Experimental Business Research II springer 2005 phần 2 docx

12 Ex
p
erimental Business Research Vol. I
I
T
able 3. Theoretical predictions with the intended parameters of the residual
q
ualit
y
d
i
s
tribution:
µ
=
−
1 an
d

σ
=
0
.2
Th
eory New-
l
ease pro
b
. Return rate Average Aggregate Pro
d
ucer

per perio
d
per per
l
ease use
d
-goo
d
surp
l
us per revenue pe
r
c
onsumer price perio
d
per perio
d
per
con
s
umer con
s
umer
k
=
80 0.34 0.
5
310
5
104 13

5
k
=
1
6
0 0.33 0.89 12
6
9
6
14
4
d
etermined; 4) a
gg
re
g
ate surplus per period, which measures how consumers as a
whole benefit from participating in the market; and
5
) producer revenue per period,
w
h
ose sources o
f
contr
ib
ut
i
on
i

nc
l
u
d
e new-
l
eases, exerc
i
se
d
opt
i
ons an
d
resa
l
e o
f
u
sed
g
oods. Variables normalized b
y
the number of periods and/or number of
subjects will enable us to combine results obtained from different experiments
o
f
t
h
e same sett

i
ng, an
d
to compare resu
l
ts
f
rom
diff
erent exper
i
menta
l
sett
i
ngs
i
n a
m
eanin
g
ful manner.
I
n order to have an appreciation of how finite sampling correction affects the
t
h
eoret
i
ca
l

pre
di
ct
i
on, we
fi
rst
li
st t
h
ese pre
di
ct
i
ons w
i
t
h
t
h
e or
i
g
i
na
ll
y c
h
osen
parameters for the residual qualit

y
distribution
µ
=
−
1

a
n
d
σ
=
0.2 in Table 3.
T
ypically, the finite sampling implies about
5
% corrections to the mean and 10%
c
orrect
i
ons to t
h
e vo
l
at
ili
ty. As we w
ill
see s
h

ort
l
y, a
ll
aggregate var
i
a
bl
es, except
return rate, are not ver
y
sensitive to the finite samplin
g
correction
.
Table 4 lists the results of Experiments 1 to 4, along with the corresponding
t
h
eoret
i
ca
l
pre
di
ct
i
ons correcte
d

b

y t
h
e
fi
n
i
te-samp
li
ng e
ff
ect. S
i
nce Exper
i
ments
2, 3 and 4 share the same
k
=
160, we first avera
g
e the a
gg
re
g
ate results from these
three experiments and then compare the average to the theory. The differences
b
etween t
h
ese t

h
ree exper
i
ments a
l
so serve as a cru
d
e measure o
f

b
e
h
av
i
or
fl
uctuat
i
on
s
from rather small sample sizes of sub
j
ects. Given the fact that there is no fittin
g
pro-
c
ess involved in the comparison, the level of the agreement between experimental
resu
l

ts an
d
t
h
eoret
i
ca
l
pre
di
ct
i
ons
i
n Ta
bl
e 4
i
s qu
i
te remar
k
a
bl
e. Quant
i
tat
i
ve
l

y, t
h
e
worst case is the return rate, in which the experimental values are s
y
stematicall
y
l
ower than that of the theory by about 30%. One way to interpret this systemati
c
diff
erence
i
s r
i
s
k
avers
i
on. T
h
e on
l
y uncerta
i
nty
i
n t
hi
s mo

d
e
l

i
s t
h
e consumpt
i
on
i
n
the first period of a new lease, represented b
y
an unknown residual qualit
y
that i
s
only realized at the lease-end. Thus, risk averse agents may be inclined to keep the
l
ease
d
un
i
t, w
h
ose va
l
ue
i

s
k
nown at t
h
e t
i
me o
f
exerc
i
s
i
ng t
h
e opt
i
on,
i
nstea
d
o
f
startin
g
another new lease. Consequentl
y
, return rate will be lower than the theor
y
that assumes risk neutral consumers. Another possible way to interpret the systemati
c

di
screpancy may
b
e trace
d
to owners
hi
p e
ff
ects. However, to sett
l
e t
h
e true cause,
a
dditional theoretical modelin
g
and experimental investi
g
ation are needed.
D
U
RABL
E
G
E
OODS
L
S
EASE

LL
C
E
O
NTRA
C
T
S
AN
D
U
S
ED
U
U
-
G
OODS
M
S
ARKET
M
M
B
T
E
HA
V
I
OR

13
T
able 4. Experimental results and theoretical predictions with the
fi
nite-sample parameter
s
o
f the residual
q
uality distribution realized in each experimen
t
Experiment New-lease prob. Return rate Average Aggregate Producer
New-lease prob. Return rate Average Aggregate
per period per per lease used-good surplus per surplus per
per lease used-good surplus per
consumer price period per period per
price period per
consumer consumer
1

(
k
=
80)
0.33 0.26 115 94 130
0.26 115 94
T
h
eory
2

0.33 0.37 113 101 130
0.37 113 101
2

(
k
=
160) 0.24 0.54 147 52 107
0.24 0.54 147 52
3

(
k
=
160) 0.27 0.70 122 70 117
0.27 0.70 122 70
4

(
k
=
160) 0.31 0.63 90 88 130
0.31 0.63 90 88
Avera
g
e
(2
,
3
,

4)
(
k
=
1
6
0
)
0.27 0.62 120 70 118
0.62 120 70
T
h
eory
3
0.32 0.80 132 91 142
0.80 132 91
A
primary policy question that a producer is interested in is how the market
wou
ld
respon
d
to a c
h
ange
i
n t
h
e str
ik

e pr
i
ce. T
h
e t
h
eory pre
di
cts t
h
at an
i
ncrease
i
n
t
he strike
p
rice from
k
=
80 to
k
=
160 at a fixed lease price will lead to a sli
g
ht
decrease in total lease volume, a substantial increase in the return rate, an increase in
average use
d

-goo
d
pr
i
ce, a re
d
uce
d
aggregate surp
l
us
f
or consumers, an
d
an
i
ncrease
i
n producer revenue. All these directional chan
g
es are confirmed in Table 4, with the
e
xception of producer revenue, which went the opposite way of the theoretical
p
re
di
ct
i
on. We attr
ib

ute t
hi
s
d
ev
i
at
i
on to t
h
e
f
act t
h
at t
h
ere are too
f
ew new
l
eases
i
n Experiments 2 and 3, caused b
y
issues of market rules and sub
j
ect samplin
g
m
entioned earlier. It is worth noting that the theory predicted a substantial change

on
l
y
i
n t
h
e return rate w
hil
e a
ll
ot
h
er c
h
anges are more mo
d
erate. Exper
i
menta
l
r
esults confirmed this substantial chan
g
e in the return rate.
We chose not to report standard deviation statistics. Since the game is dynamic
i
n nature,
d
ata across per
i

o
d
s were not
i
n
d
epen
d
ent. T
h
us, ca
l
cu
l
at
i
ng stan
d
ar
d
deviations, or an
y
other variance estimates, across periods would not be useful.
Furthermore, variations in subject behavior were mostly driven by their differ-
e
nt w
illi
ngness-to-pay parameter
θ
. Therefore, reporting variance estimates across

θ
i
ndividuals would not trul
y
reveal hetero
g
eneous individual characteristics such as
r
isk aversion. However, most of the comparative static holds true between any of
Exper
i
ment 2, 3, or 4 (w
i
t
h

k
=
1
6
0) and Experiment 1 (with
k
=
80
)
. T
h
us, we
h
av

e
s
ome confidence that the com
p
arison is valid.
14 Ex
p
erimental Business Research Vol. I
I
4
.3. Detailed Level Compariso
n
We now exam
i
ne
h
ow t
h
e exper
i
menta
l
resu
l
ts an
d
t
h
eoret
i

ca
l
pre
di
ct
i
ons compare
a
t a detailed level. In particular, we are interested in seein
g
how patterns of con-
sumer
b
e
h
av
i
or emerge as a
f
unct
i
on o
f
w
illi
ngness-to-pay. We are a
l
so
i
ntereste

d

i
n
see
i
n
g

h
ow use
d
-
g
oo
d
pr
i
ces c
h
an
g
e w
i
t
h
var
i
at
i

ons o
f
res
id
ua
l
qua
li
t
y
. For t
h
e sa
k
e
of space limitation, we will onl
y
use the results for Experiment 1 as illustratin
g
e
xamples. In most of the cases, the results of Experiment 1 are quite typical. Due to
t
h
e
f
act t
h
at t
h
e use

d
-
g
oo
d
mar
k
et
i
s treate
d
terse
ly

i
n t
h
e t
h
eor
y
, we expect t
h
at
the theor
y
will fare less well at a detailed level than at an a
gg
re
g

ate level.
I
n the following we treat the same subjects with a different
θ
essentially as a
θ
diff
erent consumer. I
f
a
ll
t
h
e
d
ata were use
d
, eac
h
su
bj
ect wou
ld

yi
e
ld
two po
i
nts.

T
hus, we observe a total of twice as man
y
consumers as the number of sub
j
ects
in each experiment. It can be argued that the data in the first two periods with
f
res
hly
ass
ig
ne
d

θ
values should be thrown away because of start-game effects.
θ
H
owever, we found that the conclusions are not de
p
endent on whether we exercise
this o
p
tion
.
4
.3.1. Average Payoff and Used-good Price
Fi
g

ure 1 shows avera
g
e pa
y
off per period as a function of consumer hetero
g
eneit
y

θ
.
I
n t
h
e
l
e
f
t pane
l
o
f
t
h
e
fi
gure, t
h
e t
h

eoret
i
ca
l
payo
ff
curve trac
k
s very c
l
ose
l
y t
h
e
e
xperimental pa
y
offs. The ri
g
ht panel of the fi
g
ure indicates that the observed used-
g
ood prices are clustered around the theoretical prediction. The trend that hi
g
her
res
id
ua

l
qua
li
ty
i
mp
li
es a
hi
g
h
er use
d
-goo
d
pr
i
ce
i
s repro
d
uce
d
, t
h
oug
h
w
i
t

h

l
arge
fluctuations. There is a small number of observations whose residual
q
ualities are
h
i
g
her than the point where the theor
y
curve ends. This si
g
nals a sli
g
ht behavior
d
ev
i
at
i
on
f
rom t
h
e t
h
eory, w
hi

c
h
pre
di
cts t
h
at t
h
ere
i
s an upper
li
m
i
t
i
n res
id
ua
l
qualities in the used-
g
ood market due to the presence of the option. Nevertheless,
Fi
g
ure 1 allows us to conclude safel
y
the followin
g
results.

−
50
0
50
100
15
0
200
25
0
300
350
0.0 0.2 0.4 0.6 0.8 1.0
.
.
Consumer Hetero
g
ene
i
t
y
Average Payoff
0
50
100
15
0
2
00
250

300
350
0.0 0.1 0.2 0.3 0.4 0.
5
0.6
R
es
id
ua
l
Qua
li
t
y
Used-good Pric
e
Figure 1. Average payoff as a function of consumer
h
eterogeneity (
l
eft pane
l
) an
d
use
d
-goo
d
price as a function of resi
d

ua
l
qua
l
ity (rig
h
t pane
l
). Curves are t
h
eoretica
l
pre
d
ictions an
d

d
iamon
d
points are experimenta
l
o
b
servations in Experiment 1.
D
U
RABL
E
G

E
OODS
L
S
EASE
LL
C
E
O
NTRA
C
T
S
AN
D
U
S
ED
U
U
-
G
OODS
M
S
ARKET
M
M
B
T

E
HA
V
I
OR
1
5
Result 1: Observed payoffs are consistent with the theory.
py y
Result 2: Observed used-good prices are consistent with the theory.
gp y
4
.3.2. Behavioral Segmentation
T
he theoretical model predicts that sub
j
ects would be se
g
mented endo
g
enousl
y
into
t
h
ree c
l
asses o
f

b
e
h
av
i
or. Lower va
l
uat
i
on consumers
θ
ʦ

(
0,
θ
m
)
are pr
i
ce
d
out o
f
the market. Medium
v
aluation consumers in
θ
ʦ

(
θ
m
,
θ
M
θ
)
p
artici
p
ate in the used-
g
ood market. Hi
g
h valuation consumers
θ
ʦ

(
θ
M
θ
,
1) lease new
g
oods and occasion-
all
y exerc
i

se t
h
e opt
i
on em
b
e
dd
e
d

i
n t
h
e
l
ease contract at
l
ease-en
d
.
Behavior se
g
mentation can be captured in two measures: new-lease probabilit
y
a
nd auction-winnin
g
probabilit
y

. Fi
g
ure 2 shows these probabilities as functions of
θ
. In Experiment 1, the theory predicts
θ
θ
m
=
0
.
33
an
d
θ
M
θ
=
0.47, respect
i
ve
l
y. As one
can see from Fi
g
ure 2, both new-lease probabilities and auction winnin
g
probabil-
ities are
q

uite low when
θ
<
0.3. This supports the conclusion that on avera
g
e, low
v
a
l
uat
i
on consumers are pr
i
ce
d
out o
f
t
h
e mar
k
et. New
l
ease pro
b
a
bili
t
i
es

b
eg
i
n to
ri
se

at

a
r
ou
n
d

θ
=
0.4 and become
q
uite close to the theoretical curve from around
θ
=
0.
5
onward. On the other hand, thou
g
h still rou
g
hl
y

concentratin
g
at around
t
h
e r
i
g
h
t reg
i
on, auct
i
on-w
i
nn
i
ng pro
b
a
bili
t
i
es are muc
h
more sprea
d
t
h
an t

h
e
theor
y
’s prediction. From time to time, consumers who would be theoreticall
y
the
pure used-
g
ood bu
y
ers also enter the new-lease market, and consumers who would
b
e t
h
eoret
i
ca
ll
y pure
l
essees venture
i
nto t
h
e use
d
mar
k
et. One

i
nterpretat
i
on
i
s t
h
at
the fundamental economics forces were operatin
g
correctl
y
. However, the perfect
rationalit
y
assumption in the theor
y
is obviousl
y
violated, leadin
g
to the smearin
g
i
n consumer segmentat
i
on.
Interest
i
ng

l
y, t
h
e smeare
d

b
e
h
av
i
or
d
oes not cause a su
b
stant
i
a
l
payo
ff
gap,
a
s can be inferred from the left panel in Fi
g
ure 1. This implies that the economic
i
ncent
i
ve t

h
at
i
s respons
ibl
e
f
or t
h
e s
h
arp segmentat
i
on
i
n t
h
eory
i
s not very strong
0
.
0
0
.2
0
.
4
0
.

6
0
.
8
1.
0
0
.
00
.2
0
.4
0
.
60
.
8
1.
0
C
onsumer Heterogeneit
y
N
ew-
l
ease Pro
b
a
bili
t

y
0
.
0
0
.
2
0
.
4
0
.
6
0
.
8
1
.
0
0
.
00
.2
0
.4
0
.
60
.
8

1.
0
C
onsumer Hetero
g
eneit
y
A
uction Winnin
g
Probabilit
y
Figure 2. New-
l
ease pro
b
a
b
i
l
ity (
l
eft pane
l
) an
d
auction winning pro
b
a
b

i
l
ity (rig
h
t pane
l)
as functions of consumer’s
h
eterogeneity
.
L
ines are t
h
eoretica
l
pre
d
ictions an
d

d
iamon
d
points are experimenta
l
o
b
servations in Experiment 1
.
16 Ex

p
erimental Business Research Vol. I
I
for those consumers whose willin
g
ness-to-pa
y
s are in the middle, and occasional
“
mistakes” are
g
racefull
y
tolerated. In addition, Fi
g
ure 2 also provides evidence on
w
h
y severa
l
su
bj
ects
h
ave t
h
e
i
r payo
ff

s muc
h

l
ower t
h
an t
h
e t
h
eoret
i
ca
l
curve. For
e
xam
p
le, consumers whose
θ
values lie between 0.8 and 0.9 should have leased
θ
m
ore new
g
oods rather than participated in auctions. Nevertheless, the followin
g
c
onc
l

us
i
on can
b
e
d
ra
w
n.
Result 3: Strong but Imperfect Patterns of Behavioral Segmentation.
gp g
4
.3.3. Cherry Picking
T
heoreticall
y
, units with a hi
g
her residual qualit
y
have a hi
g
her chance of bein
g
purc
h
ase
d

b

y t
h
e consumer exerc
i
s
i
ng
hi
s
l
ease-en
d
opt
i
on. T
h
us, t
h
e un
i
ts returne
d
to t
h
e pro
d
ucer wou
ld

h

ave a
di
str
ib
ut
i
on s
k
ewe
d
towar
d
s t
h
e
l
ow-en
d
compare
d
to
the ori
g
inal distribution of residual qualities. This kind o
f
cherry picking
p
henomeno
n
i

s a
l
so o
b
serve
d

i
n t
h
e exper
i
ment. F
i
gure 3 s
h
ows t
h
e
di
str
ib
ut
i
on o
f
res
id
ua
l

qualities for all the units and the distribution for those units that were returned to
the producer and subsequentl
y
entered the used-
g
ood market. Notice that not all
hi
g
h
res
id
ua
l
qua
li
ty un
i
ts were returne
d
to t
h
e pro
d
ucer as pre
di
cte
d.
F
urthermore, Kolmogorov-Smirnov Tests (Table 5) show that, in three out of
four ex

p
eriments, the distribution of residual
q
ualities of the returned units is con-
s
i
stent w
i
t
h
mo
d
e
l
pre
di
ct
i
ons. Exper
i
menta
l
ev
id
ence not on
l
y con
fi
rms t
h

e c
h
erry
p
i
c
ki
ng p
h
enomenon
i
n a qua
l
itativ
e
f
as
hi
on,
b
ut a
l
so suggests t
h
at t
h
e t
h
eory
is

sou
n
d
q
uantitativel
y
despite all the handicappin
g
factors mentioned before.
Result 4: Cherry Picking Observed and Consistent with Theory.
yg y
0
5
10
15
20
25
30
0
.2
0
.
30
.4
0
.
50
.
60
.

7
R
esidual Quality
F
requenc
y
0
3
6
9
12
15
0
.2
0
.
30
.4
0
.
50
.
60
.
7
R
esidual Quality
F
requency
F

igure 3. Distri
b
utions of resi
d
ua
l
qua
l
ities for a
ll
use
d
units (
l
eft pane
l
) an
d
for t
h
os
e
th
at enter t
h
e use
d
-goo
d
mar

k
et (rig
h
t pane
l
)
.
B
ars are ex
p
erimenta
l
o
b
servations i
n
Ex
p
eriment 1, an
d
curves are t
h
eoretica
l

p
re
d
ictions, w
h

ic
h
are norma
l
ize
d
to
h
av
e
t
h
e same masses as in t
h
e ex
p
eriment
.
D
U
RABL
E
G
E
OODS
L
S
EASE
LL
C

E
O
NTRA
C
T
S
AN
D
U
S
ED
U
U
-
G
OODS
M
S
ARKET
M
M
B
T
E
HA
V
I
OR
17
T

able 5. Kolmogorov-Smirnov Test to see if residual
q
ualities of the returned units wer
e
c
onsistent
w
ith the theoretical distribution
s
Ex
p
eriment Observations K-S Statistics P-Value
15
4 0.177 0.97
2
8
5
0.092 0.78*
3
122 0.0
6
9 0.70*
4
9
5
0.0
5
7 0.48*
*
cannot reject the null hypothesis at 95% confidence that observed residual qualities obey

t
he distribution specified b
y
the theoretical model
.
5
.
CO
N
C
L
US
I
O
N
A sequence o
f
exper
i
ments was con
d
ucte
d
at Hew
l
ett-Pac
k
ar
d
La

b
s,
i
n co
ll
a
b
orat
i
on
with Ford Research Lab, to stud
y
consumer behavior in a durable
g
oods market
where leasing is prevalent. The experiments have mostly confirmed aggregate pre-
di
ct
i
ons o
f
t
h
e t
h
eor
y
an
d
va

lid
ate
d
severa
l
qua
li
tat
i
ve
f
eatures o
f
t
h
e t
h
eoret
i
ca
l
m
odel. We observed sub
j
ects se
g
mentin
g
themselves into classes of behavior based
o

n their willingness-to-pay parameters. Subjects at the low end of willingness-to-pay
were pr
i
ce
d
out o
f

b
ot
h
t
h
e use
d
- an
d
t
h
e new-
g
oo
d
s mar
k
ets. Su
bj
ects at t
h
e

high
e
nd leased with increasin
g
frequencies. The
y
sometimes exercised their options
d
epending on the realization of the residual quality and the potential value achiev-
abl
e at t
h
e use
d
-
g
oo
d
s mar
k
et. T
h
e
l
ast se
g
ment o
f
t
h

e su
bj
ects
li
ve
d

i
n t
h
e m
iddl
e
a
nd primaril
y
participated in the used-
g
oods market. The sizes of these three
g
roups
were qualitatively consistent with the theoretical model. Furthermore, when we
i
ncrease
d
t
h
e str
ik
e pr

i
ce
i
n a
diff
erent treatment, t
h
e exper
i
menta
l
mar
k
et most
ly
responded in the direction predicted b
y
the model. This result is robust even with
small variations of market rules and sampling of subjects. Given the fact that the
t
h
eoret
i
ca
l
mo
d
e
l

h
as
l
ar
g
e
ly

g
rosse
d
over
i
ssues o
f
mar
k
et ru
l
es
i
n t
h
e use
d
-
g
ood market, the near a
g
reement between the theor

y
and experiment is hi
g
hl
y
n
on-trivial
.
On t
h
e ot
h
er
h
an
d
,
i
n a
ll
t
h
e exper
i
ments, t
h
e su
bj
ects w
i

t
h

high
va
l
uat
i
on
a
re more likel
y
to exercise the option relative to the theoretical prediction. There
a
re multiple possible explanations. One such possibility is risk aversion that is
n
ot a
dd
resse
d

by
t
h
e t
h
eoret
i
ca
l

mo
d
e
l
. W
i
t
h
r
i
s
k
avers
i
on, a
l
eas
i
n
g
su
bj
ect
h
as
the tendenc
y
to keep the used unit that entails no uncertaint
y
relative to lease a

n
ew good that has an unknown consumption in the first period. Other explana-
t
i
ons suc
h
as owners
hi
p e
ff
ects ma
y
a
l
so account
f
or t
h
e
di
screpanc
y

b
etween
18 Ex
p
erimental Business Research Vol. I
I
t

h
eory an
d
exper
i
menta
l
resu
l
ts. More ev
id
ence
i
s nee
d
e
d
to p
i
npo
i
nt t
h
e correct
e
x
p
lanation
.
The effect of learning in the experiment appears to manifest mostly in whether

su
bj
ects are use
d
to t
h
e econom
i
c context o
f
t
h
e exper
i
ment. Once su
bj
ects
f
am
ili
ar-
i
ze themselves with the decision-makin
g
process, there is no obviousl
y
discernable
e
ffect associated with progressive stages of the experiment. However, due to the
c

omp
l
ex sett
i
ng o
f
t
h
e exper
i
ment,
l
ess exper
i
ence
d
su
bj
ects, as exemp
lifi
e
d

i
n
Experiment 2, took a lon
g
time to fi
g
ure out what the

y
ou
g
ht to behave and hence
e
arned significantly less payoffs comparing to more experienced subjects.
T
h
ere are se
v
era
l

di
rect
i
ons t
h
at can
b
e
vi
e
w
e
d
as natura
l
extens
i

ons o
f
t
h
e
c
urrent work. To settle whether the aforementioned s
y
stematic bias in return rate is
c
aused by risk aversion or something else can be pursued by extending the theory to
i
nc
l
u
d
e r
i
s
k
avers
i
on an
d
con
d
uct
i
ng a
ddi

t
i
ona
l
exper
i
ments t
h
at are spec
ifi
ca
ll
y
d
esi
g
ned for this purpose. Another interestin
g
direction is to treat the residual qualit
y
being only partially observable, which in turn will allow the possibility of studying
t
h
e
i
nterp
l
ay
b
etween opt

i
ona
li
ty an
d
a
d
verse se
l
ect
i
on. Invest
i
gat
i
ons o
f

l
ease con-
tracts with more sophisticated options and under oli
g
opol
y
market structure are other
topics for future exploration. In addition, it is important to realize that the setting of
t
h
e current exper
i

ment
i
s not very
f
ar
f
rom many rea
li
st
i
c
b
us
i
ness env
i
ronments.
Adaptin
g
the experiment described in this paper to field studies has the potential to
provide useful business insights. Finally, work has already begun to use a modified
v
ers
i
on o
f
t
hi
s exper
i

ment to exam
i
ne
b
us
i
ness strateg
i
es
i
n ot
h
er aspects o
f
t
h
e
a
utomotive market
.
N
O
TE
S
1
I
f
t
h
e res

id
ua
l
qua
li
t
y
were
k
nown to t
h
e
l
essee at t
h
e s
ig
n
i
n
g
o
f
t
h
e
l
ease contract, t
h
ere wou

ld

h
ave
b
een no risk factor in each consumer’s decision-makin
g
process, at least theoreticall
y
. This, in turn,
w
ould have made the option embedded in the lease contract meanin
g
less.
2
T
h
e
fi
n
i
te-samp
l
e parameters o
f
t
h
e res
id
ua

l
qua
li
ty
di
str
ib
ut
i
on rea
li
ze
d

i
n Exper
i
ment 1 are
µ
=
−
0
.
9
5
a
n
d
σ
=

0
.
18
.
3
The finite-sample parameters of the residual qualit
y
distribution realized in Experiments 2, 3 and 4 are
µ
=
−
0.96 and
σ
=
0.22.
R
EFERENCES
Bl
ac
k
, F. an
d
Sc
h
o
l
es, M., (1973). “T
h
e Pr
i

c
i
ng o
f
Opt
i
ons an
d
Corporate L
i
a
bili
t
i
es.” Journa
l
of Po
l
it-
ical Econom
y
, 81, 637–6
5
9.
C
amerer, C., “Individual Decision Makin
g
.” In
T
he Handbook o

f
Experimental Economic
s
,
edited b
y
K
agel, J. and Roth, A. Princeton Univ. Press, 199
5
.
H
uan
g
, S. an
d
Yan
g
, Y., (2002). “Pr
i
c
i
n
g
Lease Contracts w
i
t
h
Opt
i
ons

i
n Imper
f
ect Mar
k
ets o
f
Dura
bl
e
G
oo
d
s.” Tec
h
n
i
ca
l
Report, For
d
Researc
h
La
b
orator
y.
H
uan
g

, S., Yan
g
, Y. and Anderson, K., (2001). “A Theor
y
of Finitel
y
Durable-Goods Monopol
y
wit
h
U
se
d
-
G
oo
d
s Mar
k
et an
d
Transact
i
on
C
osts.” Mana
g
ement Scienc
e
,

56
,
549–569.
D
U
RABL
E
G
E
OODS
L
S
EASE
LL
C
E
O
NTRA
C
T
S
AN
D
U
S
ED
U
U
-
G

OODS
M
S
ARKET
M
M
B
T
E
HA
V
I
OR
19
Mas
ki
n, E. an
d
T
i
ro
l
e, J., (1988). “A T
h
eory o
f
Dynam
i
c O
li

gopo
l
y: I an
d
II.” Econometrica
,
56
,
5
49–
5
69 and
5
71–
5
99.
Merton, R., (1973). “T
h
eory o
f
Rat
i
ona
l
Opt
i
on Pr
i
c
i

ng.”
B
e
ll
Journa
l
o
f
Economics
,
4
,
141–183
.
M
il
grom, P., (1981). “Rat
i
ona
l
Expectat
i
ons, In
f
ormat
i
on Acqu
i
s
i

t
i
on, an
d
Compet
i
t
i
ve B
iddi
ng.”
Eco
n
o
m
et
r
ica
,

49
,
921
–
943
.
Wilson, R., (1977). “A Biddin
g
Model of Perfect Competition.” Review of Economic Studies,
44,

5
11–
5
18.
APPENDIX: PAY
O
FF
CU
RVE
S
Th
e
f
o
ll
ow
i
ng
fi
gures s
h
ow payo
ff
s o
f
a
ll

f
our exper

i
ments. Eac
h
po
i
nt represents
the avera
g
e pa
y
off of a sub
j
ect under the same willin
g
ness-to-pa
y
parameter. It is
i
nterestin
g
to note that earnin
g
s for all sub
j
ects in Experiments 1 and 4 and for
m
ost su
bj
ects
i

n t
h
e ot
h
er two exper
i
ments are very c
l
ose to t
h
e pre
di
cte
d
va
l
ues.
As pointed out in section 4, some sub
j
ects in Experiments 2 and 3 were earnin
g
substantiall
y
less mone
y
.
E
x
p
eriment

1
−
50
0
50
100
15
0
200
250
300
350
0.0 0.2 0.4 0.6 0.8 1.0
.
.
C
onsumer Hetero
g
ene
i
t
y
Avera
g
e Pa
y
o
ff
E
x

p
er
i
ment
4
−
50
0
50
1
00
1
50
20
0
2
50
300
350
0.0 0.2 0.4 0.6 0.8 1.0
.
.
0
0
Consumer Heterogeneit
y
Average Payoff
Experiment
3
−

50
0
50
1
00
15
0
2
00
2
50
300
350
0.0 0.2 0.4 0.6 0.8 1.0
.
.
00
C
onsumer Heterogeneit
y
A
vera
g
e Pa
y
o
ff
Experiment
2
−

50
0
50
100
150
200
250
300
3
50
0.0 0.2 0.4 0.6 0.8 1.0
.0 0.2 0.4 0.6 0.8 1.
0
0
2
2
Consumer Hetero
g
eneit
y
Average Payoff
F
igure 4. Average payoff as a function of consumer
h
eterogeneity in a
ll
four experiments
.
K
agel, J., “Auctions: A Survey of Experimental Research.” In The Handbook o

f
Experimental Economic
s
,
e
dited by Kagel, J. and Roth, A. Princeton Univ. Press 1995.
M
ICROECONOMIC
M
M
AN
D
F
INANCIAL
FF
P
L
RICE
P
P
A
E
DJUSTMENT
P
T
ROCESSES
PP
21
21
Ch

apter 2
T
OWARDS A HYBRID MODEL O
F
M
ICROECONOMIC AND FINANCIAL PRICE
ADJU
S
TMENT PR
OC
E
SS
E
S
: THE
C
A
S
E
O
F A
M
ARKET WITH
CO
NTINU
O
U
S
LY REFRE
S

HED
SU
PPLY AND DEMAN
D
P
au
l
J Brewe
r
Hong Kong University of Science and Technology
Abs
tr
act
Microeconomics and financial economics
p
rovide alternative models of market
dy
nam
i
cs. A
l
on
g

hi
stor
y
o
f

l
a
b
orator
y
resu
l
ts s
h
ows t
h
at mar
k
et pr
i
ces
i
n t
h
e
laborator
y
conver
g
e towards the static predictions of microeconomic theor
y
with
a resulting classical efficiency of allocation. Yet, the informational efficiency
o
f

mar
k
et pr
i
ces, o
f
ten treate
d
as a start
i
n
g
ax
i
om
f
or
fi
nanc
i
a
l
mar
k
et t
h
eor
y
,
r

equires instead that current prices represent fair
g
ambles over an unknown distri-
bution of future
p
rices: financial
p
rice
p
rocesses are idealized as random walks with
i
n
d
epen
d
ent
i
ncrements per
h
aps mo
difi
e
d

by
some not
i
on o
f

h
eteros
k
e
d
ast
i
c
i
t
y
s
uch as stochastic volatilit
y
. Unlike prices followin
g
a Marshallian path, random
walks do not generally converge towards an equilibrium price. The conflict between
t
h
ese two v
i
ews o
f
mar
k
et processes
i
s exp
l

ore
d
an
d
a mo
d
e
l
t
h
at
i
s a
hyb
r
id
of the microeconomic and financial a
pp
roaches is constructed and com
p
ared
against data from laboratory markets involving continuously refreshed supply and
d
eman
d.
1. INTRODUCTION
T
his chapter is a ver
y
rou

g
h first attempt to inte
g
rate some ideas from acros
s
m
icroeconomics and finance about the price dynamics of competitive markets.
Th
e researc
h

i
s
f
rom t
h
e po
i
nt o
f
v
i
ew o
f
an exper
i
menta
l
econom
i

st
i
ntereste
d

i
n
laborator
y
market equilibration, not from the point of view of
g
eneral asset pricin
g
or finance in general. The goal is not to resolve all the questions one might have
a
b
out t
h
e nature o
f
pr
i
ce
dy
nam
i
cs, conver
g
ence or t
h

e
diff
er
i
n
g
approac
h
es or
assumptions that ma
y
be involved across various fields.
©
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
,
21–4
5.
22 Ex
p
erimental Business Research Vol. II
I
nstea
d
, t
h
e goa
l

i
s more mo
d
est, to put
f
orwar
d
t
h
e not
i
on t
h
at t
h
e no
i
sy equ
ili
-
b
rat
i
on o
f
a
f
a
i

r
l
y s
i
mp
l
e s
i
ng
l
e mar
k
et
i
s st
ill
a su
bj
ect wort
h
y o
f
stu
d
y. T
h
ere are
n
o “states of the world” in the sense of classical finance and, correspondin
g

l
y
, no
l
a
b
oratory
b
ets on secur
i
t
i
es w
h
ose va
l
ues are
b
ase
d
on co
i
n tosses or
di
ce ro
ll
s.
I
nstea
d

, t
h
ere
i
s a pa
i
r o
f
mar
k
ets, a pr
i
vate mar
k
et an
d
a pu
bli
c mar
k
et. Buyers an
d
sellers receive private, seemin
g
l
y
random opportunities to bu
y
or sell a
g

ood from
t
h
e “exper
i
menter”
i
n t
h
e
i
r pr
i
vate mar
k
et an
d
are a
bl
e to tra
d
e w
i
t
h
eac
h
ot
h
er

i
n
t
h
e pu
bli
c mar
k
et. Su
bj
ects are not to
ld
anyt
hi
ng a
b
out t
h
e
di
str
ib
ut
i
on o
f
t
h
ese
opportunities. The suppl

y
and demand curves representin
g
the a
gg
re
g
ate of these
pr
i
vate mar
k
et opportun
i
t
i
es are
h
e
ld
stat
i
onary an
d
t
h
e exper
i
menter o
b

serves t
h
e
t
i
me ser
i
es o
f
vo
l
untary tra
di
ng pr
i
ces
i
n t
h
e pu
bli
c mar
k
et.
Since the market
p
artici
p
ants do not know ex-ante what the
p

ublic market
p
rice
s
h
ou
ld

b
e, t
h
ere
i
s a
ki
n
d
o
f
en
d
ogenous
h
eterogene
i
ty an
d
comp
l
ex

i
ty o
f

b
e
li
e
f
s an
d
k
now
l
e
d
ge a
b
out mar
k
et con
di
t
i
ons more typ
i
ca
l
to t
h

e exper
i
menta
l
econom
i
cs
l
iterature than the classical finance literature. It is the
g
eneral success of experi-
m
enta
l
econom
i
cs
i
n prov
idi
ng a means o
f
stu
d
y
i
ng t
hi
s pecu
li

ar
ki
n
d
o
f
comp
l
ex
i
ty
t
h
at
i
s
h
ope
d
to ma
k
e suc
h
a
l
a
b
oratory approac
h
wort

h
w
hil
e
.
Althou
g
h a broad view of some of the problems one encounters in mer
g
in
g
id
eas
f
rom
diff
erent
fi
e
ld
s
i
s
i
mportant, u
l
t
i
mate
l

y t
h
e researc
h
reporte
d

h
ere
i
s muc
h
m
ore narrow
l
y
f
ocuse
d
upon a part
i
cu
l
ar
d
ata set an
d
a part
i
cu

l
ar
f
orm o
f
t
i
me-
series anal
y
sis. One can then attempt to ask questions about the adequac
y
of simple,
stat
i
onary mo
d
e
l
s: Can pr
i
ce equ
ilib
rat
i
on
b
e
d
escr

ib
e
d

b
y a s
i
mp
l
e mat
h
emat
i
ca
l
e
quat
i
on w
i
t
h

fi
xe
d
parameters or
i
s a mo
d

e
l
w
i
t
h
two or more reg
i
mes more appro-
priate? Does somethin
g
happen when markets equilibrate that we can detect in the
t
i
me-ser
i
es propert
i
es o
f
t
h
e
d
ata? T
h
e
d
ata reporte
d

h
ere
i
s an attempt to get at t
h
ese
quest
i
ons, among ot
h
ers. T
h
e researc
h

i
s not expecte
d
to answer many quest
i
ons at
this sta
g
e, but instead it is an attempt to stimulate new questions and to be
g
in a lon
g
process o
f

o
b
ta
i
n
i
ng answers ma
d
e poss
ibl
e t
h
roug
h
t
h
e cont
i
nue
d
wor
k
o
f

f
uture
researc
h
ers.

The remainder of this section will
p
rovide an overview of some literature, but
d
oes not preten
d
to
b
e a gu
id
e to t
hi
s su
bj
ect
f
or newcomers nor can
i
t even
h
ope
to even
b
r
i
e
fl
y cre
di
t a

ll
t
h
ose w
h
ose researc
h

f
orme
d
t
h
e present un
d
erstan
di
ng o
f
m
arkets. The introduction concludes with a brief road map or
g
anizin
g
the research
to
b
e presente
d
.

E
arly laboratory studies into market behavior, beginning with Smith (19
6
2),
were not desi
g
ned merel
y
to confirm or demonstrate known principles of economics.
Ear
l
y exper
i
menta
l
env
i
ronments
b
y
d
es
i
gn v
i
o
l
ate
d
t

h
ree common assumpt
i
ons
once t
h
oug
h
t appropr
i
ate
f
or t
h
e app
li
ca
bili
ty o
f
compet
i
t
i
ve mo
d
e
l
s: (
i

) perfec
t
in
f
ormation was violated as student sub
j
ects t
y
picall
y
knew onl
y
their own costs and
v
a
l
ues w
h
en tra
di
ng, not t
h
e costs or va
l
ues o
f
ot
h
ers, t
h

e aggregate supp
l
y an
d
d
eman
d
, or t
h
e
di
str
ib
ut
i
ons
f
rom w
hi
c
h
costs an
d
va
l
ues were
d
rawn;
(ii)
continuit

y
was violated at the unit level and the a
g
ent level because the units traded in the
m
ar
k
et are
i
n
di
v
i
s
ibl
e an
d

b
ecause agents were not tra
di
ng sma
ll
quant
i
t
i
es re
l
at

i
ve
to t
h
e aggregate mar
k
et; (
iii
) perfect rationa
l
ity was pro
b
a
bl
y v
i
o
l
ate
d

b
ecause t
h
e
M
ICROECONOMIC
M
M
AN

D
F
INANCIAL
FF
P
L
RICE
P
P
A
E
DJUSTMENT
P
T
ROCESSES
PP
23
s
tu
d
ent su
bj
ects o
f
ten
h
a
d
no prev
i

ous exposure to tra
di
ng an
d
t
h
ere
f
ore cou
ld
not
b
e
e
xpecte
d
to tra
d
e as we
ll
as t
h
e per
f
ect
l
y rat
i
ona
l

h
omo economicu
s
,
an
d
poss
ibl
y
n
ot even as well as a businessman or
p
rofessional trader.
H
i
g
h
e
ffi
c
i
enc
i
es o
f
a
ll
ocat
i
on an

d
convergence o
f
o
b
serve
d
pr
i
ces an
d
tra
d
e
d
q
uant
i
t
i
es to t
h
e pre
di
ct
i
ons o
f
compet
i

t
i
ve t
h
eory nevert
h
e
l
ess occurre
d

i
n ear
l
y
laborator
y
markets. A critic who onl
y
saw the experiments as a misconstruction relat-
i
ve to t
h
e requ
i
rements o
f
ex
i
st

i
ng t
h
eor
i
es,
i
na
d
equate
l
y “s
i
mu
l
at
i
ng” a
l
arger mar
k
et,
or re
l
y
i
ng “too muc
h
” on
d

ata
f
rom stu
d
ents
i
nstea
d
o
f
exper
i
ence
d

b
us
i
nessmen or
p
rofessional traders would potentiall
y
miss an interestin
g
result re
g
ardin
g
the robust-
n

ess o
f
compet
i
t
i
ve processes. T
h
ese ear
l
y
l
a
b
oratory mar
k
ets were rea
l
mar
k
ets.
T
h
e resu
l
ts s
h
owe
d
t

h
at t
h
e
d
eta
il
s o
f
tra
di
ng
i
nst
i
tut
i
ons matter: t
h
e pr
i
ces
i
n t
h
e
m
arkets of Chamberlin (1948) did not conver
g
e nearl

y
as well as Smith (1962)
b
ecause Sm
i
t
h

i
nc
l
u
d
e
d
spec
ifi
c
ki
n
d
s o
f
tra
di
ng structure – t
h
e pu
bli
c

l
y o
b
serva
bl
e
bid
s an
d
as
k
s recor
d
e
d
on a
bl
ac
kb
oar
d
an
d
t
h
e
i
mprovement requ
i
rement (

bid
s go
u
p
, asks come down until a trade occurs) inherent to double auction rules – while
C
h
am
b
er
li
n’s comp
l
ete
l
y unstructure
d
approac
h

l
e
f
t tra
d
ers on t
h
e
i
r own to

d
ec
id
e
wh
at to
d
o as t
h
ey wa
lk
e
d
aroun
d
an
d
searc
h
e
d
out tra
d
es w
i
t
h
ot
h
ers

i
n t
h
e room.
Charles Plott and a number of other researchers duplicated Smith’s earl
y
laborator
y
r
esu
l
ts, go
i
ng on to
l
a
b
oratory
i
nvest
i
gat
i
ons
i
nvo
l
v
i
ng mu

l
t
i
p
l
e mar
k
ets, trans-
f
ormat
i
on an
d
pro
d
uct
i
on, an
d
ot
h
er comp
l
ex scenar
i
os.
T
he broad
p
attern of these results demonstrated that markets could function

f
a
i
r
l
y we
ll
– g
i
ven t
h
e proper structure an
d
a
bi
t o
f

l
earn
i
ng
b
y repet
i
t
i
on – w
i
t

h
l
umpy goo
d
s an
d
on
l
y a
f
ew
i
nexper
i
ence
d
tra
d
ers
i
n a var
i
ety o
f
s
i
tuat
i
ons an
d

applications. Plott (2000) has ar
g
ued that laborator
y
research on market processes
an
d
equ
ilib
rat
i
on can support a mo
d
ern
i
zat
i
on o
f
Haye
k
’s v
i
ew o
f
t
h
e mar
k
et. Haye

k
(
1945) viewed markets as human institutions providing a means of imperfect, but
s
elf-correctin
g
, coordination and solution to a demand/suppl
y
problem without
h
av
i
ng to convey a
ll
t
h
e
i
n
f
ormat
i
on a
b
out mar
k
et con
di
t
i

ons to a s
i
ng
l
e m
i
n
d
.
P
rev
i
ous
l
a
b
oratory stu
di
es revea
l
mar
k
et equ
ilib
rat
i
on
lik
ene
d

to a rat
i
ona
l

b
ut
almost mechanical process, possibl
y
unreco
g
nized b
y
the market participants,
attempt
i
ng to
fi
n
d
t
h
e so
l
ut
i
on o
f
an equat
i

on
b
a
l
anc
i
ng supp
l
y an
d

d
eman
d
. Even
th
oug
h
no one (except t
h
e exper
i
menters)
k
nows t
h
e equat
i
ons or
h

as
f
u
ll

k
now
l
e
d
ge
of the parameter values needed to solve the equations, the rationalit
y
inherent in
p
ro
fi
t-see
ki
ng
b
e
h
av
i
or wou
ld

d
r

i
ve t
h
e process to equ
ilib
r
i
um.
I
n contrast, t
h
e
f
ramewor
k
Go
d
e an
d
Sun
d
er (1993)
d
eve
l
ope
d
as an a
l
ternat

i
ve
e
xplanation for market equilibration b
y
wa
y
of their Zero Intelli
g
ence (ZI) robot
a
l
gor
i
t
h
m
d
emonstrate
d
a strong potent
i
a
l

f
or a mec
h
an
i

ca
l
, non-rat
i
ona
l
converg-
e
nce processes
b
ase
d
on
l
y on
b
u
d
get constra
i
nts an
d
not on pro
fi
t max
i
m
i
zat
i

on.
The ZI robot framework is still a popular environment for be
g
innin
g
a stud
y
of
m
ore comp
l
ex p
h
enomena (see Farmer, Pate
lli
an
d
Zov
k
o (2004)
f
or a recent
e
xamp
l
e or Du
ff
y (2004)
f
or a rev

i
ew). Pr
i
ces
i
n mar
k
ets popu
l
ate
d

b
y t
h
e ZI ro
b
ots
appear to conver
g
e towards competitive equilibria and exhibit ne
g
ative autocorrela-
t
ion of price changes. Cason and Friedman (199
6
) find negative autocorrelations
o
f
pr

i
ce c
h
anges
i
n
l
a
b
oratory mar
k
ets popu
l
ate
d

b
y
i
nexper
i
ence
d

h
uman tra
d
ers,
24 Ex
p

erimental Business Research Vol. II
w
i
t
h
t
h
e autocorre
l
at
i
ons mov
i
ng towar
d
s zero an
d
pos
i
t
i
ve autocorre
l
at
i
on w
i
t
h
m

ore exper
i
ence
d
su
bj
ect poo
l
s. Bot
h
stu
di
es a
l
so s
h
ow t
h
at
l
arge surp
l
us tra
d
es
would occur earlier in the market, with conver
g
ence bein
g
driven b

y
the fact that
t
hi
s
l
eaves t
h
e pr
i
ce-constra
i
ne
d

l
ow surp
l
us tra
d
es to occur
l
ater
i
n t
h
e mar
k
et
per

i
o
d
.
While laborator
y
microeconomics has developed a bod
y
of empirical re
g
ularities
surroun
di
ng
i
mper
f
ect –
b
ut
f
unct
i
ona
l
– mar
k
ets, stan
d
ar

d

fi
nanc
i
a
l
t
h
eory genera
ll
y
b
eg
i
ns w
i
t
h
a set o
f
ax
i
omat
i
ca
ll
y
d
e

fi
ne
d
per
f
ect mar
k
ets an
d

d
er
i
ves
f
urt
h
er prop-
e
rties under various conditions in an uncertain world usin
g
mathematical probabilit
y
t
h
eory. Ta
k
e,
f
or examp

l
e, t
h
e case o
f
a popu
l
ar an
d
regu
l
ar
l
y tra
d
e
d
stoc
k
on t
h
e
NYSE or NASDAQ. Ana
l
ysts
f
o
ll
ow t
h

e
b
us
i
ness c
l
ose
l
y. T
h
ere
f
ore, at
l
east among
the ma
j
or market participants settin
g
prices, one mi
g
ht assume perfect information
or at
l
east
h
omogeneous
i
n
f

ormat
i
on. M
illi
ons o
f
s
h
ares are tra
d
e
d
, so cont
i
nu
i
ty
i
s
vi
rtua
ll
y sat
i
s
fi
e
d
. T
h

e ma
j
or mar
k
et part
i
c
i
pants are genera
ll
y expert tra
d
ers, an
d
so
should be actin
g
rationall
y
. If one assumes that all known information has been full
y
processe
d

b
y a per
f
ect mar
k
et, t

h
e pre
di
ct
i
on o
f

fi
nance
i
n t
h
e s
h
ort term
i
s amaz-
i
ng
l
y s
i
mp
l
e: t
h
e s
h
are pr

i
ce s
h
ou
ld
represent a
f
a
i
r gam
bl
e
b
ase
d
on t
h
e pro
b
a
bili
ty
d
istribution of
p
ossible share
p
rices in the near future.
Over t
i

me, pr
i
ces s
h
ou
ld
ex
hibi
t t
h
e propert
i
es o
f
a Mart
i
nga
l
e process, suc
h
as
z
ero autocorre
l
at
i
on o
f
pr
i

ce c
h
anges. F
i
e
ld
tests on
fi
nanc
i
a
l
mar
k
et
d
ata y
i
e
ld
v
arious non-zero results.
1
However, a careful theorist can still ar
g
ue that the Martin-
g
a
l
e property

i
s an ex-ant
e
property re
l
ate
d
to
h
istorica
l
ex
p
ectation
s
a
b
out
f
uture
pr
i
ces an
d
t
h
ere
f
ore
i

mposs
ibl
e to test
e
x-pos
t
based solely on observed prices alone
t
without some additional assum
p
tions – see for instance, Bossaerts (2002;
pp
. 42–
43). W
i
t
h
out certa
i
n s
i
mp
lif
y
i
ng assumpt
i
ons, one wou
ld
wou

ld

i
nstea
d
nee
d
to
b
e
abl
e to some
h
ow recor
d
w
h
at t
h
e “mar
k
et was t
hi
n
ki
ng” a
b
out
f
uture pr

i
ces, an
d
test
whether the
p
rice at each moment in time e
q
ualed this ex
p
ectation as beliefs evolve.
O
f
course, t
hi
s ex-ante
ki
n
d
o
f
Mart
i
nga
l
e t
h
eory
i
s muc

h
more
diffi
cu
l
t to
f
a
l
s
ify
, an
d
a
l
so causes t
h
e
fi
ne
d
eta
il
s o
f

b
e
li
e

f
s to
b
ecome
i
mportant. Are
b
e
li
e
f
s
a
ctuall
y
homo
g
eneous so that all market participants have the same expectations or
i
s t
hi
s mere
l
y a conven
i
ent approx
i
mat
i
on? I

f

b
e
li
e
f
s are
h
omogeneous, are t
h
ey
c
orrect or at
l
east un
bi
ase
d
? Does
i
t matter
if

h
omo
g
eneous, correct
b
e

li
e
f
s
d
o not
i
nitiall
y
exist but do form over time as the market conver
g
es? Or do the correct
b
e
li
e
f
s ex
i
st
b
ecause t
h
e mar
k
et part
i
c
i
pants ex

i
st
i
n a wor
ld
o
f
stat
i
onary pro
b
a
b
-
ili
t
i
es w
h
ere t
h
e
f
requenc
y
o
f
var
i
ous

ki
n
d
s o
f
events, an
d
t
h
e
i
r e
ff
ects on pr
i
ces, are
well known? Without evokin
g
criticism of an
y
microeconomic or financial theor
y
a
n
d
s
h
y
i
ng away

f
or now
f
rom t
h
e tec
h
n
i
ca
l

d
eta
il
s t
h
at ma
k
e t
h
e approac
h
es o
f
mi
croeconom
i
cs an
d

fi
nance to equ
ilib
rat
i
on so
diff
erent,
i
t
i
s
i
nterest
i
n
g
to note t
h
at
the Ha
y
ekian view of market equilibration as a process of solvin
g
for prices without
c
onvey
i
ng a

ll
t
h
e necessary
i
n
f
ormat
i
on to a s
i
ng
l
e m
i
n
d

i
s
i
n suc
h
star
k
contrast to
t
h
e v
i

ew o
f
more w
id
e
ly
stu
di
e
d
t
h
eor
i
es
i
n
fi
nance t
h
at assume t
h
at a
ll
mar
k
et
participants are indeed of a sin
g
le mind in the sense of holdin

g
identical, correct
b
e
li
e
f
s. T
h
ese quest
i
ons are a
l
rea
d
y we
ll

k
nown
b
ut are tr
i
c
k
y an
d
qu
i
te tec

h
n
i
ca
l
to
d
ea
l
w
i
t
h
, an
d
are
b
e
y
on
d
t
h
e
i
mme
di
ate scope o
f
t

hi
s wor
k
.
M
ICROECONOMIC
M
M
AN
D
F
INANCIAL
FF
P
L
RICE
P
P
A
E
DJUSTMENT
P
T
ROCESSES
PP
2
5
S
evera
l

ear
li
er
l
a
b
oratory exper
i
menta
l
approac
h
es to
fi
nanc
i
a
l
econom
i
cs are
r
eviewed by Sunder (1995). Information aggregation from insiders to the general
m
arket and belief formation were common areas for exploration. More recentl
y
,
B
ossaerts (2002) rev
i

ews many t
h
eoret
i
ca
l

i
ssues
i
n
fi
nance an
d

di
scusses
l
a
b
oratory
e
xper
i
ments structure
d
spec
ifi
ca
ll

y to test asset-pr
i
c
i
ng mo
d
e
l
s
i
n a mu
l
t
i
-asset r
i
s
k
y
e
nvironment. Bossaerts (2002; p. 129) notes that laborator
y
markets conver
g
e slowl
y
,
an
d
t

hi
s s
l
ow convergence
i
n pr
i
ces may requ
i
re mo
d
e
l
s w
i
t
h
a
dj
ustments or
bi
ases
o
f
“mar
k
et”
b
e
li

e
f
s away
f
rom t
h
e per
f
ect
b
e
li
e
f
s assume
d

b
y t
h
e e
ffi
c
i
ent mar
k
et
h
y
pothesis

.
Most prev
i
ous wor
k

i
n
fi
nance-
b
ase
d

l
a
b
oratory exper
i
ments,
i
nc
l
u
di
ng t
h
e wor
k
ci

te
d
a
b
ove, requ
i
re
d
exper
i
ments w
i
t
h
many mar
k
ets an
d
many uncerta
i
n states o
f
t
he world in order to fit the mold of the financial models. Instead, the research to b
e
r
eporte
d

h

ere
f
ocuses on equ
ilib
rat
i
on o
f
a s
i
ng
l
e mar
k
et. T
h
e connect
i
on to
fi
nance
i
s
i
n t
h
e e
ffi
c
i

ent mar
k
et
h
ypot
h
es
i
s an
d

i
ts
i
mp
li
cat
i
on
f
or Mart
i
nga
l
e or ran
d
om
walks in
p
rices.

I
rregar
dl
ess o
f
w
h
et
h
er c
h
anges
i
n
fi
nanc
i
a
l
mar
k
et pr
i
ces are
d
ue to ran
d
om
sh
oc

k
s to t
h
e pro
fi
ta
bili
ty o
f
an un
d
er
l
y
i
ng
b
us
i
ness or ran
d
om no
i
se tra
d
ers,
if
t
h
ere

i
s a pattern to the price chan
g
es then there is a potential for profit that should not
e
x
i
st
i
n a per
f
ect mar
k
et. T
h
e Mart
i
nga
l
e or ran
d
om wa
lk

h
ypot
h
es
i
s can

b
e t
h
oug
h
t
o
f
as an ax
i
omat
i
c
d
escr
i
pt
i
on o
f
per
f
ect mar
k
et pr
i
ces w
i
t
h

out re
f
erence to an
underl
y
in
g
firm or asset or an
y
specific requirement limitin
g
the scope to onl
y
fi
nanc
i
a
l
mar
k
ets.
D
oes t
h
e not
i
on o
f
pr
i

ce as a Mart
i
nga
l
e process app
l
y to
l
a
b
oratory mar
k
ets? I
f
p
rices do not follow a Martin
g
ale or random walk, is the notion of a random walk
s
t
ill
use
f
u
l
some
h
o
w
?

C
an t
h
e ran
d
om
w
a
lk
some
h
o
w

b
e reconc
il
e
d

wi
t
h
t
h
e not
i
on
o
f

an
i
mper
f
ect mar
k
et t
h
at
i
s atta
i
n
i
ng compet
i
t
i
ve equ
ilib
r
i
um over t
i
me? T
h
e
answer to the first question will be no, both on principle and empiricall
y
prices in

l
a
b
oratory mar
k
ets c
l
ear
l
y
d
o not
f
o
ll
ow a Mart
i
nga
l
e process. But t
h
e
i
n
i
t
i
a
l
answer

t
o t
h
e
l
atter two quest
i
ons w
ill
surpr
i
s
i
ng
l
y
b
e yes.
T
he process of reachin
g
this result is as follows: Section 2 describes the Continu-
ous
l
y Re
f
res
h
e
d

Supp
l
y an
d
Deman
d
(CRSD) Env
i
ronment t
h
at
i
s use
d
to generate
l
ong
d
ata sets an
d

di
srupt t
h
e means
b
y w
hi
c
h

ZI ro
b
ot popu
l
ate
d
mar
k
ets converge
t
o equilibrium. Human-populated CRSD markets still appear to conver
g
e towards
an equ
ilib
r
i
um pr
i
ce, so somet
hi
ng more
i
s
h
appen
i
ng w
i
t

h
t
h
e
h
umans t
h
at
d
o not
h
appen w
i
t
h
t
h
e ZI ro
b
ots. Sect
i
on 3
id
ent
ifi
es t
h
e m
i
croeconom

i
c an
d

fi
nanc
i
a
l
approaches to market conver
g
ence. Section 4 compares and contrasts these two
approac
h
es an
d

id
ent
ifi
es some
i
ssues t
h
at wou
ld
appear to prevent t
h
e
fi

nanc
i
a
l
m
odel from describing the behavior of laboratory markets. Section 5 shows how to
use the random walk to desi
g
n a new kind of tradin
g
robot that captures some of, but
n
ot a
ll
o
f
, t
h
e
d
ynam
i
cs o
f
t
h
e
h
uman-popu
l

ate
d
mar
k
et
i
n t
h
e CRSD env
i
ronment.
Mar
k
ets popu
l
ate
d

b
y t
h
e ran
d
om wa
lk
ro
b
ots s
h
ow pr

i
ce
d
ynam
i
cs t
h
at can
b
e
described fairl
y
well as an AR(1) process. However, markets populated b
y
humans
a
l
so s
h
ow a
ki
n
d
o
f
out
li
er-correct
i
on w

h
ere
b
y pr
i
ces
d
ev
i
ate
f
rom t
h
e convergence
p
at
h
an
d
t
h
en pop
b
ac
k
up to near t
h
e prev
i
ous pr

i
ce. Out
li
ers an
d
correct
i
ons can
b
e
26 Ex
p
erimental Business Research Vol. II
m
o
d
e
l
e
d
as a type o
f
MA process so t
h
at t
h
e
j
o
i

nt process
b
ecomes an ARMA
process. Section
6
analyzes ARMA models of the price convergence of human-
populated markets and summarizes the findin
g
s. Section 7 discusses conclusions.
2. THE
CO
NTIN
UOUS
LY REFRE
S
HED
SU
PPLY AND DEMAND
ENVIR
O
NMEN
T
F
ig
ure 1 s
h
ows a set o
f

i

nstantaneous supp
ly
an
d

d
eman
d
curves t
h
at are
h
e
ld
c
onstant in the continuously refreshed supply and demand (CRSD) experimental
stu
d
y o
f
Brewer, Huang, Ne
l
son an
d
P
l
ott (2002). T
h
e env
i

ronment
i
s
i
mp
l
emente
d
by
means o
f
a set o
f

j
ava-
b
ase
d
pro
g
rams accesse
d

f
rom a stan
d
ar
d
we

b

b
rowser
such as Microsoft Internet Explorer. Human traders sitting at a web browser see
t
h
e
i
r screen
di
v
id
e
d

i
nto a pu
bli
c mar
k
et,
f
or tra
di
ng w
i
t
hi
n t

h
e group, an
d
a pr
i
vate
m
ar
k
et, w
hi
c
h

di
sp
l
a
y
s a set o
f
pr
i
vate tra
di
n
g
opportun
i
t

i
es (pro
d
uct
i
on costs or
redemption values for a single unit of good) available only to that subject. Sub-
j
ects comp
l
ete tra
d
es an
d
ma
k
e money
b
y ar
bi
trag
i
ng t
h
e
i
r pr
i
vate mar
k

et pr
i
ces
a
va
il
a
bl
e
f
rom t
h
e exper
i
menter a
g
a
i
nst t
h
e pu
bli
c mar
k
et pr
i
ces ava
il
a
bl

e
f
rom
i
nteraction with other experimental subjects. For example, if a subject can buy a
25
0
200
150
1
00
5
0
0
0
1
4
0
30
12
5
3
5
11
0
40
9
5
4
5

80
50
65
55
6
0
5
0
4
5
65
4
0
7
0
3
5
7
5
30
80
25
85
20
9
0
1
5
95
10

100
5
1
0
1
5
2
0
“
P1D
e
m
a
n
d”
“
P1Supp
l
y
”
F
igure 1. Samp
l
e Supp
l
y/Deman
d
Environment
.
M

ICROECONOMIC
M
M
AN
D
F
INANCIAL
FF
P
L
RICE
P
P
A
E
DJUSTMENT
P
T
ROCESSES
PP
27
unit in the public market for
$
50 and sell it in the private market for
$
70, they wil
l
e
arn a profit of
$

70
−
$
50
=
$
20. Net profits are paid in cash at the end of the
e
x
p
eriment.
Th
e costs an
d
va
l
ues
i
n F
i
gure 1 are
di
str
ib
ute
d
among t
h
e su
bj

ects v
i
a t
h
e
p
r
i
vate mar
k
ets v
i
s
ibl
e on t
h
e
i
r
i
n
di
v
id
ua
l
tra
di
ng screens an
d

are recyc
l
e
d
among
t
he sub
j
ects as trade occurs. The details of this rec
y
clin
g
will be explained below.
Th
e exper
i
menter
i
s not pr
i
mar
il
y concerne
d
w
i
t
h
t
hi

s pr
i
vate mar
k
et recyc
li
ng,
b
ut
i
nstea
d
t
h
e
f
ocus
i
s on o
b
serv
i
ng t
h
e tra
di
ng
b
etween t
h

e
h
umans
i
n t
h
e pu
bli
c
m
arket
.
C
ont
i
nuous
l
y re
f
res
h
e
d
supp
l
y an
d

d
eman

d

i
s a tec
h
n
i
que
f
or recyc
li
ng t
h
e
c
osts an
d
re
d
empt
i
on va
l
ues
i
n a
d
ou
bl
e auct

i
on exper
i
ment. In contrast to stan
d
-
ard double auction experiments where
g
ains from tradin
g
are finite and naturall
y
e
x
h
auste
d
as t
h
e tra
di
ng per
i
o
d
progresses (see,
f
or
i
nstance, t

h
e c
l
ass
i
ca
l
exper
i
-
m
ents described by Smith (19
6
2) or Plott (1982)), in the CRSD environment there
i
s no natural end to tradin
g
.
B
rewer, et a
l
. (2002)
d
escr
ib
e t
h
e part
i
cu

l
ars o
f
t
h
e CRSD env
i
ronment as
f
o
ll
o
w
s
:
“

if

b
uyer #3 use
d
a pr
i
vate mar
k
et o
ff
er (a re
d

empt
i
on va
l
ue)
f
rom t
h
e
e
xper
i
menter, t
hi
s same o
ff
er wou
ld

i
mme
di
ate
l
y
b
e ma
d
e to t
h

e nex
t
buyer
t
(e.
g
., bu
y
er #4). Similarl
y
, offers to sell (costs) were rec
y
cled to the next seller.
S
u
bj
ects
h
a
d
no
k
now
l
e
d
ge at a
ll
a
b

out t
hi
s re
f
res
hi
ng. Su
bj
ects
k
new on
l
y t
h
at
n
ew or
d
ers cou
ld
appear
i
n t
h
e
i
r pr
i
vate mar
k

ets at any t
i
me.
Refreshin
g
the private offers in this wa
y
keeps the instantaneous suppl
y
and
d
eman
d
curves constant at every moment
i
n t
i
me. I
f
an o
ff
er
i
s use
d
or exp
i
res,
i
t

d
oes not van
i
s
h

f
rom t
h
e poo
l
o
f
supp
l
y an
d

d
eman
d
. Instea
d
,
i
t
i
s recyc
l
e

d
to
s
omeone else. Thus, the opportunities of
g
ains from trade are never exhausted.
Th
e mar
k
et
d
eman
d
an
d
supp
l
y
f
unct
i
ons as represente
d

b
y re
d
empt
i
on va

l
ues
a
n
d
costs are a
l
ways constant –
i
n
d
epen
d
ent o
f
t
h
e patterns o
f
tra
d
e.”
F
i
gure 2 s
h
ows t
h
e
d

ata set o
f
pu
bli
c mar
k
et tra
di
ng pr
i
ces pro
d
uce
d

f
rom 2
1
/
1
2
h
ours o
f
tra
di
ng
i
n t
h

e env
i
ronment o
f
F
i
gure 1. T
h
e
d
ata s
h
own
h
ere
h
as
b
een
‘
sanitized’ b
y
removin
g
possible outliers or errors – trades with lar
g
e price move-
m
ents – an
d

w
ill
serve as t
h
e pr
i
mary
d
ata source
f
or t
hi
s paper.
Th
ere are t
h
ree pr
i
mary
b
ene
fi
ts o
f
t
h
e CRSD env
i
ronment over ot
h

er sources o
f
data: (i) CRSD can produce lon
g
time series (there are 793 trades in the sample we
will
use
v
s.
∼
2
0
i
n t
h
e typ
i
ca
l

d
ou
bl
e auct
i
on per
i
o
d
) use

f
u
l
w
h
en exam
i
n
i
ng t
i
me
s
er
i
es propert
i
es as t
h
e accuracy o
f
some o
f
t
h
e re
l
ate
d
est

i
mators sca
l
es on
l
y as
1
/
N
;
(ii) because of the nature of the refreshin
g
, the instantaneous suppl
y
and
d
eman
d

i
s
h
e
ld
stat
i
onary; one
d
oes not
h

ave to cons
id
er t
h
e poss
ibili
ty o
f
an equ
ili
-
b
r
i
um pr
i
ce t
h
at
i
s c
h
ang
i
ng as tra
d
ers ex
i
t t
h

e mar
k
et; (
iii
) stat
i
onary
i
nstantaneous
s
uppl
y
and demand can be useful in separatin
g
models of market behavior and
c
onvergence. Certa
i
n pr
i
ce convergence processes – suc
h
as Mars
h
a
lli
an pat
h
pro-
c

esses an
d
no
i
sy ana
l
ogs
lik
e t
h
e Go
d
e an
d
Sun
d
er (1993) ZI Ro
b
ots – t
h
at operate
28 Ex
p
erimental Business Research Vol. II
i
n the ordinar
y
double auction can not operate in the CRSD environment and therefore
c
an not be an explanation for why human-populated CRSD markets are observed to

c
onverge to an equ
ilib
r
i
um pr
i
ce.
3
.
S
TANDARD M
O
DEL
S
C
urrent
l
y,
f
un
d
amenta
l
mo
d
e
l
s o
f

mar
k
et processes
diff
er somew
h
at
i
n
b
ot
h

f
orm
a
nd function between the fields of microeconomics and finance. The
p
ur
p
ose of this
sect
i
on
i
s to
ill
ustrate t
h
ese

b
as
i
c mo
d
e
l
s – muc
h
o
f
w
hi
c
h
may
b
e qu
i
te
f
am
ili
ar to
some rea
d
ers. Sect
i
on 4 w
ill

t
h
en cons
id
er
h
ow t
h
ese mo
d
e
l
s over
l
ap
i
n ways t
h
at
m
i
g
ht be compatible or incompatible
.
3.1. The Microeconomics Approach – Law o
f
Supply and Demand, Allocation
E
fficiency, an
d

Dynamic A
d
justmen
t
T
he Law of Suppl
y
and Demand is a static theor
y
of market equilibrium, and pro-
vid
es t
h
at t
h
e equ
ilib
r
i
um o
f
a compet
i
t
i
ve mar
k
et occurs at t
h
e pr

i
ce an
d
quant
i
ty
g
iven b
y
the intersection of the demand and suppl
y
curves. For example, in Fi
g
ure 1,
the intersection of the demand and suppl
y
curves
g
ives
Q
=
6 and
55
≤
P
≤
60
.
I
n an or

di
nary mar
k
et exper
i
ment w
i
t
h
out t
h
e cont
i
nuous re
f
res
hi
ng
d
escr
ib
e
d
i
n section 2, the e
q
uilibrium
Q
=
6 and

55
≤
P
≤
60 would be the
p
redicted outcom
e
0 200 400
6
00
−
10 0
1
0
2
030
4
0
Pminus
63
F
igure 2. Price Time Series P1 from Brewer, Huang, Ne
l
son, an
d
P
l
ott (sanitize
d

)
.
M
ICROECONOMIC
M
M
AN
D
F
INANCIAL
FF
P
L
RICE
P
P
A
E
DJUSTMENT
P
T
ROCESSES
PP
29
o
f
m
i
croeconom
i

c compet
i
t
i
ve t
h
eory. W
i
t
h
cont
i
nuous re
f
res
hi
ng o
f
t
h
e supp
l
y/
d
eman
d
curves, t
h
e correct equ
ilib

r
i
um concept
i
s
l
ess c
l
ear. F
i
rst, t
h
ere
i
s no pre-
d
i
ct
i
o
n f
o
r
Q
because refreshin
g
allows trade to continue. Brewer, et al. (2002)
m
a
i

nta
i
ne
d
a
h
ypot
h
es
i
s t
h
at compet
i
t
i
ve t
h
eory cou
ld
poss
ibl
e st
ill
pre
di
ct pr
i
ces
i

n
t
h
ese env
i
ronments: t
h
e pre
di
ct
i
on
f
or
P
from the Figure 1 of 55
≤
P
≤
60
is th
e
“
instantaneous competitive equilibrium” of Brewer, et al. (2002), and there ma
y
also
b
e a ve
l
oc

i
ty-
b
ase
d
equ
ilib
r
i
um
b
ase
d
on o
b
serve
d
supp
l
y an
d

d
eman
d
curves t
h
at
are ca
l

cu
l
ate
d
ex-post.
A
llocation efficienc
y
measures the ratio of the
g
ains from trade achieved in a
m
ar
k
et versus t
h
e max
i
mum poss
ibl
e ga
i
ns
f
rom tra
d
e. Or
di
nar
il

y,
l
a
b
oratory mar-
k
ets
i
n t
h
e a
b
sence o
f
externa
li
t
i
es w
ill
equ
ilib
rate to pr
i
ces near t
h
ose pre
di
cte
d

b
y
the Law of Suppl
y
and Demand, supportin
g
an allocation havin
g
nearl
y
100%
a
ll
ocat
i
on e
ffi
c
i
ency. In cont
i
nuous
l
y re
f
res
h
e
d
mar

k
ets, a
ll
ocat
i
on e
ffi
c
i
ency
i
s
dif
-
fi
cu
l
t to
d
e
fi
ne
b
ecause t
h
e proper
d
e
fi
n

i
t
i
on o
f
max
i
mum poss
ibl
e ga
i
ns
f
rom tra
d
e
i
n the presence of refreshin
g
is not obvious
.
Th
e Law o
f
Supp
l
y an
d
Deman
d

i
s not a
d
ynam
i
c t
h
eory o
f
pr
i
ce a
dj
ustment.
T
wo ear
l
y mo
d
e
l
s o
f
pr
i
ce a
dj
ustments are
d

ue to Mars
h
a
ll
an
d
Wa
l
ras. E
i
t
h
er cou
ld
be expressed in the form of a differential equation, thou
g
h there is no exact differ
-
e
nt
i
a
l
equat
i
on
k
nown to
b
e accepte

d
as an exact rea
li
zat
i
on o
f
e
i
t
h
er t
h
eory.
Th
e pr
i
mary
diff
erence
b
etween t
h
e two a
dj
ustment mo
d
e
l
s

i
s w
h
et
h
er a
dj
ustment
occurs alon
g
the quantit
y
axis or the price axis
.
3
.2. Mars
h
a
ll
ian A
d
justment
Th
e Mars
h
a
lli
an a
dj
ustment process can

b
e wr
i
tten as
:
d
Q
/d
t
=
F
(
P
D
P
P
(
Q
)
−
P
S
P
P
(
Q
))
where
P
D

P
P
(
Q
)
=
Deman
d
Pr
i
ce (or Marg
i
na
l
Va
l
ue) at
Q
P
S
P
P
(
Q
)
=
Suppl
y
Price (or Mar
g

inal Cost) a
t

Q
F
(
) is a sufficientl
y
well-behaved unknown monotone function
3
.3. Wa
l
rasian A
d
justmen
t
Th
e Wa
l
ras
i
an A
dj
ustment Process can
b
e wr
i
tten as:
d
P

/d
P
t
=
G
(
Q
D
(
P
)
−
Q
S
(
P
))
where
Q
D
(
P
)
−
Q
S
(
P
)
g

i
ves t
h
e quant
i
ty o
f
t
h
e excess
d
eman
d
at pr
i
ce
P
an
d
G
(
)
i
s a su
ffi
c
i
ent
l
y we

ll

b
e
h
ave
d
un
k
nown monotone
f
unct
i
on.
Th
e Mars
h
a
lli
an a
dj
ustment process was or
i
g
i
na
ll
y assoc
i
ate

d
w
i
t
h
a
dj
ustment o
f
m
ar
k
ets t
h
at are repeate
d
over a ser
i
es o
f

d
ays, mont
h
s, or years. One genera
l
3
0Ex
p
erimental Business Research Vol. II

a
rgument
i
s t
h
at
if

P
D
PP
>
P
S
PP
it will be easy for sellers to sell their goods in excess of
S
t
h
e
i
r marg
i
na
l
cost, an
d
pro
d
uct

i
on w
ill
expan
d
. However,
if

P
D
PP
<
P
S
P
P
trade will be
S
d
ifficult since bu
y
ers are willin
g
to pa
y
less than sellers require to meet production
c
osts. Because some se
ll
ers w

ill

b
e pro
d
uc
i
ng at
l
east part o
f
t
h
e
i
r pro
d
uct
i
on at
m
ar
gi
na
l
costs t
h
at are
high
er t

h
an w
h
at
b
u
y
ers are w
illi
n
g
to pa
y
(
P
D
PP
)
, se
ll
ers mus
t
n
ecessaril
y
take a loss on this excess production. Failure to sell at a price
g
reater
t
h

an marg
i
na
l
cost wou
ld
rat
i
ona
ll
y
l
ea
d
to a contract
i
on o
f
pro
d
uct
i
on over t
i
me as
se
ll
ers
l
earn to correct overpro

d
uct
i
on
.
Walrasian ad
j
ustment can be thou
g
ht of as either a virtual or real tatonnement
process t
h
at occurs
b
e
f
ore tra
d
e to set a pr
i
ce, or
i
t can
b
e t
h
oug
h
t o
f

as occurr
i
ng
w
i
t
hi
n tra
d
e t
h
rou
gh
s
h
orta
g
es an
d
surp
l
uses. In t
hi
s researc
h
, we are ma
i
n
ly
concerne

d
with the latter a
pp
roach. The basic idea is that if
p
rices are above e
q
uilibrium, there
i
s excess supp
l
y, an
d
pr
i
ces w
ill

f
a
ll
over t
i
me, an
d

if
pr
i
ces are

b
e
l
ow equ
ilib
r
i
um
t
h
ere
i
s excess
d
eman
d
, an
d
pr
i
ces w
ill
r
i
se over t
i
me. It
i
s wort
h

not
i
ng t
h
at t
h
e
Walrasian ad
j
ustment process, as a first-order differential equation, implies an expon
-
e
nt
i
a
l
approac
h
to equ
ilib
r
i
um. A
fi
rst-or
d
er
diff
erent
i

a
l
equat
i
on
f
or pr
i
ce over t
i
me
d
oes not perm
i
t more a
d
vance
d

b
e
h
av
i
or seen
i
n some p
h
ys
i

ca
l
(non-econom
i
c)
s
y
stems: for example, the oscillation of a sprin
g
(with or without dampin
g
) is the
resu
l
t o
f
a 2
n
d
or
d
er
diff
erent
i
a
l
equat
i
on o

f
mot
i
on over t
i
me.
M
ore recent
l
y, Eas
l
ey an
d
Le
d
yar
d
(1993) prov
id
e a mo
d
e
l
o
f

d
ou
bl
e auct

i
on
price conver
g
ence that has both Marshallian and Walrasian aspects. However, this
m
o
d
e
l
app
li
es to t
h
e stan
d
ar
d

d
ou
bl
e auct
i
on w
i
t
h

fi

n
i
te per
i
o
d
s, not t
h
e CRSD
d
ou
bl
e auct
i
on.
Attempts at comparin
g
the Walrasian and Marshallian ad
j
ustment processes in
stan
d
ar
d

d
ou
bl
e auct
i

ons
h
ave
b
een ma
d
e
b
y P
l
ott an
d
George (1992) an
d
Jam
i
son
a
n
d
P
l
ott (1997). T
h
ese stu
di
es
i
nvo
l

ve
d
t
h
e creat
i
on o
f
externa
li
t
i
es a
l
ternat
i
ve
l
y
g
eneratin
g
upward slopin
g
demand or downward slopin
g
suppl
y
(called “perverse-
s

h
ape
d
” curves
b
ecause norma
ll
y
d
eman
d

i
s
d
ownwar
d
s
l
op
i
ng an
d
supp
l
y
i
s up-
war
d

s
l
op
i
ng) to create part
i
cu
l
ar reg
i
ons o
f
Wa
l
ras
i
an
i
nsta
bili
ty/Mars
h
a
lli
an sta
bili
ty
o
r Marshallian instabilit
y

/Walrasian stabilit
y
. Plott (2001; Introduction p. xxv)
summar
i
zes t
h
ese resu
l
ts as
f
avor
i
ng a Mars
h
a
lli
an t
h
eory w
h
en externa
li
t
i
es cause
perverse-s
h
ape
d

supp
ly
an
d

d
eman
d
curves
b
ut
f
avor
i
n
g
Wa
l
ras
i
an t
h
eor
y
w
h
en
i
ncome effects cause
p

erverse-sha
p
ed curves.
One can see t
h
at t
h
ere
i
s no we
ll
-accepte
d
c
h
o
i
ce
b
etween Mars
h
a
lli
an an
d
Wa
l
ras
i
an

dy
nam
i
cs. It
i
s
b
e
li
eve
d
t
h
at t
h
e use o
f
t
h
e Cont
i
nuous
ly
Re
f
res
h
e
d
Supp

ly
a
nd Demand in the research reported here will select a
g
ainst Marshallian d
y
namics
b
ecause t
h
ere w
ill

b
e no s
h
ortage o
f
tra
di
ng opportun
i
t
i
es a
l
ong t
h
e
Q

ax
i
s to
f
orce
a
n outcome. T
hi
s consequence o
f
CRSD exper
i
ment
d
es
ig
n w
ill

b
e rev
i
s
i
te
d
a
g
a
i

n
i
n
the next section
.
3.4. T
h
e Financia
l
Economics Approac
h
– Informationa
l
Efficiency
Mar
k
et pr
i
ces are sa
id
to
b
e informationa
ll
y efficien
t

if
pr
i

ces summar
i
ze ex
i
st
i
n
g
i
n
f
ormat
i
on to t
h
e extent t
h
at t
h
ere
i
s zero expecte
d

g
a
i
n
f
rom

b
u
yi
n
g
or se
lli
n
g
M
ICROECONOMIC
M
M
AN
D
F
INANCIAL
FF
P
L
RICE
P
P
A
E
DJUSTMENT
P
T
ROCESSES
PP

31
b
ase
d
on ex
i
st
i
ng
i
n
f
ormat
i
on. Ex
i
st
i
ng
i
n
f
ormat
i
on
i
nc
l
u
d

es a
ll
current an
d
pr
i
or
p
r
i
ces
{
P
t
P
P
,
P
t
PP
−
1
,
P
t
PP
−
2
,
. . .} as we

ll
as an
y
ot
h
er common
ly

k
nown
i
n
f
ormat
i
on a
b
out
the market
.
More
f
orma
ll
y, g
i
ven
i
n
f

ormat
i
on
I
t
I
I
at time
t
t
, pr
i
ces are a Martinga
l
e proces
s
w
h
ere
b
y t
h
e expectat
i
on
E
t
[
P
t

P
P
+
t
t
k
|
I
t
II
]
=
P
t
P
P
for all
t
k
>
0
.
3
.5. Normal Random
W
al
k
For the purpose of this paper, a normal random walk is an inte
g
rated time series

P
t
wh
ose
fi
rst
diff
erences
∆
P
t
P
P
=
P
t
P
P
+
t
t
1
−
P
t
P
P
are independently and identically distributed
t
n

orma
l

v
ar
i
a
bl
es
wi
t
h
E
(
∆
P
t
P
P
)
= 0 an
d
Var
(
∆
P
t
PP
)
=

σ
2
.
Mo
d
e
li
ng pr
i
ces
i
n a mar
k
et
as a random walk necessaril
y
satisfies the informational efficienc
y
requirement:
if
t
h
e mean o
f
t
h
e
diff
erence process
i

s zero, t
h
en
E
[
P
t
P
P
+
t
t
k
|
P
t
P
P
]
=
P
t
P
P
+
E
(
∆
P
t

P
P
)
+
E
(
∆
P
t
PP
+
t
t
1
)
+

=
P
t
PP
+

0
+

0
+

=

P
t
P
P
.
Note t
h
at t
h
e norma
l
ran
d
om wa
lk

h
as
li
near
l
y
i
ncreasin
g
prediction variance Var
[
P
t
PP

+
t
t
k
|
P
t
P
P
]
=
k
σ
2
as the
p
rediction horizon k i
s
i
ncrease
d
.
3
.6. Heteroskedastic Martingales
A

h
eteros
k
e

d
ast
i
c Mart
i
nga
l
e
i
s a t
i
me ser
i
es t
h
at sat
i
s
fi
es t
h
e
i
n
f
ormat
i
ona
l
e

ffi
c
i
-
e
nc
y
h
y
pothesis but is not a normal random walk due to chan
g
es over time in the
variance
p
arameter of
p
rice differences
σ
2
.
The variance could be time de
p
endent or
p
r
i
ce
d
epen
d

ent. We
ll

k
nown examp
l
es o
f
t
hi
s c
l
ass o
f
processes wou
ld

i
nc
l
u
d
e t
h
e
A
RCH and GARCH time-series models, which add a se
p
arate e
q

uation for variance
t
hat induces heteroskedasticit
y
.
4. COMPARING AND CONTRASTING THE STANDARD MODELS
The financial and microeconomic theories appear to overlap only in the case of a
p
er
f
ect mar
k
et t
h
at
i
nstantaneous
l
y
fi
n
d
s t
h
e compet
i
t
i
ve equ
ilib

r
i
um pr
i
ce. A constan
t
p
r
i
ce
i
s tr
i
v
i
a
lly
a Mart
i
n
g
a
l
e an
d

if
t
hi
s constant pr

i
ce
i
s at t
h
e t
h
eoret
i
ca
l
equ
ilib
-
r
ium then both kinds of theories can be satisfied. However, noisy prices are an
e
mp
i
r
i
ca
l
regu
l
ar
i
ty common to
b
ot

h
t
h
e
l
a
b
an
d
t
h
e
fi
e
ld
. T
h
e ma
i
n tens
i
on
b
etween
th
e two approac
h
es o
f
Sect

i
on 3
i
s t
h
at t
h
e ex
i
stence o
f
a pr
i
ce a
dj
ustment process
i
n
Microeconomics converging towards the static prediction of the Law of Supply and
D
eman
d

i
s
i
ncompat
ibl
e w
i

t
h
t
h
e not
i
on t
h
at mar
k
ets pr
i
ces ex
hibi
t
i
n
f
ormat
i
ona
l
effi
c
i
enc
y

d
etecta

bl
e t
h
rou
gh
autocorre
l
at
i
on propert
i
es o
f
pr
i
ce
diff
erences.
4.1. Random Walk destro
y
s conver
g
ence
If prices were a random walk, the market would have informational efficienc
y
but
th
en pr
i
ces wou

ld
not converge towar
d
s any
fi
xe
d

l
eve
l
. Pr
i
ce
i
ncrements are a
l
ways
i
n
d
epen
d
ent an
d

id
ent
i
ca

ll
y
di
str
ib
ute
d
an
d
t
h
ere
f
ore
d
o not ten
d
to move pr
i
ce
3
2Ex
p
erimental Business Research Vol. II
towar
d
s t
h
e m
i

croeconom
i
c compet
i
t
i
ve equ
ilib
r
i
um g
i
ven
b
y t
h
e Law o
f
Supp
l
y
a
n
d
Deman
d.
4
.2. Convergence of prices towards competitive e
q
uilibrium implies

non-Martin
g
a
l
e
b
e
h
avior
C
onvergence o
f
pr
i
ces towar
d
s a compet
i
t
i
ve equ
ilib
r
i
um pr
i
ce
p
*
wou

ld
seem to
suggest t
h
a
t

E
t
[
P
t
P
P
+
k
|
I
t
II
]
<
P
t
PP
when
t
P
t
P

P
>
p
* an
d
E
t
[
P
t
P
P
+
k
|
I
t
II
]
>
P
t
PP
wh
en
P
t
PP
<
p

*
. In contrast
,
a
Martin
g
ale Process alwa
y
s has expectation
E
t
[
P
t
PP
+
k
|
I
t
II
]
=
P
t
P
P
for all
t
k

>
0.
Vo
l
untary tra
d
e w
i
t
hi
n a set o
f
supp
l
y an
d

d
eman
d
curves necessar
il
y generates
a
pr
i
ce ce
ili
ng an
d

a
fl
oor outs
id
e o
f
w
hi
c
h
tra
d
e w
ill
never occur. T
hi
s creates
problems for random walk and Martin
g
ale models
.
4
.3. Vo
l
untary Tra
d
e an
d
T
h

e Support o
f
Possi
bl
e Prices
Nothing in a random walk theory prevents prices from wandering outside of the
support o
f
vo
l
untary tra
d
e. For examp
l
e,
i
n F
i
gure 1 t
h
e
l
owest se
ll
er’s marg
i
na
l
cost
i

s 30 an
d
t
h
e
high
est
b
u
y
er’s mar
gi
na
l
va
l
ue
i
s 140. Vo
l
untar
y
tra
d
es can on
ly
occur
a
t prices greater than or equal to 30, and less than or equal to 140.
4

.4. A Censore
d
Norma
l
Ran
d
om Wa
lk
is no
l
on
g
er a Martin
g
a
l
e process
C
ensoring the random walk above and below ceiling and floor values (
P
H
,
P
L
P
)
woul
d
ten
d

to v
i
o
l
ate t
h
e Mart
i
n
g
a
l
e requ
i
rement t
h
at
E
[
P
t
PP
+
k
|
P
t
P
P
]

=
P
t
P
P
.
To see t
hi
s
,
con-
sider a price ceilin
g
P
H
,
then at
P
t
PP
=
P
H
we would necessarily have
H
E
[
P
t
PP

+1
|
P
t
PP
]
<
P
t
P
P
.
Unless
P
t
P
P
+
t
t
1
=
P
t
P
P
=
P
H
with certainty (which is never true for a censored iid normal

H
ran
d
om wa
lk

b
ut cou
ld

b
e true
f
or a
h
eteros
k
e
d
ast
i
c censore
d
ran
d
om wa
lk
on
ly
f

or the unusual case that the variance falls to zero at the ceilin
g
) the mean of the
next
p
rice
P
t
P
P
+
1
must be less than the ceiling because the probability support does
n
ot
i
nc
l
u
d
e an
y
pr
i
ces a
b
ove t
h
e ce
ili

n
g
. T
h
e ar
g
ument
f
or v
i
o
l
at
i
on at a
fl
oor
i
s
similar
.
4
.5. Bounded Martingales seem to re
q
uire various non-economic properties
A Bounded Martin
g
ale is a Martin
g
ale price process bounded between two limits

[
P
L
,
P
H
]
. From t
h
e prev
i
ous paragrap
h
we
k
now t
h
at t
h
e
fi
rst non-econom
i
c property
t
h
at a Boun
d
e
d

Mart
i
nga
l
e must
h
ave
i
s t
h
at t
h
e pr
i
ce
b
oun
d
s are st
i
c
k
y. I
f
at some
t
im
e
t
the price

t
P
t
P
P
=
P
H
or
H
P
t
P
P
=
P
L
, it remains a
t

P
H
or
H
P
L
forever. If one considers
L
e
xponent

i
a
ll
y
d
ecreas
i
ng, ever-t
i
g
h
ten
i
ng
b
oun
d
s on t
h
e var
i
ance o
f
t
h
e Mart
i
nga
l
e

process over t
i
me, one may o
b
ta
i
n pr
i
ce convergence to an
i
nter
i
or po
i
nt,
b
ut t
h
ere
i
s no reason to believe that this interior point should alwa
y
s coincide with the
e
conom
i
c not
i
on o
f

compet
i
t
i
ve equ
ilib
r
i
um nor
d
oes c
l
ass
i
ca
l
econom
i
cs prov
id
e
a

d
e
fi
n
i
t
iv

e source or mo
d
e
l
assoc
i
ate
d

wi
t
h
t
hi
s
d
ecrease
i
n
v
ar
i
ance.
C
on
di
t
i
ona
l

M
ICROECONOMIC
M
M
AN
D
F
INANCIAL
FF
P
L
RICE
P
P
A
E
DJUSTMENT
P
T
ROCESSES
PP
33
h
eteros
k
e
d
ast
i
c

i
ty
b
ase
d
upon t
h
e
di
stance o
f
t
h
e pr
i
ce
P
t
PP
from equilibrium might be
t
h
e
l
p
f
u
l
,
b

ut once aga
i
n t
h
ere
i
s no o
b
v
i
ous econom
i
c source o
f
t
hi
s e
ff
ect an
d
one
m
ust still have a variance of 0 at
P
L
and
L
P
H
with the possibility of prices becoming

H
s
tuc
k
at or near t
h
ese
l
ocat
i
ons. In contrast, econom
i
c t
h
eory wou
ld
seem to say t
h
at
th
e
f
orces pus
hi
n
g
pr
i
ces towar
d

s t
h
e equ
ilib
r
i
um wou
ld

b
e stron
g
est at
b
oun
d
ar
y
p
rices
P
L
and
L
P
H
because it is at these prices that excess demand or excess supply
H
w
ill

b
e greatest.
Th
e next note a
b
out con
fli
cts amon
g
t
h
e mo
d
e
l
s
h
as more to
d
o w
i
t
h
t
h
e spec
ifi
c
c

hoice of a CRSD environment for
g
eneratin
g
the experimental data
.
4.6. CRSD environment selects against Marshallian Price Adjustment Processes
B
rewer, et a
l
. (2002) cons
id
ere
d
an a
l
ternat
i
ve
i
nterpretat
i
on o
f
t
h
e Mars
h
a
lli

an
a
dj
ustment process act
i
n
g
w
i
t
hi
n a s
i
n
gl
e tra
di
n
g
per
i
o
d
: t
h
e
M
ar
sh
a

ll
ian Pat
h
.
T
he
i
dea is simpl
y
that the sequence of trades in a market will be from left to ri
g
ht alon
g
th
e supp
l
y an
d

d
eman
d
curves at any ser
i
es o
f
pr
i
ces
P

n
P
P

wh
ere
P
S
P
P
(
n
)
≤
P
n
PP
≤
P
D
PP
(
n
)
.
For examp
l
e,
f
or t

h
e mar
k
et o
f
F
i
gure 1, t
h
e Mars
h
a
lli
an Pat
h
t
h
eory wou
ld

i
mp
l
y
the followin
g
sequence of trade: (bu
y
er with value 140/seller with cost 30), (bu
y

e
r
with value 125/seller with cost 35), (buyer with value 110/seller with cost 40),
(buyer with value 95/seller with cost 45), (buyer with value 80/seller with cost 50),
(bu
y
er with value 6
5
/seller with cost
55
). The equilibrium quantit
y
of trades would
b
e
Q
*
=
6
. No further trades will be possible since
P
D
PP
<
P
S
P
P
at
S

Q
= 7
.
Go
d
e an
d
Sun
d
er (1993) a
d
vance
d
t
h
e
id
ea t
h
at
f
u
ll
y
h
uman rat
i
ona
li
ty suggeste

d
i
n the ad
j
ustment processes above was not necessar
y
because markets populated
b
y so-ca
ll
e
d
“Zero Inte
lli
gence” ro
b
ots, w
hi
c
h
pat
i
ent
l
y
bid
/as
k
ran
d

om
l
y w
i
t
hi
n
th
e
i
r
b
u
d
get constra
i
nt, converge
d
to mar
k
et equ
ilib
r
i
um pr
i
ces. ZI ro
b
ots e
ff

ect
i
ve
l
y
follow a nois
y
Marshallian path, because at an
y
time the robots with the
g
reatest
p
ro
b
a
bili
ty o
f
tra
di
ng are t
h
e
hi
g
h
va
l
ue

b
uyer an
d
t
h
e
l
ow cost se
ll
er. By remov
i
ng
th
e
hi
g
h
-va
l
ue an
d

l
ow-cost tra
d
ers ear
l
y, pr
i
ces are stoc

h
ast
i
ca
ll
y
f
orce
d
towar
d
s
t
he competitive equilibrium at the suppl
y
-demand intersection. Cason and Friedman
(199
6
) provide additional evidence that suggests markets populated by humans follow
s
uc
h
a no
i
sy Mars
h
a
lli
an pat
h

.
T
he continuousl
y
-refreshed environment of Brewer, et al. (2002) removes the
Mars
h
a
lli
an pat
h
as a poss
ibl
e mec
h
an
i
sm
f
or a
dj
ustment
b
ecause t
h
e
hi
g
h
-va

l
ue an
d
l
ow-cost un
i
ts are recyc
l
e
d

b
ac
k

i
nto t
h
e mar
k
et. Pr
i
ces are st
ill
seen to converge.
This mi
g
ht be seen as lendin
g
support towards a Walrasian ad

j
ustment model at least
f
or t
h
e
C
R
S
D c
l
ass o
f
en
vi
ronments.
2
5
. A HYBRID M
O
DEL – R
O
B
O
T
S
IM
U
LATI
O

N
S
F
ig
ure 3 s
h
ows mar
k
et pr
i
ces
g
enerate
d

by
t
h
ree
g
roups o
f
spec
i
a
lly

d
es
ig

ne
d
tra
di
n
g
r
obots. These prices are seen to conver
g
e towards a kind of equilibrium, similar to
t
h
e convergence o
f
t
h
e
h
umans. T
h
e ro
b
ots, w
hi
c
h
we w
ill
ca
ll

constra
i
ne
d
ran
d
om
wa
lk
ers, use a pr
i
c
i
n
g
a
lg
or
i
t
h
m
b
ase
d
part
i
a
lly
upon a ran

d
om-wa
lk
. T
h
e purpose o
f
3
4Ex
p
erimental Business Research Vol. II
0
10
20
30
40
5
0
6
0
70
8
0
90
1 101 201 301 401 501 601 701 801
9
0
1
T
P

r
i
c
e
s
dev = 0.
5
s
de
v
=
0
.1 sde
v
=
0
.
3
F
igure 3. Prices from Constraine
d
Ran
d
om Wa
lk
ers attain equi
l
i
b
rium over time

.
t
hi
s sect
i
on
i
s to exp
l
a
i
n t
h
e a
l
gor
i
t
h
m o
f
t
h
ese ro
b
ots, compare t
hi
s a
l
gor

i
t
h
m to t
h
e
Z
ero Intelli
g
ence al
g
orithm of Gode and Sunder (1993), and compare and contrast the
behavior of markets populated by the robots. The potential significance of these robo
t
s
i
mu
l
at
i
ons
f
or a com
bi
ne
d
m
i
croeconom
i

c/
fi
nanc
i
a
l
t
h
eory o
f
mar
k
ets
i
s exp
l
ore
d
.
5.1.
C
onstrained Random
W
alkers
C
onstrained Random Walkers obe
y
the followin
g
al

g
orithm: at each moment in time
one robot representing a particular buyer or seller is selected to act. This robot will
t
h
en (1)
f
etc
h
t
h
e prev
i
ous transact
i
on pr
i
ce
p
t
−
1
.
T
hi
s transact
i
on pr
i
ce

i
s t
h
e pr
i
ce
of the last com
p
leted trade, not the advertised
p
rice of a
p
revious bid or ask. (2) add
a
n independent, identically distributed deviate
ε
∼
N
(0,
NN
σ
2
)
to obtain the
p
otential
pr
i
ce
p

*
=
p
t
−
1
+
ε
, an
d
(3) su
b
m
i
t a
bid
or as
k
at pr
i
ce
p
*

if
an
d
on
l
y

if

p
*
i
s
wi
t
hi
n
the robot’s bud
g
et constraint – that is,
p
*
>
cost for a seller, o
r
p
*
<
value for a
buyer. Potential prices that fail step (3) are discarded.
5
.2. Go
d
e an
d
Sun
d

er (1993) ZI Ro
b
ot
s
Th
e ZI Ro
b
ots o
b
ey t
h
e
f
o
ll
ow
i
ng a
l
gor
i
t
h
m: at eac
h
moment
i
n t
i
me one ro

b
ot
representin
g
a particular bu
y
er or seller is selected to act. This robot will the
n
randomly bid over the budget constraint without regard to previous prices. A Buyer
ro
b
ot w
ill

bid
a pr
i
ce
b
*

f
rom a un
if
orm ran
d
om
di
str
ib

ut
i
on o
v
er
0

≤
b
*
≤
v
,
w
h
ere
v is the redem
p
tion value. A Seller robot will ask a
p
rice
a
*
fr
o
m
a

u
nif

o
rm r
a
n
do
m
M
ICROECONOMIC
M
M
AN
D
F
INANCIAL
FF
P
L
RICE
P
P
A
E
DJUSTMENT
P
T
ROCESSES
PP
35
di
str

ib
ut
i
on o
v
er
c
≤
a
*
≤
H
,
w
h
ere c
i
s t
h
e cost o
f
t
h
e un
i
t to t
h
e se
ll
er an

d

H
is an
H
ar
bi
trary ce
ili
ng pr
i
ce c
h
osen to
b
e
hi
g
h
er t
h
an t
h
e
hi
g
h
est
b
uyers’ va

l
ue.
5
.3. Dou
bl
e Auction Tra
d
in
g
Ru
l
es
A
s bids and asks arrive, the
y
are interpreted under the two rules of the double
auction. The first rule is an improvement rule that discards bids and asks if they are
n
ot
b
etter t
h
an any prev
i
ous stan
di
ng
bid
or as
k

. T
h
e secon
d
ru
l
e
i
s a tra
di
ng ru
l
e
t
h
at spec
ifi
es t
h
at a tra
d
e occurs w
h
en a new
bid

i
s
g
reater t

h
an t
h
e as
k
pr
i
ce, or a
n
ew ask is less than the bid
p
rice. When a trade occurs, the earlier bid or ask of the
p
a
i
r
d
eterm
i
nes t
h
e tra
di
ng pr
i
ce
.
5
.4. Effect of In
d

ivi
d
ua
l
Bu
d
get Constraints
Th
e e
ff
ect o
f

i
n
di
v
id
ua
l

b
u
dg
et constra
i
nts man
if
est
i

n
g
t
h
e supp
ly
an
d

d
eman
d
curves
m
ust be significant for any organized trend of prices towards an equilibrium price
p
re
di
cte
d

b
y t
h
e Law o
f
Supp
l
y an
d

Deman
d
. Go
d
e an
d
Sun
d
er (1993)
d
emonstrate
t
h
at w
i
t
h
out t
h
e
i
n
di
v
id
ua
l

b
u

dg
et constra
i
nt an
d
t
h
e
d
ou
bl
e auct
i
on
i
mprovement ru
l
e
r
equiring bids to be ascending and asks to be descending, the ZI robots do not converge
to an equ
ilib
r
i
um pr
i
ce
b
ut
i

nstea
d
generate
i
n
d
epen
d
ent,
id
ent
i
ca
ll
y
di
str
ib
ute
d
p
r
i
ces over t
h
e
i
nterva
l
[0, H

]
. Brewer, et a
l
. (2002)
d
emonstrate
d
t
h
e a
ddi
t
i
ona
l
requirement of scarcity or finiteness of supply and demand for the ZI robots to reach
e
qu
ilib
r
i
um pr
i
ces. In t
h
e CRSD env
i
ronment, ZI ro
b
ots

f
a
il
to reac
h
an equ
ilib
r
i
um
pr
i
ce,
i
nstea
d

g
enerat
i
n
g
an
iid
sequence o
f
pr
i
ces. However, t
h

e exact s
h
ape o
f
t
h
e
i
id distribution is affected by the particulars of the supply and demand curves
.
W
i
t
h
out
i
n
di
v
id
ua
l

b
u
d
get constra
i
nts, t
h

e Constra
i
ne
d
Ran
d
om Wa
lk
ers wou
ld
g
enerate pr
i
ces t
h
at are a Mart
i
n
g
a
l
e process. T
h
e
i
n
di
v
id
ua

l

b
u
dg
et constra
i
nts are
i
mposed at step (3). Without step (3), each proposed bid or ask price is simply a
n
orma
l

b
ase
d
aroun
d
t
h
e prev
i
ous pr
i
ce. But w
i
t
h
step (3) a

dd
e
d
, pr
i
ces appear to
c
onver
g
e. It
i
s c
l
ear
f
rom F
ig
ure 3 t
h
at t
h
e rate o
f
conver
g
ence
d
epen
d
s on t

h
e
d
eviation
p
aramete
r

σ
2
o
f
t
h
e Norma
l

di
str
ib
ut
i
on generat
i
ng success
i
ve
bid
s an
d

as
k
s. Over a range o
f
sma
ll

σ
2
,

hi
g
h
er
σ
2
appears to a
ll
ow convergence to procee
d
at a faster
p
ace.
5
.5. Effect of Dou
bl
e Auction Tra
d
ing Ru

l
es
T
he effect of the double auction tradin
g
rules is to impose a t
y
pe of order on the
c
ompet
i
t
i
ve process t
h
at converts streams o
f

bid
s an
d
as
k
s
i
nto transact
i
on pr
i
ces.

Th
e
i
mportance o
f
t
h
ese ru
l
es, an
d
o
f
c
h
anges to t
h
em,
i
s
b
orne out
b
y t
h
e r
i
c
h
literature of double auction processes. Chamberlin’s (1948) experiments showin

g
t
h
e apparent non-convergence o
f
mar
k
et pr
i
ces
did
not
i
mpose t
h
e
f
orma
li
t
i
es o
f
d
ou
bl
e auct
i
on tra
di

ng,
b
ut
i
nstea
d

h
a
d
su
bj
ects c
i
rcu
l
ate t
h
e room to
fi
n
d
partners.
In contrast, Smith (1962) showed that when the rules of the double auction were
app
li
e
d
to tra
di

ng, pr
i
ces converge
d
a
f
ter a ser
i
es o
f
repet
i
t
i
ons to matc
h
t
h
e
p
re
di
ct
i
ons o
f
t
h
e Law o
f

Supp
l
y an
d
Deman
d
.
3
6Ex
p
erimental Business Research Vol. II
5.6. Price Convergence in CRSD markets populated by Constrained Random
W
a
lk
Ro
b
ot
s
B
rewer, et a
l
. (2003) s
h
owe
d
t
h
at w
i

t
h
a CRSD env
i
ronment, t
h
e or
d
er
i
ng e
ff
ect o
f
t
h
e
d
ou
bl
e auct
i
on mar
k
et
l
ac
k
s su
ffi

c
i
ent strengt
h
to tame t
h
e aggregate pr
i
c
i
ng
behavior of the ZI robots. However, because prices of markets populated b
y
humans
c
onverge
i
n t
h
e CRSD
d
ou
bl
e auct
i
on env
i
ronment,
i
t was

h
ypot
h
es
i
ze
d
t
h
at some
addi
t
i
ona
l
e
l
ement o
f

h
uman rat
i
ona
li
ty, a
b
sent
i
n t

h
e ZI ro
b
ots, was respons
ibl
e.
With the demonstrated conver
g
ence of market prices in double auctions populated
b
y t
h
e Constra
i
ne
d
Ran
d
om Wa
lk
ers, t
h
e e
l
ement o
f

b
e
h

av
i
or requ
i
re
d
may
h
ave
b
een
id
ent
ifi
e
d
:
b
as
i
ng o
f

bid
an
d
as
k
s upon t
h

e prev
i
ous pr
i
ce, w
hil
e st
ill
censor
i
ng
bids and asks a
g
ainst the bud
g
et constraint, causes the market prices to conver
g
e.
N
ot
i
ce w
h
at
h
appens as t
h
e ro
b
ots compete

i
n F
i
gure 3. Pr
i
ces
d
r
if
t towar
d
s
e
qu
ilib
r
i
um at a rate t
h
at r
i
ses w
i
t
h

i
ncreas
i
ng

i
nnovat
i
on
σ
2
.
A
f
ter not
i
ng t
h
e
p
a
tt
ern,
σ
2
was varied in an attempt to
g
enerate time series comparable to the human
tra
d
ers. But w
h
y s
h
ou

ld
pr
i
ces converge at a
ll
? T
h
e
k
ey
i
s to recogn
i
ze t
h
e com
bi
ne
d
eff
ect o
f

b
u
d
get constra
i
nts,
d

ou
bl
e auct
i
on ru
l
es, an
d
anc
h
or
i
ng
bid
s an
d
as
k
s to t
h
e
p
revious transaction
p
rice
.
If
t
h
e prev

i
ous pr
i
ce
i
s
l
ow compare
d
to compet
i
t
i
ve equ
ilib
r
i
um, t
h
en t
h
e
b
u
d
get
c
onstra
i
nts

i
mp
l
y a
l
arger poo
l
o
f

b
uyers su
b
m
i
tt
i
ng
bid
s t
h
an se
ll
ers su
b
m
i
tt
i
ng

a
sks. The double auction rules require bids to be ascendin
g
and asks to be descendin
g.
Suppose pr
i
ces are so
l
ow t
h
at
i
t
i
s
lik
e
l
y t
h
at 2
b
uyers w
ill
su
b
m
i
t

bid
s
b
e
f
ore t
h
e
n
ext se
ll
er w
ill
su
b
m
i
t an as
k
. T
h
en t
h
e
d
ou
bl
e auct
i
on ru

l
es w
ill

fil
ter out t
h
e
hi
g
h
est
o
f these two bids, which has a 7
5
% probabilit
y
of bein
g
hi
g
her than the previous
transact
i
on pr
i
ce. W
hil
e t
h

e
bid
pr
i
ce w
ill

lik
e
l
y move up,
i
t
i
s un
lik
e
l
y
i
t moves up
b
y muc
h
more t
h
an
σ
because of the anchoring effect of the bid generation process
σ

where
b
∼
p
t
−
tt
1
+
N
(0,
σ
2
). When the seller robot
g
enerates an ask, with about
5
0
%
pro
b
a
bili
ty t
h
e as
k
pr
i
ce w

ill

b
e
b
e
l
ow t
h
e prev
i
ous transact
i
on pr
i
ce an
d
a tra
d
e w
ill
occur at t
h
e ear
li
er, an
d

hi
g

h
er,
bid
pr
i
ce. T
h
ere
f
ore t
h
e tra
d
e pr
i
ce w
ill
ten
d
to move
slowl
y
towards the equilibrium, with the stren
g
th of the drift decreasin
g
as prices
m
ove towar
d

s t
h
e equ
ilib
r
i
um. W
h
en t
h
e pr
i
ces are too
hi
g
h
, t
h
ere are more poten-
t
i
a
l
se
ll
ers t
h
an potent
i
a

l

b
uyers, an
d
a s
i
m
il
ar process occurs to
l
ower t
h
e pr
i
ce.
This t
y
pe of slow conver
g
ence su
gg
ests an AR(1) process mi
g
ht reasonabl
y
fit
pr
i
ces converg

i
ng towar
d
s compet
i
t
i
ve equ
ilib
r
i
um, compat
ibl
e w
i
t
h
t
h
e not
i
on o
f
Wa
l
ras
i
an a
dj
ustment processes:

(
P
t
P
P
+
1
−
P
eq
P
P
)
=
a
1
(
P
t
P
P
−
P
eq
P
P
)
+
ε
t

;
|
a
1
|
<

1,
ε
t
iid
t
N
(0,
NN
σ
*
2
)
Th
e mar
k
et pr
i
ces o
f
t
h
e Constra
i

ne
d
Ran
d
om Wa
lk
ers
fi
t an AR(1) process
f
a
i
r
ly
well. It is possible that there could be some price-based heteroskedasticit
y
that does
n
ot
fi
t t
h
e stan
d
ar
d
AR(1) mo
d
e
l

, or t
h
e res
id
ua
l
s may
b
e non-norma
l
. T
h
ese e
ff
ects
were not teste
d

f
orma
lly
. W
h
en we
l
oo
k
at t
h
e

d
ata o
f
t
h
e
h
uman popu
l
ate
d
mar
k
ets,
there is also an additional effect that does not fit a AR(1)
p
rocess: correction of
out
li
er pr
i
ces. T
h
e ana
l
ys
i
s o
f
mar

k
ets popu
l
ate
d

b
y
h
umans w
ill

b
e t
h
e
f
ocus o
f
t
h
e
n
ext sect
i
on
.
M
ICROECONOMIC
M

M
AN
D
F
INANCIAL
FF
P
L
RICE
P
P
A
E
DJUSTMENT
P
T
ROCESSES
PP
37
6
. ARMA BEHAVI
O
R
O
F MARKET
S
P
O
P
U

LATED BY H
U
MAN
S
Th
e purpose o
f
t
hi
s sect
i
on
i
s to exam
i
ne ARMA mo
d
e
l
s o
f
t
h
e CRSD
d
ou
bl
e
auction market populated b
y

humans. The impetus for usin
g
ARMA models is
b
ase
d

i
n part upon t
h
e
h
ypot
h
es
i
s t
h
at mar
k
ets popu
l
ate
d

b
y Constra
i
ne
d

Ran
d
om
W
alker robots of section 5, which demonstrate convergence towards competitive
eq
uilibrium, a
pp
ear to fit an AR model in
p
rices
.
H
owever, w
i
t
h
t
h
e
h
umans, t
h
e v
i
sua
l
ev
id
ence suggests a

h
an
dli
ng o
f
out
li
ers
i
ncons
i
stent w
i
t
h
a s
i
mp
l
e AR(1) mo
d
e
l
. In an AR(1) mo
d
e
l
, an out
li
er

i
n pr
i
c
e
would
g
enerate a new slow drift towards the equilibrium price. But in this data, the
o
b
serve
d
e
ff
ect
i
s t
h
at t
h
e pr
i
ce corrects to a pr
i
ce near t
h
e prev
i
ous pr
i

ces. T
hi
s
i
s a
p
roperty o
f
a mov
i
ng average or MA mo
d
e
l
w
h
ere t
h
e error terms
f
o
ll
ow a
li
near
p
rocess and allow for such self-correction. An ARMA(1, 1) model incor
p
orates
b

ot
h
e
ff
ects.
(
P
t
P
P
+
1
−
P
eq
P
P
)
=
a
1
(
P
t
PP
−
P
eq
PP
)

+
ε
t
;
ε
t
∼
b
1
ε
t
−
1
+
iid
N
(0,
NN
σ
*
2
)
In t
hi
s mo
d
e
l,
t
h

e
a
1
term
i
s typ
i
ca
ll
y
d
enote
d
t
h
e AR(1) or autoregress
i
ve term an
d
th
e
b
1
term
i
s t
y
p
i
ca

lly

d
enote
d
t
h
e MA(1) or mov
i
n
g
-avera
g
e term. S
l
ow conver-
g
ence towards equilibrium is described b
y
a near unit
y

a
1
∼
1
−
φ
, with the speed of
φ

c
onvergence
i
ncreas
i
ng w
i
t
h

φ
. The
φ
b
1
term
i
n
di
cates “memory”
i
n t
h
e s
h
oc
k
s. A
p
os

i
t
i
ve
b
1
ma
y

i
n
di
cate a run-on e
ff
ect
i
n
l
ar
g
e s
h
oc
k
s
b
e
i
n
g

f
o
ll
owe
d

by
a run o
f
s
maller and smaller shocks. A ne
g
ative
b
1
ma
y
indicate that shocks tend to partiall
y
s
e
lf
-correct
i
ng
i
n success
i
ve tra

d
es. From a v
i
sua
l

i
nspect
i
on o
f
t
h
e
h
uman tra
di
ng
d
ata, we expec
t

b
1
to
b
e ne
g
at
i

ve
i
n
h
uman popu
l
ate
d
mar
k
ets
.
T
he anal
y
sis of the data
y
ields six results. Result 1 states that neither a fixed
r
an
d
om process nor a ran
d
om-wa
lk
un
i
t-root process a
d
equate

l
y
d
escr
ib
es t
h
e
h
uman
m
ar
k
et
d
ata. Resu
l
t 2
id
ent
ifi
es t
h
e
d
r
if
t
i
n t

h
e pr
i
c
i
n
g
process an
d

id
ent
ifi
es a
l
ar
g
e
s
ource of variance from outliers, or lar
g
e movements in price that are almost imme-
di
ate
l
y correcte
d
3
. Base
d

on t
hi
s, we remove
d

l
arge movements
i
n pr
i
ce to “san
i
t
i
ze”
t
h
e t
i
me ser
i
es. T
h
e goa
l

i
s to separate t
h
e e

ff
ects o
f
t
h
ese se
lf
-correct
i
ng pr
i
c
e
m
ovements from other features of the time series. Result 3 finds a curious relation-
s
hip between price variance and price in the sanitized time series. Results 4–
6
ch
aracter
i
ze
f
eatures o
f
ARMA mo
d
e
l
s

fi
tte
d
to t
h
e t
i
me ser
i
es.
R
e
s
u
l
t 1: Ne
i
t
h
er an
iid

fi
xe
d
ran
d
om process nor a un
i
t-root process – suc

h
as
a
r
an
d
om wa
lk
– a
d
equate
l
y
d
escr
ib
es t
h
e pr
i
ce
d
ata
.
S
u
pp
ort: V
i
sua

ll
y,
i
t
i
s un
lik
e
l
y t
h
at t
h
e
d
ata cou
ld

b
e
i
n
d
epen
d
ent an
d

id
ent

i
ca
l
d
raws
f
rom a
fi
xe
d
ran
d
om
di
str
ib
ut
i
on
b
ecause t
h
e mean an
d
var
i
ance o
f
t
h

e pro-
c
ess are chan
g
in
g
. Visuall
y
, a unit-root process is unlikel
y
because shocks to a unit-
r
oot process are pers
i
stent. T
hi
s means,
f
or
i
nstance, t
h
at
l
arge c
h
anges
i
n t
h

e pr
i
ce
sh
ou
ld
not
b
e
f
o
ll
owe
d

b
y reversa
l
s. Two
f
orma
l
tests were per
f
orme
d
to exam
i
ne