ma
k
e
hi
mse
lf
worse off b
y
advertisin
g
a sealed-bid auction heavil
y

. An increase in the number of potential bidders
i
ncreases the self-selection effect, causin
g
less and less risk-averse bidders to enter the auction, and
th
ere
b
y caus
i
ng
l
ess aggress
i
ve
biddi
ng, as r
i
s
k
avers
i
on
i
s we
ll
-
k
nown to
i

ncrease
bid
s
i
n a
fi
rst-pr
i
ce
s
ea
l
e
d
-
bid
auct
i
on
.
7
Al
t
h
oug
h
s
i
mu
l

taneous auct
i
ons are not tra
di
t
i
ona
l

f
or
f
am
ili
ar auct
i
ons, suc
h
as t
h
ose o
f
art, estate
g
oods, or tulip bulbs, such formats have been used for timber and offshore oil auctions. The advent of
c
omputerized biddin
g
appears to be makin
g

the simultaneous auction format even more common.
In a
ddi
t
i
on to t
h
e car
d
auct
i
ons
i
n t
hi
s newsgroup mar
k
et, s
i
mu
l
taneous We
b
-
b
ase
d
auct
i
ons are

becomin
g
common at commercial sites such as eBa
y
, and a simultaneous-auction format was used for
t
he recent FCC auctions of spectrum ri
g
hts (see McMillan (1994) for details).
8
A
lthou
g
h the standard practice in this marketplace is for auctioneers and other card sellers to char
g
e
b
uyers
f
or postage an
d
/or
h
an
dli
ng, I c
h
ose not to
d
o t

hi
s. I wante
d

bidd
ers to
bid

i
n
d
epen
d
ent
l
y, as
m
uc
h
as poss
ibl
e, on eac
h
o
f
t
h
e car
d
s

i
n w
hi
c
h
t
h
ey were
i
ntereste
d
. Someone ser
i
ous
l
y
i
ntereste
d

i
n
one card mi
g
ht decide to bid hi
g
her on a second card in the same auction than the
y
would if the cards
were auctioned independentl

y
, because the
y
would like to spread out the posta
g
e costs per card b
y
p
urc
h
as
i
ng more t
h
an one car
d
s
i
mu
l
taneous
l
y
f
rom t
h
e same source. In a
ddi
t
i

on, some o
f
t
h
e car
d
s I
auct
i
one
d

h
a
d
rat
h
er
l
ow va
l
ues, an
d
I wante
d
to avo
id

h
av

i
n
g
t
h
e car
d
va
l
ues
b
e swampe
d

by
t
h
e cost
of shippin
g
. For example, if a bidder won a sin
g
le card for 20 cents and then had to pa
y
a fixed 50-cent
s
hippin
g
char
g

e on top of that, the amount of useful information which could be derived from her bid
would be rather suspect. Therefore, in the interests of keepin
g
bid data as clean as possible, I decided
t
o pay postage costs myse
lf
, an
d
announce
d

i
n a
d
vance t
h
at
fi
rst-c
l
ass s
hi
pp
i
ng was
i
nc
l
u

d
e
d

i
n t
h
e
amount of each bid
.
9
A
sma
ll
num
b
er o
f
w
i
nn
i
ng
bidd
ers
f
a
il
e
d

to pay
f
or t
h
e car
d
s t
h
ey
h
a
d
won. In a
ll
, I rece
i
ve
d
payment
for 90% of the cards sold, constitutin
g
89% of the reported revenue in the within-card auctions. Almost
a
ll
o
f
t
h
e “
d

ea
db
eat”
bidd
ers were t
h
ose w
h
o won on
l
y a s
i
ng
l
e car
d
, an
d
w
h
o exp
l
a
i
ne
d
t
h
at t
h

ey
h
a
d
or
i
g
i
na
ll
y
h
ope
d
to w
i
n more car
d
s, an
d

did
n’t
f
ee
l

i
t was wort
h

i
t to comp
l
ete t
h
e transact
i
on. I
discoura
g
ed such behavior, but was unable to eliminate it. Onl
y
one or two individuals won multiple
c
ards but failed to pa
y
for them. Since none of the unpaid cards seemed to have outlandishl
y
hi
g
h
winning bid amounts, I have taken the point of view that all bids were made in good faith, and have no
t
e
xc
l
u
d
e

d
any o
b
servat
i
ons
f
rom my ana
l
ys
i
s.
10
Both auctions lasted exactly seven days. The same 8
6
cards were up for bid in each auction.
Each auction announcement was posted exactl
y
three times to the marketplace news
g
roup, and was
e
mailed to primaril
y
the same list of potential bidders. Even the sub
j
ect line of the announcements
and mailings was kept identical, except that in the second auction, the words “
5
Cent Minimum”

w
ere remo
v
e
d.
1
1
For examp
l
e, certa
i
n car
d
s
f
rom t
h
e Ara
bi
an N
i
g
h
ts expans
i
on set
i
ncrease
d

i
n va
l
ue
b
y a
f
actor o
f
ten
durin
g
their first
y
ear out of print. It turns out that market prices for cards were actuall
y
rather stable
during the month in which this experiment was conducted, but I did not know a
p
r
i
or
i
what was going
t
o
h
appen to car
d
pr

i
ces
.