Experimental Business Research II springer 2005 phần 3 pptx

M
ICROECONOMIC
M
M
AN
D
F
INANCIAL
FF
P
L
RICE
P
P
A
E
DJUSTMENT
P
T
ROCESSES
PP
39
A
RMA (1, 1) model AR(1) MA(1)
σ
2
Lo
g
(Likelihood
)
R

a
w
P
[
t
] no filtering 0.9952
−
0
.
80
4
3
2
3
.7
3
−
2
382
(se) 0.0041 0.03
6
|∆
P
|
> 15 removed 0.9877
−
0
.6429 15.95
−
21

5
1.
6
(se) 0.00
6
7 0.0419
AR onl
y
0.872
6
– 19.80
−
2234
.
0
M
A onl
y
– 0.6
5
67 42.4
4
−
2
5
26.0
Re
s
u
l

t 4: T
h
e ARMA(1,1)
fi
ts revea
l
(
i
) an AR coe
ffi
c
i
ent compat
ibl
e w
i
t
h
a ver
y
s
low Walrasian d
y
namic to
g
ether with (ii) a stron
g
er MA coefficient compatible
w
i

t
h
s
h
ort-term correct
i
ons o
f
rema
i
n
i
ng out
li
ers aga
i
nst t
h
e s
l
ow
l
y mov
i
ng mean.
S
an
i
t
i

z
i
n
g
t
h
e
d
ata ena
bl
es
b
etter
d
etect
i
on o
f
t
h
e s
l
ow Wa
l
ras
i
an
dy
nam
i

c.
S
u
pp
ort: T
h
e strengt
h
o
f
t
h
e convergence process
d
epen
d
s on (1
−
a
1
)
. As t
h
e
a
1
c
oefficient is almost 1.0, the conver
g
ence process is ver

y
slow and furthermore does
n
ot
h
ave goo
d
stat
i
st
i
ca
l
s
i
gn
ifi
cance g
i
ven t
h
e stan
d
ar
d
error o
f
t
h
e

a
1
coefficient.
Th
e MA
(
1
)
coe
ffi
c
i
ent
b
1

i
s negat
i
ve an
d

i
s p
i
c
ki
ng up t
h
e

b
ounce or correct
i
on o
f
lar
g
e movements in price. Removin
g
the lar
g
e price chan
g
es from the time series
i
mproves t
h
e
l
og
lik
e
lih
oo
d

b
y over 200 an
d
s

h
ows a s
li
g
h
t
l
y stronger convergence
d
ynam
i
c now sa
f
e
l
y a
b
ove t
h
e no
i
se. T
h
e AR(1) an
d
MA(1) process est
i
mate
d
s

eparatel
y
show that both terms are si
g
nificant. A lo
g
-likelihood
χ
2
test would re
j
ect
r
emov
i
ng e
i
t
h
er term at we
ll
a
b
ove t
h
e 0.999
l
eve
l.
R

e
s
ult 5
:
A structural chan
g
e in the ARMA process ma
y
occur rou
g
hl
y
correspond-
i
ng to t
h
e atta
i
nment o
f
equ
ilib
r
i
um.
S
upport:
F
i
g

ure
5
shows a standard lo
g
-likehood test for detectin
g
the breakpoint
for a single structural change in a time series model. Figure 5 suggests, based on
lo
g
-likelihood, a structural break around
T
∼
2
9
0. When we look at the time series
of prices this does correspond to a rou
g
h visual assessment of where equilibrium
appears to
h
ave
b
een atta
i
ne
d

(
T

∼

300
–
400).
C
oefficient
s
A
RMA 1, 1 mo
d
e
l
sAR
(
1
)
MA
(
1
)
σ
2 Log(L
ik
e
lih
oo
d)
|∆
P

|
>
1
5
removed
T
≤
290 0
.
9882
−
0
.
59
18 26.02
−
88
5
.2
5
s
.e. 0.0088 0.0631
T
>
290 0.7368
−
0
.461
5
9.0

5
−
1
204.7
0.0846 0.1138
Combine
d
−
2
08
9
.
95
40 Ex
p
erimental Business Research Vol. II
100
2
00 300
4
00 500 600
7
00
−
2
14
0
−
2
1

30
−
2
12
0
−
211
0
−
21
00
−
20
9
0
Sum of Lo
g
-Likelihoods of Separate ARMA
(
1, 1
)
Model
s
combinedlo
g
likelihood
0
2
00
4

00 600
−
100 10203040
P
rice Time Series P1 from Brewer, Huang, Nelson, and Plott
(
sanitized
)
P
minus
6
3
A
pp
roximate location of structural break
in ARMA
(
1, 1
)
models
F
igure
5
.
M
ICROECONOMIC
M
M
AN
D

F
INANCIAL
FF
P
L
RICE
P
P
A
E
DJUSTMENT
P
T
ROCESSES
PP
41
Wi
t
h
t
h
e caveat t
h
at sma
ll
er
d
ata sets y
i
e

ld

l
ess accurate
fi
ts,
i
t
i
s poss
ibl
e to
b
rea
k
up t
h
e t
i
me ser
i
es
i
nto groups o
f
100 tra
d
es.
C
oe

ffi
c
i
ent
s
A
RMA 1, 1 mo
d
e
l
sAR
(
1
)
MA
(
1
)
σ
2
Log(Likelihood
)
D
at
a
all data, no filterin
g
t
rades 1–100 0.99
54

−
0
.908
5
78.98 –
1
01–200 0.
996
−
0
.74
63
24.
65
–
201
–
300 0
.
9
7
89
−
0.
6
8
9
2 20.11 –
3
01–400 0.8

57
−
0.4291 12.3
5
–
401–500 0.248
9
−
0
.1
50
7 22.
6
–
501–600 0.1
9
25 0.032
9
8.53 –
6
01–700 0.871
1
−
0.6732 9.23 –
7
01
–7
92 0
.
41

7
2
−
0.0
99
5.
99
–
|
∆
P
|
>
1
5
remo
v
e
d
t
rades 1–100 0.98
3
−
0.4676 3
5
.44
−
3
21.97
101

–
200 0
.
9907
−
0
.
6
7
6
2
0
.
33
−
29
3.
6
8
201–300 0.
96
2
−
0
.5767 1
9
.84
−
291
.

9
7
301–400 0.90
5
8
−
0
.6693 12.23
−
2
67.30
40
1–
500 0
.
6
74
−
0
.
42
7
98
.
49
−
248
.
91
501–600 0.0083 0.1263

9
.6
8
−
255
.42
601–700 0.7797
−
0
.422 6.68
−
237.00
7
01–767 0.52
9
5
−
0.17
9
5.68
−
1
53
.
3
4
C
om
bi
ne

d
−
2
06
9
.5
9
The pattern is
g
iven as Result 6.
R
esult 6:
T
he price convergence process is not purely stationary but there is (i) a
sl
ow tren
d
towar
d
s
l
ower var
i
ance, an
d

(ii)
a s
hif
t

i
n
b
e
h
av
i
or aroun
d
atta
i
nment o
f
p
rice equilibrium toward stron
g
er price-related effects and awa
y
from outlier effects.
Su
pp
ort: The variance effect is clearl
y
shown in the table above, and is also ex-
p
ecte
d
g
i
ven Resu

l
t 3. T
h
ere are
l
arge c
h
anges
i
n t
h
e coe
ffi
c
i
ents
b
eg
i
nn
i
ng w
i
t
h
T
=
301–400. Fi
g
ure

6
(constructed from the unfiltered data) su
gg
ests that the AR(1
)
c
oefficient drops, indicatin
g
a stron
g
er stren
g
th of the price conver
g
ence process.
A
t t
h
e same t
i
me, t
h
e MA(1) coe
ffi
c
i
ent
d
rops
i

n a
b
so
l
ute va
l
ue,
i
n
di
cat
i
ng t
h
at
l
ess
o
f
t
h
e pr
i
ce movements seem to
b
e correct
i
ons o
f
prev

i
ous s
h
oc
k
s.
Note also that the coefficients be
g
in to wander after
T
>

5
00. This wanderin
g
m
ay
i
nvo
l
ve e
ff
ects o
f

di
screteness
i
n pr
i

ces, g
i
ven t
h
at pr
i
ces are constra
i
ne
d
to
un
i
t va
l
ues an
d
t
h
e o
b
serve
d
pr
i
ce var
i
ance
i
s ver

y

l
ow.
42 Ex
p
erimental Business Research Vol. II
−
1
−
0
.
8
−
0
.
6
−
0
.
4
−
0
.
2
0
0
.
2
0

.
4
0.
6
0
.
8
1
600 700 800
0
0 100 200 300 400 500
0
500
G
rou
p
A
RMA(1
,
1) Fit
s
AR(1) component
ent
M
A(1) com
p
onent
F
igure
6

. ARMA(1, 1) fits to raw subsamples
.
An alternative, but
p
erha
p
s im
p
ortant, inter
p
retation for Result
6
is that as the
m
arket equilibrates, there is initiall
y
an advanta
g
e for sub
j
ects who pa
y
attention to
t
h
e tren
d

i
n mar

k
et pr
i
ces an
d
w
h
et
h
er a pr
i
ce o
ff
er
i
s an out
li
er an
d
t
hi
s generates
t
h
e near un
i
ty va
l
ues
f

or t
h
e t
i
me-ser
i
es coe
ffi
c
i
ents t
h
at we see. But as t
h
e mar
k
et
e
quilibrates, there is less and less variance in price and therefore less and less mone
y
t
h
at cou
ld

b
e earne
d

b

y care
f
u
l
t
i
m
i
ng o
f
, or attent
i
on to, mar
k
et act
i
v
i
t
i
es. T
h
e
ch
anges an
d
var
i
a
bili

ty
i
n t
h
e t
i
me-ser
i
es propert
i
es t
h
at occur upon, or
j
ust a
f
ter
e
quilibrium, could be simpl
y
due to the fact that there is almost nothin
g
to be
g
ained
b
y tra
di
ng
i

n t
h
e prev
i
ous manner.
7.
CO
N
C
L
US
I
O
N
S
T
his paper began with the question of whether it might be possible to integrate or
reconc
il
e
id
eas o
f
mar
k
et
dy
nam
i
cs

f
oun
d

i
n m
i
croeconom
i
cs w
i
t
h
t
h
ose
f
oun
d

i
n
the random walk or Martin
g
ale theor
y
of finance. The use of lon
g
time series
g

enerated
by a CRSD laboratory market provided a practical framework for an initial study of
t
h
ese quest
i
ons
.
Two conclusions can be found in the
p
resent research. The first conclusion is that
something like a random walk process can be useful in modeling the slow conver-
g
ence component o
f
pr
i
ces
f
oun
d

i
n CRSD mar
k
ets. W
h
en a ran
d
om wa

lk

i
n
bid
s
a
nd asks is censored a
g
ainst individual bud
g
et constraints the resultin
g
market
M
ICROECONOMIC
M
M
AN
D
F
INANCIAL
FF
P
L
RICE
P
P
A
E

DJUSTMENT
P
T
ROCESSES
PP
43
prices appear to slowl
y
conver
g
e towards the predictions of suppl
y
and demand.
T
he innovative ste
p
in this model is that the random walk is not in transaction
p
rices,
b
ut
i
nstea
d

i
s a component
i
nvo
l

ve
d

i
n t
h
e process generat
i
ng
bid
s an
d
as
k
s.
The second conclusion is that the price d
y
namics of human-populated markets
c
ontain a number of different kinds of effects that seem to be operatin
g
simult-
a
neous
l
y. Smoot
hi
ng s
h
ows a AR(1) process s

i
m
il
ar to t
h
at seen
i
n t
h
e constra
i
ne
d
random walk robots. However,
p
rices in the human-
p
o
p
ulated markets also show a
c
omplex outlier
g
eneration and correction process. A lar
g
e move in prices at one
tra
d
e
i

s o
f
ten correcte
d

b
ac
k
towar
d
s t
h
e average w
i
t
h
t
h
e next tra
d
e. T
hi
s type o
f
“
memor
y
” of the process is not captured b
y
an AR(1) statistical process or a con-

strained random walk of bids/asks. Removin
g
man
y
of the lar
g
e outliers and addin
g
a
n MA(1) component to a
b
sor
b
t
h
e rema
i
n
i
ng out
li
er/correct
i
on process y
i
e
ld
s an
ARMA(1, 1) model that varies as the market conver
g

es towards equilibrium.
A structural break in the ARMA
p
arameters seems to occur as e
q
uilibrium is
reac
h
e
d
. T
h
e nature o
f
t
hi
s structura
l

b
rea
k

i
s
l
e
f
t
f

or
f
urt
h
er researc
h
. It may suggest
the use of models with multiple re
g
imes for price discover
y
and equilibrium behavior
rather than a simple stationar
y
model.
H
ope
f
or a com
bi
ne
d
t
h
eory o
f
m
i
croeconom
i

c an
d

fi
nanc
i
a
l
a
dj
ustment suggeste
d
i
n this work possibl
y
relies on classif
y
in
g
markets alon
g
what is for now a somewhat
speculative
g
roupin
g
: (i) Markets with finite endin
g
times and finite trade can be
roug

hl
y mo
d
e
l
e
d
as a no
i
sy Mars
h
a
lli
an process an
d

i
t
i
s poss
ibl
e t
h
at scarc
i
ty an
d
the likelihood of lar
g
e surplus traders tradin

g
earl
y
are all that is necessar
y
for the
a
ppearance of prices conver
g
in
g
to the competitive equilibrium. Prices followin
g
a
no
i
sy Mars
h
a
lli
an process w
ill
not
b
e Mart
i
nga
l
es
b

ut
i
nstea
d
w
ill
ex
hibi
t negat-
i
ve autocorrelation of price chan
g
es. (ii) Markets with no fixed endin
g
time and
c
ontinuousl
y
refreshed suppl
y
and demand, such as the CRSD market presented
h
ere, ex
hibi
t pr
i
ce convergence w
h
en popu
l

ate
d

b
y
h
umans t
h
at can not
b
e exp
l
a
i
ne
d
a
s a Marshallian process, but onl
y
as either a Walrasian class of ad
j
ustment process
o
r some other t
y
pe of process
y
et to be defined. Within the Walrasian class of
adj
ustment processes

i
s t
h
e poss
ibili
ty t
h
at a ran
d
om-wa
lk
approac
h
to su
b
m
i
tt
i
ng
bids and asks can explain market price conver
g
ence when the random walk
g
enerat-
i
n
g
bids and asks is censored, at the individual level, a
g

ainst an individual seller’s
supp
l
y costs or
b
uyer’s re
d
empt
i
on va
l
ues ma
ki
ng up t
h
e supp
l
y an
d

d
eman
d
. T
hi
s
c
onvergence a
l
so re

li
es upon t
h
e
d
eta
il
s o
f
tra
di
ng, e.g., t
h
e
i
mprovement ru
l
es o
f
the double auction
.
I
t
i
s t
hi
s secon
d
group
i

ng o
f
mar
k
ets
i
nvo
l
ves a
h
y
b
r
id
mo
d
e
l
o
f
CRSD mar
k
et
pr
i
ce convergence
i
ncorporat
i
ng

b
ot
h

id
eas
f
rom
fi
nance (t
h
e ran
d
om wa
lk
) an
d
m
icroeconomics
.
I
n a
ddi
t
i
on, t
h
e
h
y

b
r
id
mo
d
e
l
can y
i
e
ld

b
ac
k
a pure
l
y
fi
nanc
i
a
l
mo
d
e
l
, w
h
en t

h
e
mi
croeconom
i
c constra
i
nts o
f
supp
l
y an
d

d
eman
d
are remove
d
. Suppose a
fi
nanc
i
a
l
m
arket is modeled as bein
g
like the CRSD environment, but without the individual
c

onstra
i
nts on tra
d
ers’ costs an
d
va
l
ues typ
i
ca
ll
y assoc
i
ate
d
w
i
t
h
supp
l
y an
dd
eman
d.
If

i
n

di
v
id
ua
l

b
e
h
av
i
or
b
ase
d
on (poss
ibl
y
f
au
l
ty)
f
uture expectat
i
ons turns out to
b
e
quite different from behavior based on a known arbitra
g

e opportunit
y
, this ma
y
be
44 Ex
p
erimental Business Research Vol. II
a
sensible rou
g
h model. In the absence of individual bud
g
et constraints associated
with suppl
y
and demand curves, a random walk
g
eneratin
g
bids and asks would
b
e uncensore
d
,
d
epen
di
ng on
l

y on t
h
e prev
i
ous transact
i
on pr
i
ce. T
h
us, w
h
en t
h
e
rules of double auction tradin
g
are applied, the random walk process in bids and asks
would
g
enerate a random walk in prices, which is the expected result in a informa-
t
i
ona
l
e
ffi
c
i
ency mo

d
e
l
o
f
a pr
i
ce a
dj
ustment
.
As warned in the introduction, this approach ma
y
be seen b
y
some as overl
y
broa
d
or raisin
g
more questions than it answers. However, as pointed out in section 4,
t
h
ere are a num
b
er o
f
apparent con
fli

cts
b
etween m
i
croeconom
i
c pr
i
ce processes as
c
onfirmed b
y
laborator
y
experiments and the standard assumptions of finance. Rather
than simpl
y
assume that the latter do not appl
y
to the former, it is hoped that the
searc
h

f
or a com
bi
ne
d
t
h

eory o
f
pr
i
ce a
dj
ustment may – w
i
t
h
cont
i
nue
d
contr
ib
ut
i
on
b
y
theorists and empiricists in both fields –
y
ield further insi
g
hts into the behavior of
m
arkets not discernable with the tools of one field alone.
ACKNOWLEDGMEN
T

Thi
s researc
h
was supporte
d

i
n part
b
y Hong Kong Researc
h
Grants Counc
il
Com-
p
etitive Earmarked Research Grant HKUST6215/00H. I also wish to thank Tim
C
ason, Leonard Chen
g
, S. H. Chew, Jim Cox, John Dickhaut, Dan Friedman, Steve
G
j
ersta
d
, Jo
h
n Le
d
yar
d

, C
h
ar
l
es Noussa
i
r, C
h
ar
l
es R. P
l
ott, Jason S
h
ac
h
at, an
d
Sh
y
am Sunder for their comments on previous installments of this research: none
a
re responsible for m
y
errors.
NOTES
1
F
ama [1965] finds positive autocorrelations of returns on 75% of the Dow 30 stocks. Solnik [1973],
L

awrence [198
6
], and Butler and Malaikah [1992] find man
y
examples of ne
g
ative autocorrelations of
dail
y
returns in the stock markets. Hawawini and Keim [199
5
] provide a surve
y
of this literature in their
i
ntro
d
uct
i
on. Dacorogna, Gençay, Mü
ll
er, O
l
sen an
d
P
i
ctet [2001; pp. 123–4]
b
r

i
e
fl
y
di
scuss negat
i
ve
autocorre
l
at
i
ons
f
oun
d

i
n t
h
e pr
i
ce
f
ormat
i
on process o
f

f

ore
ig
n exc
h
an
g
e mar
k
ets t
h
at are stron
g

f
or
ver
y
s
h
ort t
i
me
h
or
i
zons
b
ut van
i
s

h
over t
h
e course o
f
30 m
i
nutes or so
.
2
The ar
g
ument is that in a CRSD environment, the Marshallian d
y
namic is precluded. Nothin
g
precludes
M
ars
h
a
lli
an or mu
l
t
i
p
l
e a
dj

ustment mo
d
e
l
s
f
rom act
i
ng
i
n t
h
e or
di
nary c
l
ass
i
ca
l
env
i
ronment or ot
h
er
d
oma
i
ns not stu
di

e
d

h
ere.
3
T
h
e
i
nter
f
ace
f
or tra
di
ng was a grap
hi
ca
l
screen rat
h
er t
h
an numer
i
c
i
nput o
f

bid
s an
d
as
k
s, an
d
so
i
t
i
s
a
l
so poss
ibl
e t
h
at t
h
ese out
li
ers are cause
d

by
su
bj
ects rec

kl
ess
ly
sen
di
n
g

i
n as
k
s t
h
at are too
l
ow (or
b
ids that are too hi
g
h) in an attempt to quickl
y
accept a desirable bid (ask). Priorit
y
for input from
mu
l
t
i
p
l

e su
bj
ects t
h
at wou
ld
cause acceptance o
f
a
bid
/as
k
was
b
ase
d
on t
i
me on
l
y not on pr
i
ce. A
t
en
d
ency
f
or some su
bj

ects to sen
d

i
n out
li
er pr
i
ces can a
l
so
b
e seen as a
h
uman/computer
i
nter
f
ace
desi
g
n flaw because sub
j
ects could have been warned and
g
iven a pop-up box to confirm questionable
b
ehavior. The desi
g
n used did not involve an

y
such handholdin
g
, settlin
g
for simplicit
y
and minimal
i
nteract
i
on or gu
id
ance o
f
t
h
e su
bj
ect
.
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ICROECONOMIC
M
M
AN
D
F
INANCIAL
FF

P
L
RICE
P
P
A
E
DJUSTMENT
P
T
ROCESSES
PP
4
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uct
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ott, C
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ott, C
h
ar
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es R.
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k
ets Institutions an

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g

el and A. E. Roth (eds.) T
he
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f
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5
–49
5.
C
HOOS
IN
G
C
C
A
M
O
DE
L
OU
T
OF
M
F
ANY
MM

P
Y
OSSIBLE
A
E
L
TERNATI
V
E
S
47
4
7
C
h
apter
3
C
H
OOS
IN
G
A M
O
DEL
OU
T
O
F MANY P
OSS

IBLE
ALTERNATIVE
S
: EMI
SS
I
O
N
S
TRADIN
G
A
S
AN EXAMPLE
T
atsu
y
os
hi
Sa
ij
o
Osaka Universit
y
A
bstrac
t
T
he main
p

ur
p
ose of this
p
a
p
er is to consider how to choose a model when there
a
re many poss
ibl
e a
l
ternat
i
ves to c
h
oose
f
rom. We use g
l
o
b
a
l
warm
i
ng, espec
i
a
ll

y,
e
m
i
ss
i
ons tra
di
ng, as an examp
l
e. F
i
rst, we
d
escr
ib
e eac
h
mo
d
e
l

i
n a very s
i
mp
l
e
settin

g
and then consider implicit and explicit assumptions underl
y
in
g
each model.
I
n ot
h
er wor
d
s, we try to
id
ent
if
y t
h
e env
i
ronments
i
n w
hi
c
h
t
h
e mo
d
e

l
rea
ll
y wor
k
s.
O
ur mo
d
e
l
s y
i
e
ld
resu
l
ts t
h
at may
b
e
diff
erent or occas
i
ona
ll
y
i
ncons

i
stent. In or
d
er
to evaluate the results, we ar
g
ue that the settin
g
of the models and the implications
of
t
h
e
i
r
i
mp
li
c
i
t assumpt
i
ons are
i
mportant
.
1
. INTR
O
DU

C
TI
O
N
Sulfur dioxide emissions in the atmos
p
here have detrimental effects on human healt
h
through acid rain and soil pollution. Carbon dioxide emissions do not have direct
d
e
l
eter
i
ous e
ff
ects on
h
umans,
b
ut t
h
e
y
ma
y
cause
gl
o
b

a
l
warm
i
n
g

i
n t
h
e
f
uture.
B
ecause of both the direct and indirect effects of these
g
reenhouse
g
ases (GHGs), a
f
ew methods have been
p
ro
p
osed to control their emissions into the atmos
p
here. The
tra
di
t

i
ona
l
met
h
o
d

i
s t
h
rou
gh

di
rect re
g
u
l
at
i
ons or t
h
e comman
d
an
d
contro
l
met

h
o
d.
A
n
ot
h
e
r m
et
h
od
i
s
emissions trading whereb
y
emissions tar
g
ets are set and a
g
ents
are given incentives to reduce emissions further since they can sell any surplus emis-
si
ons perm
i
ts
i
n t
h
e mar

k
et. In t
h
e case o
f

di
rect re
g
u
l
at
i
on, once an a
g
ent sat
i
s
fi
es
the re
g
ulation, there is no incentive to reduce emissions further.
T
he December 1997 Kyoto Protocol to the United Nations Convention on Climat
e
C
h
an
g

e ca
ll
e
d

f
or Annex B countr
i
es (
i
.e., a
d
vance
d
countr
i
es an
d
some countr
i
es
that are in transition to market economies) to reduce their avera
g
e
g
reenhouse
g
as
e
missions over the years 2008–2012 to at least five percent below the 1990 levels.

I
n or
d
er to
i
mp
l
ement t
hi
s
g
oa
l
, t
h
e protoco
l
aut
h
or
i
zes t
h
ree ma
j
or mec
h
an
i
sms

c
ollectivel
y
called the Kyoto Mechanism. These are 1) emissions tradin
g
, 2)
j
oint
©
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
,
4
7
–
8
1
.
48 Ex
p
erimental Business Research Vol. I
I
i
m
p
lementation, and 3) the Clean Develo
p
ment Mechanism. As almost no directions

a
re
g
iven in the Protocol for implementin
g
these mechanisms, the details of the
i
mp
l
ementat
i
on must
b
e
d
es
i
gne
d.
This paper is or
g
anized as follows. In the first part of this paper (sections 2, 3,
a
nd 4), we describe models to implement the K
y
oto Mechanism b
y
usin
g
a mar

g
inal
ab
atement cost curve
f
or eac
h
country
i
n or
d
er to
li
m
i
t t
h
e pro
d
uct
i
on o
f
green
h
ouse
g
ases. Because the total amount of
g
reenhouse

g
ases varies over time, d
y
namic
m
odels are re
q
uired. However, we restrict ourselves to static models here because
t
h
e a
i
me
d
per
i
o
d
o
f
t
h
e Kyoto Protoco
l

i
s
f
rom 2008 to 2012.
1

It
i
s o
f
ten sa
id
t
h
a
t
e
missions tradin
g
attains a fixed
g
oal of re
g
ulated emissions at minimum cost. We
focus on this statement in Section 2 and show that the emissions reduction cost is
mi
n
i
m
i
ze
d
at a compet
i
t
i

ve equ
ilib
r
i
um. We t
h
en
i
nvest
i
gate some neutra
li
ty propos
i
-
tions. Section 3 introduces a social choice model to consider if com
p
etitive e
q
ui-
l
ibrium can be attained throu
g
h the concept of strate
gy
-proofness. Strate
gy
-proofnes
s
m

eans t
h
at t
h
e
b
est strategy o
f
eac
h
country
i
s to report t
h
e true marg
i
na
l
a
b
atement
c
ost curve. We will show that a countr
y
can
g
ain b
y
not announcin
g

its true mar
g
inal
a
batement cost curve. That is, in the announcement
g
ame of mar
g
inal abatement
c
ost curves,
i
t
i
s
i
mposs
ibl
e to atta
i
n t
h
e Kyoto target at t
h
e c
h
eapest cost un
d
er
strate

gy
-proofness. Section 4 proposes a
g
ame in which prices and quantities are
strate
g
ic variables. The possibilit
y
of attainin
g
competitive equilibrium throu
g
h the
c
onstructe
d
game
i
s t
h
en cons
id
ere
d
. One suc
h
game
i
s t
h

e M
i
tan
i
mec
h
an
i
sm (1998)
,
which implements the competitive equilibrium allocation in sub
g
ame perfect equi-
l
ibrium. In GHG emissions tradin
g
startin
g
from 2008, the problem of market power
i
s an
i
mportant
i
ssue. Countr
i
es suc
h
as Russ
i

a an
d
Japan w
ill

d
om
i
nate t
h
e mar
k
et.
T
he Mitani mechanism attains the com
p
etitive e
q
uilibrium allocation even when the
n
umber of
p
artici
p
ants is small. Sections
5
and 6 describe ex
p
eriments to test the
proposed models. Section 5 tests whether the model proposed in Section 2 works in

a
laborator
y
settin
g
. We implicitl
y
assume that the price is determined where the
d
emand is equal to the suppl
y
, but we cannot determine the prices and quantities
w
i
t
h
out
h
av
i
ng a concrete tra
di
ng ru
l
e
i
n t
h
e
l

a
b
oratory. An
i
mportant
i
ssue
i
s w
h
at
tradin
g
rule should be chosen. Section
6
describes an experiment b
y
Mitani, Sai
j
o
a
nd Hama
g
uchi (1998) that uses the Mitani mechanism. The sub
j
ects in this experi-
m
ent
did
not c

h
oose t
h
e su
b
game per
f
ect equ
ilib
r
i
um strategy,
b
ut rat
h
er cooperate
d
w
i
t
h
one anot
h
er to atta
i
n a Pareto super
i
or outcome. We cons
id
er t

h
e tens
i
on
between theor
y
and these experimental results and consider wh
y
the mechanism did
n
ot wor
k
we
ll
. F
i
na
ll
y, Sect
i
on 7 prov
id
es conc
l
u
di
ng remar
k
s.
2

.A
S
IMPLE MI
C
R
O
E
CO
N
O
MI
C
APPR
O
A
C
H
Suppose t
h
at
n
countr
i
es are
i
nvo
l
ve
d

i
n em
i
ss
i
ons tra
di
ng. Let
MA
C
i
(
x
i
)

b
e a mar-
g
inal abatement cost function of countr
y

i
, where
x
i
is the amount of
g
reen house
e

m
i
ss
i
ons o
f

i
. Suppose,
f
urt
h
er, t
h
at t
h
e ass
i
gne
d
amount o
f
country
i

d
eterm
i
ne
d

b
y t
h
e Kyoto Protoco
l

i
s
Z
i
, an
d
t
h
e amount o
f
em
i
ss
i
ons
b
e
f
ore tra
di
ng
i
s
Y

i
. W
e
a
ssume that each countr
y
treats the price of emissions permits parametricall
y
. In
C
HOOS
IN
G
C
C
A
M
O
DE
L
OU
T
OF
M
F
ANY
MM
P
Y
OSSIBLE

A
E
L
TERNATI
V
E
S
49
Y
i
x
i
Z
i
p
0
i
Y
i
x
i
Z
i
p
0
i
α
β
F
i

g
ure 1-1: A Supplier Fi
g
ure 1-2: A Demande
r
F
igure 1. Determination o
f
GHG Emissions
w
h
at
f
o
ll
ows, we
d
e
fi
ne t
h
e pro
fi
t o
f
eac
h
countr
y

by
t
h
e surp
l
us earne
d
re
l
at
i
ve to
the cost of achieving the assigned amount.
C
ons
id
er
fi
rst t
h
e supp
l
y
i
ng country
i
n F
i
gure 1-1. T
h

e
h
or
i
zonta
l
ax
i
s s
h
ows t
h
e
a
mount o
f
em
i
ss
i
ons o
f
GHGs, an
d
t
h
e vert
i
ca
l

ax
i
s
gi
ves t
h
e mar
gi
na
l
cost. Countr
y
i
must reduce its emissions of GHGs from
Y
i
to
Z
i
in order to attain the tar
g
et of th
e
Kyoto Protoco
l
. On t
h
e ot
h
er

h
an
d
, t
hi
s country cou
ld
o
b
ta
i
n pro
fi
ts
f
rom t
h
eem
i
ss
i
on
s
perm
i
t pr
i
ce,
p
,

by
se
lli
n
g
perm
i
ts a
f
ter re
d
uc
i
n
g

i
ts GHGs
by
more t
h
an requ
i
re
d

i
n
the K
y

oto tar
g
et. This countr
y
should consider this fact when decidin
g
on the amoun
t
of
a
ll
owa
bl
e GHG em
i
ss
i
ons
,

x
i
,
i
n t
h
at country. F
i
rst, t
h

e country’s tota
l
revenu
e
b
ecome
s
p
(
Z
((
i
−
x
i
). A
l
t
h
ou
gh
t
h
e rea
l
cost
i
s t
h
e area

b
etween t
h
e mar
gi
na
l
a
b
atement
c
ost curve and the line se
g
ment,
Y
i
−
x
i
, we define the
p
rofit function as
π
i
(
x
(
(
i
)

=
p
(
Z
(
(
i
−
x
i
)
−
Ύ
x
i
i
Z
MA
C
i
(
t
)
dt
,
(
1
)
since we consider the profit after attainin
g

the K
y
oto tar
g
et. The shadowed area in
Figure 1-1 shows
π
i
(
x
i
).
N
ext, cons
id
er t
h
e
d
eman
di
n
g
countr
y

f
or em
i
ss

i
ons perm
i
ts. As F
ig
ure 1-2
s
hows, the domestic reduction cost to attain the Kyoto target is the area between the
m
arg
i
na
l
a
b
atement cost curve an
d
t
h
e segment
Y
i
−
Z
i
. On t
h
e ot
h
er

h
an
d
, re
d
uc
i
ng
em
i
ss
i
ons
by

Y
i
−
x
i
an
d
t
h
en
b
u
yi
n
g

em
i
ss
i
ons perm
i
ts
f
or
x
i
−
Z
i
un
d
er t
h
e pr
i
ce
p
makes the pa
y
of
f
Ύ
Z
Y
i

i
MA
C
i
(
t
)
d
t
−
Ύ
x
i
i
Y
M
AC
i
(
t
)
dt
−
p
(
x
i
−
Z
i

),
w
hi
c
h
co
i
nc
id
es w
i
t
h
(1). T
h
e payo
ff
(or pro
fi
t) correspon
d
s to t
h
e area
α
−
β
.
Notice that the profits or surplus of Fi
g

ures 1-1 and 1-2 are not maximized under p
.
5
0Ex
p
erimental Business Research Vol. I
I
I
n what follows, we assume that each countr
y
maximizes its surplus. Differentiatin
g
(1) with res
p
ect to
x
i
, and then findin
g
the maximum,
x
i
*, we have the first-order
i
c
on
di
t
i
o

n
p
=
MAC
i
(
x
i
*). (2)
i
Furthermore, the sum of emissions for each countr
y
must equal the sum of the
a
ssi
g
ned amount for each countr
y
. Thus, we hav
e
∑
x
i
*
=
∑
Z
i
.
(3)

Th
ere
f
ore,
(
p
*,
(
x
1
*,
1
x
2
*, ,
2

x
n
*)) satisfying (2) and (3) is a
n
competitive equi
l
i
b
rium
.
Since the first-order condition (2) does not de
p
end on the initial

p
osition of emis-
sions,
Y
i
, the com
p
etitive e
q
uilibrium does not de
p
end on the initial
p
osition or th
e
present amount o
f
em
i
ss
i
ons
f
rom eac
h
country. Furt
h
ermore, t
h
e compet

i
t
i
ve equ
i
-
l
ibrium is independent of the distribution of the assi
g
ned amounts for each countr
y
a
s lon
g
as the total sum of the assi
g
ned amounts,
∑
Z
i
,
which is the ri
g
ht-hand side
of
(3),
i
s
fi
xe

d
. O
f
course, t
h
e
i
n
i
t
i
a
l
pos
i
t
i
on an
d
t
h
e ass
i
gne
d
amount
d
o
i
n

fl
uence
h
ow much cost each countr
y
must bear.
F
i
g
ure 2 illustrates a competitive equilibrium in emissions tradin
g
. B
y
super-
i
mpos
i
ng t
h
e
d
otte
d
vert
i
ca
l
ax
i
s o

f
F
i
gure 1-2 on t
h
e
d
otte
d
vert
i
ca
l
ax
i
s o
f
Fi
g
ure 1-1, we create Fi
g
ure 2 in which the vertical axis at the assi
g
ned amount
c
orresponds to these dotted vertical axes. Countr
y
1 reduces its GHG emissions
m
ore t

h
an t
h
e ass
i
gne
d
amount an
d
t
h
en se
ll
s t
h
e excess amount over t
h
e ass
i
gne
d
a
mount to Countr
y
2. On the other hand, Countr
y
2 reduces emissions b
y
up to
MAC

Country 2’s
MAC
Demander’s
s
Surplus
p
S
upplier’
s
Surplus


S
1’s Status Quo
2’s Status
Quo
+
−
p*
Country
1’s MAC
x
x
2
*
*
1
2
z
i

Assi
g
ne
d
Am
ou
n
t
Em
i
ss
i
on
s
F
igure 2. Emissions Trading and the Competitive E
q
uilibrium
C
HOOS
IN
G
C
C
A
M
O
DE
L
OU

T
OF
M
F
ANY
MM
P
Y
OSSIBLE
A
E
L
TERNATI
V
E
S
51
x
2
* and then buys emissions permits from Country 1. The marginal abatement cost
2
of each countr
y
equals to the competitive equilibrium price.
C
ons
id
er now a soc
i
a

l
we
lf
are pro
bl
em
i
n w
hi
c
h
t
h
e tota
l
sum o
f
t
h
e re
d
uct
i
on
c
osts of all countries is minimized under the condition
w
here the sum of emissions
of all countries is equal to the sum of assi
g

ned amounts of all countries:
min
x
x
n
i
i
Ύ
Y
1
∑
MA
C
i
(
t
)
dt
s
u
bj
ect to
∑
x
i
=
∑
Z
i
,

wh
ere
x
=
(
x
1
x
2
,

,
x
n
)
. I
f

x
*
=

(
x
1
*,
1
x
2
*, ,

2
x
n
*) is a solution to this problem, we
n
h
a
ve
M
AC
i
(
x
i
*)
i
=
MAC
j
C
(
x
j
*) for all
j
i
a
n
d
j

.
Consider next a
p
roblem where the
sum of
p
rofits of all countries is maximized under the same condition. Then, the
sum
b
ecome
s
1
n
∑
p
(
Z
i
−
x
i
)
−
min
x
x
n
i
i
Ύ

Z
1
∑
M
AC
i
(
t
)
d
t
,
s
i
nce
∑
x
i
=
∑
Z
i
,
∑
1
n
p
(
Z
(

(
i
−
x
i
) must
b
e zero
f
or any pr
i
ce
p
. T
h
ere
f
ore
,
t
h
e
m
aximization
p
roblem of the sum of
p
rofits of all countries becomes
max
x

−
Ύ
x
n
i
i
Z
1
∑
MA
C
i
(
t
)
d
t sub
j
ect to
∑
x
i
=
∑
Z
i
.
Th
at
i

s, t
h
e pro
fi
t max
i
m
i
zat
i
on pro
bl
em
i
s exact
l
y t
h
e same as t
h
e cost m
i
n
i
m
i
za-
tion problem. Hence, the solution must satisf
y

MAC
i
(
x
(
(
i
*)
i
=
MAC
j
C
(
x
j
*) for all
j
i

a
n
d

j
.
Thi
s a
l
so

i
mp
li
es t
h
at t
h
e sum o
f
surp
l
uses (or pro
fi
ts) o
f
a
ll
countr
i
es
i
s max
i
m
i
ze
d
a
s F
i

gure 2 s
h
ows. Summar
i
z
i
ng t
h
e a
b
ove resu
l
ts, we
h
av
e
P
roposition
1
:
(1) T
h
e pr
i
ce o
f
an em
i
ss
i

ons perm
i
t
i
s equa
l
to t
h
e marg
i
na
l
a
b
atement cost o
f
eac
h
c
ountry
(
p
*
=
MAC
i
(
x
i
*) for all

i
i
)
, an
d
t
h
e sum o
f
em
i
ss
i
ons o
f
a
ll
countr
i
es
i
s equa
l
to the sum of the assi
g
ned amounts of all countries at a competitive equilibrium
(
∑
x
i

*
=
∑
Z
i
).
(2) By m
i
n
i
m
i
z
i
ng t
h
e sum o
f
re
d
uct
i
on costs o
f
GHGs o
f
a
ll
countr
i

es un
d
er
∑
x
i
=
∑
Z
i
,
we have M
AC
i
(
x
i
*)
i
=
MAC
j
C
(
x
(
(
j
*) for all
j

i
a
n
d
j
.
(
3
)
T
h
e sum o
f
t
h
e re
d
uct
i
on costs
f
or GHGs o
f
a
ll
countr
i
es
i
s m

i
n
i
m
i
ze
d
un
d
er a
c
ompet
i
t
i
ve equ
ilib
r
i
um.
(4) The sum of surpluses of emissions tradin
g
is maximized under a competitive
e
qu
ilib
r
i
um
.

(5) The competitive equilibrium price and allocation are independent of the initial
a
mount of GHG emissions.
5
2Ex
p
erimental Business Research Vol. I
I
(
6
) The com
p
etitive e
q
uilibrium
p
rice and allocation are inde
p
endent of the dis-
tribution of the assi
g
ned amounts as lon
g
as the sum of the assi
g
ned amounts of all
c
ountr
i
es

i
s
fi
xe
d
.
One of the most controversial issues in emissions tradin
g
is the so-called “hot
ai
r.” A
l
t
h
oug
h
,
f
or examp
l
e, Russ
i
a’s ass
i
gne
d
amount
i
s 100% o
f

i
ts GHG em
i
s-
sions in 1990, it is estimated that the amount of emissions would be considerabl
y
l
ess than the assi
g
ned amount after 2008 because of economic sta
g
nation. This
i
mp
li
es t
h
at Russ
i
a cou
ld
se
ll
em
i
ss
i
ons perm
i

ts w
i
t
h
out actua
ll
y re
d
uc
i
ng
i
ts GHGs
d
omesticall
y
and that bu
y
ers of the permits could in turn increase their emissions.
T
his amount of emissions is called “hot air.” In Fi
g
ure 1,
Z
i
−
Y
i
is hot air as lon
g

as
Y
i

i
s on t
h
e
l
e
f
t-
h
an
d
s
id
e o
f
Z
i
. T
hi
s
h
ot a
i
r
i
ssue cannot

b
e so
l
ve
d

b
y us
i
ng
e
missions tradin
g
since the competitive equilibrium allocation is determined inde-
pendentl
y
of hot air as Proposition 1-(
5
) shows. In other words, the sum of emis-
s
i
ons o
f
a
ll
countr
i
es must
b
e equa

l
to t
h
e sum o
f
t
h
e ass
i
gne
d
amounts o
f
a
ll
c
ountries as lon
g
as we use emissions tradin
g
3
.
The above is a protot
y
pe of emissions tradin
g
from the viewpoint of micro
-
e
conom

i
cs. We
i
mp
li
c
i
t
l
y assume
d
t
h
at t
h
e em
i
ss
i
ons perm
i
t can
b
e treate
d
as a
private
g
ood. However,
g

reenhouse
g
ases are public
g
oods (or “bads”). Behind this
a
pproach, we further assume that we can anal
y
ze public
g
oods as private
g
oods b
y
i
ntro
d
uc
i
ng a mar
k
et
f
or em
i
ss
i
ons perm
i
ts. But t

h
e c
h
aracter
i
st
i
cs o
f
pu
bli
c goo
d
s,
i
.e., non-rivalness and non-excludabilit
y
, would not disappear with the emissions
permit market. In the case of a private
g
ood, a transaction is completed if a seller
d
e
li
vers t
h
e goo
d
to a
b

uyer an
d
t
h
e
b
uyer pays
f
or
i
t. On t
h
e ot
h
er
h
an
d
,
i
n t
h
e
c
ase of a emissions permit, a seller must reduce GHGs at least b
y
the amount sold
a
nd a bu
y

er can emit GHGs b
y
at most the amount bou
g
ht in addition to the
u
sua
l
transact
i
on o
f
a pr
i
vate goo
d
. T
h
at
i
s, GHG em
i
ss
i
ons an
d
re
d
uct
i

on must
b
e
m
onitored. It is claimed that actual monitorin
g
of GHG emissions is not an eas
y
task. Furthermore, a time la
g
exists between the actual emissions and the data
c
o
ll
ect
i
on o
f
t
h
e mon
i
tor
i
ng system even w
h
en assum
i
ng t
h

at t
h
e mon
i
tor
i
ng
i
s
p
erfect. Between these two times, the
p
rice of an emission
p
ermit will fluctuate in
the market. If monitorin
g
and its verification are considerabl
y
costl
y
, we cannot be
c
erta
i
n t
h
at t
h
e mar

k
et
f
or em
i
ss
i
ons tra
di
ng m
i
n
i
m
i
zes t
h
e tota
l
costs o
f
em
i
ss
i
ons
re
d
uct
i

on
.
I
did not describe the case when a countr
y
emits more than the assi
g
ned amount.
If
t
hi
s were t
h
e case, t
h
e v
i
o
l
at
i
on o
f
t
h
e Kyoto target wou
ld

b
ene

fi
t t
h
at country
a
n
d
, at t
h
e same t
i
me, re
d
uce t
h
e country’s po
li
t
i
ca
l
trust. T
h
at
i
s, t
h
at country
should emit as much as
p

ossible to maximize its economic benefit. In other words, th
e
ab
ove mo
d
e
l

i
mp
li
c
i
t
l
y assumes t
h
at t
h
ere ex
i
sts some pena
l
ty
f
or non-comp
li
ance.
Th
at

i
s, a
ll
countr
i
es part
i
c
i
pat
i
ng
i
n em
i
ss
i
ons tra
di
ng must agree upon a pena
l
ty
s
y
stem includin
g
the lev
y
in
g

of penalties and the form of the or
g
anization that levies
t
h
e pena
l
t
i
es. T
h
e pena
l
ty system necess
i
tates a
ddi
t
i
ona
l
costs.
We
i
mp
li
c
i
t
l

y assume
d
t
h
at eac
h
country treats pr
i
ces parametr
i
ca
ll
y. However,
i
t is expected that the quantities demanded b
y
Japan and the quantities supplied b
y
C
HOOS
IN
G
C
C
A
M
O
DE
L
OU

T
OF
M
F
ANY
MM
P
Y
OSSIBLE
A
E
L
TERNATI
V
E
S
5
3
R
ussia will be relativel
y
lar
g
e. If the
y
exercise their market power, it is possible
that the total sur
p
lus will not to be maximized. We will reconsider this
p

roblem in
S
ection
5
.
Th
e
m
ode
l
desc
ri
bed
in
t
hi
s

sect
i
o
n i
s
s
tati
c
.
Further, we assume that each
countr
y

can move on the mar
g
inal abatement cost curve freel
y
. However, it usuall
y
ta
k
es qu
i
te a
l
ong t
i
me to rep
l
ace current
f
ac
ili
t
i
es an
d
equ
i
pment. Moreover, t
he
emissions reduction investment mi
g

ht be irreversible. That is, one can move from
ri
g
ht to left on the mar
g
inal abatement cost curve, but not in the opposite direction.
Th
ere
f
ore, marg
i
na
l
a
b
atement costs m
i
g
h
t not
b
e equa
li
ze
d
.
3. A SOCIAL CHOICE APPROACH: STRATEGY-PROOFNESS
C
onsider a mechanism that determines an allocation throu
g

h
g
atherin
g
information
that each agent has. Under this mechanism, country
i
reports its own marginal
ab
atement cost curve
,

M
A
C
i
,
to an a
d
m
i
n
i
strat
i
ve
i
nst
i
tut

i
on o
f
t
h
e Un
i
te
d
Nat
i
ons
.
T
he institution recommends a com
p
etitive e
q
uilibrium allocation based u
p
on the
reported marginal abatement cost curves. Let
f
t
i
f
f
(
M
A

C
1
, ,
MAC
n
C
)
be country
i
’
s
s
ur
pl
u
s
accru
i
ng
f
rom t
h
e compet
i
t
i
ve equ
ilib
r
i

um a
ll
ocat
i
on w
h
en country
i
announces
MA
C
i
,
and le
t

f
=
(
f
1
f
f
,

,
f
n
f
f

)
, be a surplus function
.
E
ach country may not necessarily have an incentive to reveal its true margina
l
ab
atement cost curve,
b
ut t
h
e request t
h
at eac
h
country announces t
h
e true marg
i
na
l
a
batement cost curve is called strate
gy
-proofness. Le
t
M
AC
* be country
i

i
’s

t
r
ue
m
arginal abatement cost curve. Then, a surplus function,
f
=
(
f
1
f
f
, ,
f
n
f
f
)
, satisfies
strategy-proo
f
nes
s

if
,
f

or eac
h
country,
I
,

i
t sat
i
s
fi
es
(
*
)
f
i
f
f
(
M
AC
1
,

,
M
A
C
i−

1
,
M
A
C
i
*,
i
M
AC
i
+
1
,

,
MAC
n
C
)f
or a
ll
MAC
j
C
≥
f
i
f
f

(
M
A
C
1
,

,
MA
C
i
−
1
,
MA
C
i
,
MA
C
i
+
1
,

,
MAC
n
C
C

)(
j
=
1, . . .
,

n
)
.
T
hat is, strate
gy
-proofness means that announcin
g
the true mar
g
inal abatement cost
c
urve
i
s t
h
e
d
om
i
nant strategy
f
or a
ll

i
.
Strate
gy
-proofness is a stron
g
condition since it requires that revealin
g
the true
m
ar
g
inal abatement cost curve is the best strate
gy
re
g
ardless of the revelations of
t
h
e ot
h
ers. On t
h
e ot
h
er
h
an
d

,
i
t wou
ld

b
e natura
l
to cons
id
er t
h
at country i
w
ou
ld
c
han
g
e its strate
gy
dependin
g
on the strate
g
ies of the others. This is in the spirit of
the Nash equilibrium. Therefore, requirin
g
that the revelation of the true mar
g

inal
c
ost curve const
i
tutes a Nas
h
equ
ilib
r
i
um, we
h
ave
(
**
)
f
i
f
f
(
MAC
*
1
,

,
M
AC
*

i
−
1
,
M
AC
*
i
,
M
AC
*
i
+
1
,

,
M
AC
*
n
)
≥
f
i
f
f
(
MAC

*
1
,

,
M
AC
*
i
−
1
,
M
AC
i
,
M
AC
*
i
+
1
,

,
M
AC
*
n
)

f
or a
ll
M
A
C
i
f
or eac
h

i
. It
i
s c
l
ear t
h
at t
h
e reve
l
at
i
on o
f
true marg
i
na
l

cost curve
i
s a Nas
h
e
qu
ilib
r
i
um
if
t
h
e surp
l
us
f
unct
i
on sat
i
s
fi
es strategy-proo
f
ness. It may seem t
h
at
c
ondition (**) is weaker than (*), but these two conditions are in fact e

q
uivalent.
5
4Ex
p
erimental Business Research Vol. I
I
P
roposition 2 (Das
g
upta, Hammond and Maskin, 1979): A surplus function satisfies
strate
gy
-proofness if and onl
y
if the revelation of the true mar
g
inal cost curve for
e
ac
h
country,
i
,
i
s a Nas
h
equ
ilib
r

i
um.
We will show that a surplus function does not satisf
y
strate
gy
-proofness b
y
u
sin
g
Proposition 2. For this purpose, it is sufficient to show that a countr
y
could
b
ene
fi
t
b
y announc
i
ng a
f
a
l
se marg
i
na
l
a

b
atement cost curve
i
n a certa
i
n pro
fil
e
of true mar
g
inal abatement cost curves. Let the solid curves be true mar
g
inal
a
batement cost curves in Fi
g
ure 3. Assume that countr
y
2 reveals its true mar
g
inal
ab
atement cost curve an
d
country 1 announces a
f
a
l
se marg
i

na
l
a
b
atement cost
c
urve, shown as a dotted curve. Then, the com
p
etitive e
q
uilibrium
p
rice under this
co
n
d
i
t
i
o
n
beco
m
es

P
′
,
which is hi
g

her than the true competitive equilibrium price
.
D
ue to t
hi
s pr
i
ce
i
ncrease, t
h
e quant
i
ty supp
li
e
d
wou
ld

b
e
l
ess t
h
an t
h
at o
f
t

h
e true
c
ompetitive equilibrium. Therefore, this reduces the surplus of countr
y
2 b
y

α
. On
α
the other hand, countr
y
2 increases its profit b
y

β
(
β
=

(
P
′
−
P*
)
×
the quantit
y

s
upp
li
e
d
)
d
ue to pr
i
ce
i
ncrease t
h
at surpass t
h
e
l
oss. T
h
ere
f
ore, country 2 cou
ld
benefit b
y
not revealin
g
its true mar
g
inal abatement cost curve. Hence, we have the

followin
g
proposition
.
P
roposition 3: A surplus function does not satisf
y
strate
gy
-proofness.
J
o
h
ansen (1977) cr
i
t
i
c
i
ze
d
t
h
e researc
h
program t
h
at cons
id
ers resource a

ll
oca-
tion throu
g
h revelation of functions. Amon
g
other thin
g
s, he pointed out that public
g
oods have never been provided through revelation of utility functions and produc-
t
i
on
f
unct
i
ons. Rat
h
er,
h
e argue
d
t
h
at t
h
ey
h
ave

b
een prov
id
e
d
t
h
roug
h
po
li
t
i
ca
l
processes such as representative s
y
stems. Therefore, he indicated that research on
F
igure 3. A surp
l
us
f
unction is manipu
l
a
bl
e
C
ountry

1
’
s true MA
C
D
e
m
a
n
de
r’
s
S
ur
p
lu
s
1’s
S
tatu
s
Q
u
o
2’s
S
tatu
s
Q
u

o
+−
P
′
P*
C
ountry 2’s true MAC
M
A
C
1
’
s
f
ake
MA
C
Ass
i
gne
d
Amounts Em
i
ss
i
ons
Supplier’s
pl
p
pp

Surplus
u
u
l
p
α
β
C
HOOS
IN
G
C
C
A
M
O
DE
L
OU
T
OF
M
F
ANY
MM
P
Y
OSSIBLE
A
E

L
TERNATI
V
E
S
55
public
g
ood provision in democratic societies was necessar
y
. Althou
g
h he expressed
this opinion more than twent
y

y
ears a
g
o, ver
y
little pro
g
ress has been made since then
.
T
h
ere are many ways to eva
l
uate Propos

i
t
i
on 3,
b
ut we
i
nterpret t
hi
s propos
i
t
i
on
a
s sa
y
in
g
that the surplus function is manipulable even thou
g
h transmission of
m
ar
g
inal abatement cost curves can be done at a nominal cost throu
g
h technolo
g
ical

i
nno
v
at
i
on. A
ddi
t
i
ona
l
e
v
a
l
uat
i
on
f
o
ll
o
w
s
i
n t
h
e next sect
i
on

.
4
.ME
C
HANI
S
M DE
S
I
G
N APPR
O
A
CH
We cons
id
er an em
i
ss
i
ons a
ll
ocat
i
on pro
bl
em t
h
rou
gh

t
h
e reve
l
at
i
on o
f
mar
gi
na
l
a
batement cost curves assumin
g
that each countr
y
does not know the mar
g
inal
a
batement cost curves of the other countries. However, once the emissions trading
starts, eac
h
countr
y
rou
ghly

k

nows t
h
e mar
gi
na
l
a
b
atement cost curves o
f
t
h
e ot
h
er
c
ountries. As Proposition 2 indicates, there is no incentive for each countr
y
to reveal
i
ts true marginal abatement cost curve since strategy-proofness is equivalent to the
c
on
di
t
i
on
i
n w
hi

c
h
t
h
e reve
l
at
i
on o
f
true mar
gi
na
l
a
b
atement cost curves
i
s a Nas
h
eq
uilibrium. Therefore, a
p
art from the revelation of curves, which re
q
uires
q
uite a
l
ot of information, it is worthwhile to consider an allocation

p
roblem in which the
transm
i
ss
i
on o
f
pr
i
ces an
d
quant
i
t
i
es o
f
em
i
ss
i
ons perm
i
ts
i
s a
ll
owe
d

to atta
i
n t
h
e
c
ompetitive equilibrium. In what follows, we show that a two-sta
g
e mechanism
c
alled the Mitani mechanism (1998) attains the com
p
etitive e
q
uilibrium allocation
t
h
rou
gh

i
n
f
ormat
i
on transm
i
ss
i
on o

f
pr
i
ces an
d
quant
i
t
i
es.
4
Th
e
Mi
ta
ni m
ec
h
a
ni
sm
works if the number of
p
artici
p
ants is at least two. That is, the mechanism can over-
c
ome t
h
e pro

bl
em o
f
a sma
ll
num
b
er o
f
part
i
c
i
pants. As state
d

i
n Sect
i
on 2, a country
m
a
y
exercise its market power when the number of countries is small. Even under
this condition, the Mitani mechanism attains a com
p
etitive e
q
uilibrium allocation.
C

ons
id
er t
h
e M
i
tan
i
mec
h
an
i
sm w
i
t
h
two countr
i
es, 1 an
d
2. In t
h
e
fi
rst stage,
e
ach countr
y
announces a price simultaneousl
y

. The dotted ellipse in Fi
g
ure 4 shows
that countr
y
2 does not know the price announcement of countr
y
1. Countr
y
2 must
F
i
g
ure 4. The Mitani mechanis
m
1
2
1
p
1
z
S
tage
1
S
ta
g
e
2
p

2
5
6Ex
p
erimental Business Research Vol. I
I
e
valuate its transaction of emissions
p
ermits from the announced
p
rice,
p
1
, of coun-
tr
y
1, and vice versa. In the second sta
g
e, knowin
g
p
1

a
n
d
p
2
in the first sta

g
e,
c
ountry 1 announces t
h
e quant
i
ty,
z
,
o
f
em
i
ss
i
ons perm
i
ts.
We define the pa
y
off functions of countries 1 and 2 in the Mitani mechanism
.
For simplicit
y
, we suppose that countr
y
1 is a supplier of emissions permits and
c
ountry 2

i
s a
d
eman
d
er. Fo
ll
ow
i
ng Sect
i
on 2, we
d
e
fi
ne t
h
e payo
ff

f
unct
i
ons
in
c
omparison with the case when each countr
y
attains the assi
g

ned amount domesticall
y.
Let
z
b
e the quantit
y
supplied b
y
countr
y
1. Then, the cost of reducin
g
fro
m

Z
1
b
y
z
i
s
C
1
(
z
)
=
Ύ

Z
Z
1
1
−
z
MA
C
1
(
t
)
d
t
. (4)
S
i
nc
e
Z
1

i
s t
h
e ass
i
gne
d
amount o

f
country 1, t
h
e cost
f
or country 1
i
s a
f
unct
i
on
of
z
.
On t
h
e ot
h
er
h
an
d
, s
i
nce t
h
e quant
i
t

y
supp
li
e
d
t
h
at
i
s
d
eterm
i
ne
d

by
countr
y
1
becomes the quantity demanded by country 2 in the Mitani mechanism, the gross
payo
ff
o
f
country 2
i
s
C
2

C
C
(
z
)
=
Ύ
Z
Z
2
2
+
z
MAC
2
C
C
(
x
)
dx
.
(
5)
Followin
g
the above, the pa
y
off function,
g

i
, becomes
g
1
(
z
,

p
1
,
p
2
)
=
−
C
1
(
z
)
+
p
2
z
−
k
(
p
1

−
p
2
)
2
where
k
>
0
(
6
)
g
2
(
z
,
p
1
)
=
C
2
C
C
(
z
)
−
p

1
z
C
ountr
y
1 sells its excess reduction,
z
,
be
y
ond its assi
g
ned amount to countr
y
2. Th
e
pr
i
ce o
f
t
hi
s transact
i
on
i
s t
h
e pr
i

ce t
h
at
i
s announce
d

b
y country 2
i
n stage 1.
T
he revenue from this transaction is p
2
z, and the last term,
k
(
p
1
−
p
2
)
2
,
in
g
1
i
s

a
penalt
y
term to make countr
y
1 announce the same price announced b
y
countr
y
2.
C
ountry 2
b
uys
z
wi
t
h
p
1
announce
d

b
y country 1.
C
ons
id
er now

h
ow t
h
e M
i
tan
i
mec
h
an
i
sm wor
k
s. F
i
rst
,
cons
id
er t
h
e secon
d
sta
g
e. Countr
y
1 determines
z
to maximize the pa

y
off. Therefore, differentiatin
g
g
1
w
i
t
h
respect to
z
an
d
equat
i
ng t
h
e resu
l
t to zero, we
h
ave
p
2
=
C
′
1
(
z

)
. T
h
at
i
s,
z
i
s
d
eterm
i
ne
d

d
epen
di
ng on
p
2
,
w
hi
c
h

i
s
d

eterm
i
ne
d

i
n t
h
e
fi
rst stage. T
h
ere
f
ore, we
c
an re
g
ard
z
as

a
f
u
n
ct
i
o
n

of
p
2
.
That is,
z
=
z
(
p
2
). B
y
substitutin
g
this expressio
n
wi
t
h
p
2
=
C
′
1
(
z
) an
d

diff
erent
i
at
i
ng w
i
t
h
respect to
p
2
,
we
h
ave
z
′
(
p
2
)
=
1
/
C
1
″
. As

l
ong
as
C
1
″
≠

0,

z
′
(
p
2
)

i
s not zero.
C
onsider now how countr
y
1 behaves. Countr
y
1 determines p
1

to
m
a

ximiz
e

t
h
e
payo
ff
. T
h
at
i
s,
b
y
diff
erent
i
at
i
ng
g
1
w
i
t
h
respect to
p
1

,
we
h
ave
p
1
=
p
2
.
O
n t
h
e ot
h
er
h
an
d
, country 2 c
h
ooses
p
2
to max
i
m
i
ze t
h

e payo
ff
ta
ki
ng
i
nto account t
h
e
b
e
h
av
i
or
,
z
(
p
2
)
, of countr
y
1. That is, b
y
substitutin
g

z
(

p
2
)
into g
2
and differentiatin
g
with
C
HOOS
IN
G
C
C
A
M
O
DE
L
OU
T
OF
M
F
ANY
MM
P
Y
OSSIBLE
A

E
L
TERNATI
V
E
S
57
res
p
ec
t

t
o
p
2
,
we have
C
′
2

·

z
′
(
p
2
)

−
p
1
z
′
(
p
2
)
=
z
′
(
p
2
)(
C
′
2
−
p
1
)
=
0. Since
z
′
(
p
2

)
is not
z
ero, we have
p
1
=
C
′
2
(
z
)
.
T
h
ere
f
ore
,
we
h
ave
p
1
=
p
2
=
C

′
1
(
z
)
=
C
′
2
(
z
)
. From
(
4
)
, we
h
ave
C
′
1
(
z
)
=
MA
C
1
(

Z
1
−
z
)
and, from (
5
), we have
C
′
2
(
z
)
=
MAC
2
CC
(
Z
2
+
z). That is, we have
p
1
=
p
2
=
M

AC
1
(
Z
1
−

z
)
=
M
AC
′
2
(
Z
2
+
z
)
. This is exactl
y
the same expression as Proposition
1-(1). T
hi
s proves t
h
at t
h
e M

i
tan
i
mec
h
an
i
sm ac
hi
eves t
h
e compet
i
t
i
ve equ
ilib
r
i
um
a
llocation in sub
g
ame perfect equilibrium.
The Mitani mechanism consists of a pa
y
off function and a
g
ame tree as depicted
i

n F
i
gure 4. I
f
marg
i
na
l
a
b
atement cost curves,
M
AC
1
an
d

MAC
2
C
C
, are g
i
ven, we
h
ave a sub
g
ame perfect equilibrium (
p
1

,
p
2
,
z
)
. The sub
g
ame perfect equilibrium
o
f the Mitani mechanism is uni
q
ue. Let the set be
N
sp
(
M
AC
1
,
MAC
2
C
C
)
. We writ
e
g
·
N

sp
(
MA
C
1
,
MAC
2
C
C
) as t
h
e eva
l
uat
i
on o
f
t
h
e set
b
y
g
.
T
h
en
,
we

h
ave
f
(
M
AC
1
,
MAC
2
C
C
)
=
g
·
N
s
p
(
M
AC
1
,
MAC
2
C
C
)
.

(
7
)
T
hat is, the payoff function coincides with the surplus function under the Mitani
m
ec
h
an
i
sm. In ot
h
er wor
d
s, t
h
e M
i
tan
i
mec
h
an
i
sm
i
mp
l
ements t
h

e surp
l
us
f
unct
i
on,
f
,
f
f
i
n sub
g
ame perfect equilibrium if (7) holds for an
y

(
MA
C
1
,
MAC
2
C
C
).
L
et us find the set of Nash e
q

uilibria of the Mitani mechanism. Since the strat-
egi
c var
i
a
bl
es o
f
countr
y
1 are
p
1
,
z,
by

diff
erent
i
at
i
n
g

g
1
w
i
t

h
respect to
p
1
an
d
z
,
we have
∂
∂
∂
∂
gzp p
∂
p
∂
kp p
g
∂
z
∂
p
2
zp p
zp
1
2
p
2

p
∂
g
( , , )
zp p
2
zp p
zp

p
),
2
p
20
k
0
0
kp
2
p
(, , )
zp p
2
zp pzp
2
zp pzp
() .
C
2
zp

z
0
C
2
zp
z
C
gpp
2
pp
p

20
0
kp p
2
p
2
pp
p
Cz p
z
2
zp
z
′
O
n t
h
e ot

h
er
h
an
d
, a
l
t
h
oug
h
t
h
e strateg
i
c var
i
a
bl
e o
f
country 2
i
s
p
2
,
t
hi
s var

i
a
bl
e
d
oes not affect the pa
y
off of countr
y
1. That is, the pa
y
off of countr
y
2 does not
d
e
p
end on the announcement o
f
p
2
. Therefore, an
y
triple
(
p
1
,
p
2

,
z
) satisf
y
in
g
p
1
=
p
2
=
C
′
1
(
z
)

i
s
a
N
as
h
equ
ilib
r
i
um o

f
t
h
e M
i
tan
i
mec
h
an
i
sm. By requ
i
r
i
ng
C
′
1
(
z
)
=
C
′
2
(
z
)
i

n addition to the condition, we obtain a sub
g
ame perfect equilibrium. That is, the set
of sub
g
ame perfect equilibria is a proper subset of the set of the Nash equilibria.
Th
ere
f
ore, t
h
e M
i
tan
i
mec
h
an
i
sm cannot
i
mp
l
ement t
h
e surp
l
us
f
unct

i
on un
d
er a
Nas
h
equ
ilib
r
i
um
.
We implicitl
y
assume that there must exist a central bod
y
that determines who
t
h
e part
i
c
i
pants
i
n t
h
e mec
h
an

i
sm are, co
ll
ects
i
n
f
ormat
i
on, an
d
con
d
ucts resource
all
ocat
i
on
b
ase
d
upon t
h
e
i
n
f
ormat
i
on t

h
at t
h
e mec
h
an
i
sm requ
i
res. In part
i
cu
l
ar,
participants must be all countries in the case of
g
lobal warmin
g
, but some countr
y
m
ay not want to part
i
c
i
pate
i
n an
d

b
ene
fi
t
f
rom t
h
e re
d
uct
i
on o
f
green
h
ouse gases
b
y
ot
h
er countr
i
es.
5
As
f
or t
h
e co
ll

ect
i
on o
f

i
n
f
ormat
i
on, a part
i
c
i
pant may not transm
i
t
the information required b
y
the mechanism to the bod
y
even thou
g
h the part-
i
c
i
pant agrees to part
i
c

i
pate
i
n t
h
e mec
h
an
i
sm. W
h
en part
i
c
i
pants announce t
h
e
i
r
w
illi
ngness to part
i
c
i
pate
i
n t
h

e mec
h
an
i
sm, t
h
e centra
l

b
o
d
y must
h
ave some power
to collect information about the strate
g
ies of the participants under the framework of
5
8Ex
p
erimental Business Research Vol. I
I
social choice or the mechanism desi
g
n approach. These two approaches implicitl
y
a
ssume that there exists a bod
y

with central power.
6
We consider the validit
y
of the
M
i
tan
i
mec
h
an
i
sm
i
n t
h
e
f
o
ll
ow
i
ng sect
i
on.
5
. AN EXPERIMENTAL APPR
O
A

C
H
Even thou
g
h we have succeeded in constructin
g
a theoretical mechanism, we are not
c
ertain that it works. Usin
g
it in the real world would be risk
y
since the economic
d
amage
f
rom a poss
ibl
e
f
a
il
ure wou
ld

b
e un
b
eara
bl

e. Furt
h
ermore, we wou
ld
not
b
e
a
ble to determine whether the failure of the mechanism is due to some flaw in the
m
echanism or some other outside factors. An alternative wa
y
to assess the perform-
a
nce o
f
t
h
e mec
h
an
i
sm
i
s a
l
a
b
oratory exper
i

ment. We construct an exper
i
menta
l
m
odel out of the theoretical model. Usuall
y
, theor
y
does not indicate the number of
ag
ents in the model, the exact shape of the functions used in the model, and what
types o
f

i
n
f
ormat
i
on eac
h
agent
h
as. In an exper
i
menta
l
mo
d

e
l
, t
h
ese var
i
a
bl
es must
be specified. Dependin
g
on how we assi
g
n these parameters, we have man
y
possible
c
ases. Our methodolo
gy
calls for recruitin
g
sub
j
ects and pa
y
in
g
them contin
g
ent

u
pon t
h
e
i
r per
f
ormance. By con
d
uct
i
ng severa
l
exper
i
ments an
d
t
h
en compar
i
ng t
h
e
results, we can understand the effects of these
p
arameters.
We utilize two experiments conducted b
y
Hizen and Sai

j
o (2001) and Hizen,
K
usa
k
awa, N
ii
zawa, an
d
Sa
ij
o (2000), w
h
ose mo
d
e
l
s o
f
t
h
e exper
i
ments are
b
ase
d
up
on the microeconomic a
pp

roach in Section 2. Section
6
describes an ex
p
eriment
that Mitani, Sai
j
o, and Hama
g
uchi (1998) desi
g
ned to assess the performance of the
M
i
tan
i
mec
h
an
i
sm
.
The main question of the experiments b
y
Hizen and Sai
j
o (2001) and Hizen,
K
usakawa, Niizawa, and Sai
j

o (2000) is whether the total surplus is maximized
u
n
d
er em
i
ss
i
ons tra
di
ng. T
h
e em
i
ss
i
ons tra
di
ng mo
d
e
l

i
n Sect
i
on 2
i
mp
li

c
i
t
l
y
a
ssumes that transactions are conducted under a com
p
etitive e
q
uilibrium, but the
surplus of each countr
y
can be different from the surplus at the competitive equilib-
r
i
um
d
epen
di
ng on t
h
e met
h
o
d
s o
f
transact
i

on. In or
d
er to avo
id
pro
bl
ems
d
ue to
n
on-compliance to the assi
g
ned amounts, Hizen and Sai
j
o (2001) desi
g
ned their
e
xperiment so that the assi
g
ned amounts are alwa
y
s satisfied in the course of
transact
i
ons an
d
compare
d
two tra

di
ng
i
nst
i
tut
i
ons, name
l
y, t
h
e
d
ou
bl
e auct
i
on an
d
bil
atera
l
tra
di
ng. On t
h
e ot
h
er
h

an
d
, H
i
zen, Kusa
k
awa, N
ii
zawa, an
d
Sa
ij
o (2000)
e
xplicitl
y
incorporated non-compliance and decision makin
g
on domestic reductions
i
nto t
h
e
i
r exper
i
ment.
Pr
i
or to H

i
zen an
d
Sa
ij
o (2001) an
d
H
i
zen, Kusa
k
awa, N
ii
zawa, an
d
Sa
ij
o (2000)
,
B
ohm (1997) conducted an important emissions tradin
g
experiment. He recruited
b
ureaucrats
f
rom t
h
e M
i

n
i
stry o
f
Energy an
d
spec
i
a
li
sts
f
rom F
i
n
l
an
d
, Denmar
k
,
Norway, an
d
Swe
d
en, an
d
t
h
en con

d
ucte
d
an em
i
ss
i
ons tra
di
ng exper
i
ment
i
n w
hi
c
h
e
ach countr
y
could bu
y

a
n
d
sell emissions permits under bilateral trading. The
d
su
bj

ects
k
new t
h
e marg
i
na
l
a
b
atement cost curves o
f
ot
h
er countr
i
es,
b
ut not t
h
e true
c
urves. It too
k

f
our
d
ays to comp
l

ete a s
i
ng
l
e per
i
o
d

b
y us
i
ng
f
acs
i
m
il
e commun-
i
cation to exchan
g
e information on prices and quantities. The avera
g
e transaction
C
HOOS
IN
G
C

C
A
M
O
DE
L
OU
T
OF
M
F
ANY
MM
P
Y
OSSIBLE
A
E
L
TERNATI
V
E
S
59
price was very close to the competitive equilibrium price and the efficiency was
97%, w
hi
c
h

i
s qu
i
te
hi
g
h
. Many econom
i
sts
h
ave expresse
d
t
h
e op
i
n
i
on t
h
at
i
t
i
s
d
ifficult to attain efficienc
y
if a tradin

g
a
g
ent is a countr
y
as a unit, but Bohm has
shown that it is possible to attain high efficiency when countries are the players.
I
start w
i
t
h
an overv
i
ew o
f
t
h
e common
f
eatures o
f
t
h
e exper
i
ments o
f
H
i

zen an
d
Sai
j
o (2001) and Hizen, Kusakawa, Niizawa, and Sai
j
o (2000). Six sub
j
ects part-
i
cipated in a session. The subjects were supposed to represent Russia, Ukraine, the
US., Po
l
an
d
, t
h
e EU, an
d
Japan. In t
h
e exper
i
ments, no country names were g
i
ven
to sub
j
ects. Sub
j

ects must have assumed that the
y
were en
g
a
g
ed in transactions of an
a
bstract commodity. Figure
5
shows the marginal abatement cost curves used in the
e
xper
i
ments. T
h
e or
igi
n
i
s t
h
e ass
ig
ne
d
amount
f
or eac
h

countr
y
. In t
h
e exper
i
ments
o
n information disclosure on the mar
g
inal abatement cost curves, ever
y
sub
j
ect had
Figure
5
at hand. On the other hand, in the experiments on information concealment,
e
ac
h
su
bj
ect on
ly

k
new
hi
s/

h
er mar
gi
na
l
a
b
atement cost curve.
Two tradin
g
methods were used in the experiments. The first one was bilateral
trading. Two out of six subjects made a pair and then negotiated the price and
quant
i
t
y
o
f
t
h
e em
i
ss
i
ons perm
i
ts. T
h
e max
i

mum num
b
er o
f
pa
i
rs was t
h
ree
b
ecause
o
f the limit of six sub
j
ects. Durin
g
the ne
g
otiation, sub
j
ects were not allowed voice
c
ommunication, but communicated by means of writing the numerical values of
pr
i
ce an
d
quant
i
t

y
. Wr
i
tten responses o
f
“
y
es” an
d
“no” were a
ll
owe
d
. Once a pa
i
r
reached an a
g
reement, the pair was supposed to inform the experimenter. In the case
o
f disclosure of information of the contract, the ex
p
erimenter wrote the information
o
n t
h
e
bl
ac
kb

oar
d
an
d
announce
d

i
t to ever
y
su
bj
ect. T
h
e pa
i
r a
g
a
i
n returne
d
to t
h
e
floor to seek other contracts. This
p
rocedure lasted u
p
to 60 minutes.

1
-Russia 2-Ukraine 3-U
S
A 4-Poland 5-EU 6-Japa
n
215
165
120
90
60
40
20
(-80)
(-73)
(-65)
(-55)
(-32)
(33)
216
166
118
70
40
20
(-50)
(-40)
(-30)
(-20)
(-10)
200

162
142
122
100
(-45)
(-35)
(-20)
(23)
(50)
240
240
180
120
80
60
30
(-27)
(-22)
(-17)
(-10)
(10)
250
170
130
90
(-15)
(-10)
(10)
(20)
210

2
50
220
1
9
0
150
118
88
(
-5)
(5)
)
)
(1
5
)
(25)
)
(35)
250
200
1
50
100
50
-
80
-
7

0
-60
-5
0
-4
0
-
30
-
2
0
-10 0
10
1
5
20
30
4
5
50
60
1
2
3
4
5
6
(-5)
(25)
(40

)
(55)
F
igure 5. Margina
l
A
b
atement Cost Curves use
d

b
y Hizen an
d
Saijo an
d
Hizen, Kusa
k
awa
,
N
iizawa, an
d
Saij
o
6
0Ex
p
erimental Business Research Vol. I
I
Table 1. An Example o

f
the Double Auctio
n
Buyers’ Bi
d
sSe
ll
ers’ As
ks
(3)
$
56, 20 units (6)
$
104, 15 unit
s
(1)
$
86, 13 units (4)
$
92, 20 unit
s
(2) gra
b
s (4
)
′
as
k
The second method was a double auction. Six sub
j

ects were placed to
g
ether.
Subjects who wanted to sell announced the price and quantity, and subjects who
wante
d
to
b
uy ma
d
e s
i
m
il
ar announcements. Ta
bl
e 1 s
h
ows an examp
l
e o
f
t
h
e
a
uction. A sub
j
ect who wanted to announce price and quantit
y

raised his/her hand.
T
he experimenter called on the subject (subject 3 in the example since he/she was
t
h
e
fi
rst person to ra
i
se
hi
s/
h
er
h
an
d
). T
h
e su
bj
ect t
h
en ca
ll
e
d
out t
h
at

h
e/s
h
e wants
to bu
y
20 units at $56 for each unit, and the experimenter wrote the information on
the blackboard. Right after this announcement, another subject (subject 6 in the
e
xample) announced his/her willingness to sell 15 units at
$
104 for each unit. Since
the spread of the price difference was quite hi
g
h, sub
j
ect 1 announced his/her will-
i
ngness to buy 13 units at
$
86. Then, subject 4 announced his willingness to sell
20 units at
$
92. Right after this announcement, subject 2 accepted the offer from
sub
j
ect 4. The maximum number of units was 20. This process then continued. An
i
mportant feature of the double auction is that each subject receives the information
o

f
t
h
e announcements s
i
mu
l
taneous
l
y. In contrast,
i
n t
h
e case o
f

bil
atera
l
tra
di
ng
onl
y
a pair knows the information as lon
g
as the experimenter does not reveal it.
N
ext, we consider the Hizen and Saijo’s (2001) experiment. In order to avoid the
n

on-comp
li
ance pro
bl
em, t
h
e start
i
ng po
i
nt o
f
t
h
e transact
i
on
f
or eac
h
su
bj
ect was
the assi
g
ned amount (see squares at the vertical axis
g
oin
g
throu

g
h the ori
g
in in
Figure 6). When this is the case, the target of the Kyoto Protocol is automatically
satisfied at any point in the transaction. As Propositions 1-(5) and 1-(6) show, the
c
ompetitive equilibrium in Fi
g
ure 2 coincides with the one in Fi
g
ure 6. The squares
i
n Figure 6 show the initial points of transactions. Furthermore, Hizen and Saijo
a
ssume
d
t
h
at su
bj
ects can move on t
h
e marg
i
na
l
cost curves
f
ree

l
y
i
n or
d
er to
a
void investment irreversibilit
y
in which a sub
j
ect cannot
g
o back to the left once
h
e/she decides to choose a
p
oint on the curve.
Su
bj
ects were pa
id

i
n proport
i
on to t
h
e
i

r per
f
ormance
i
n t
h
e exper
i
ment. In
the Hizen and Sai
j
o’s (2001) experiment, sub
j
ects were instructed about how the
y
c
ould obtain monetary reward by showing them a sample graph such as Figure 7.
T
he point of departure was the assigned amount in Figure
6
that corresponded to
“y
our position” in Fi
g
ure 7. Consider, as an example, the upper central
g
raph in
Figure 6. The horizontal line shows the price line. Since the marginal abatement cost
i
s

hi
g
h
er t
h
an t
h
e em
i
ss
i
ons perm
i
t pr
i
ce, t
h
e su
bj
ect can
b
ene
fi
t
b
y
b
uy
i
ng a perm

i
t.
I
f he/she succeeds in bu
y
in
g
the permit up to the intersection point between the


C
HOOS
IN
G
C
C
A
M
O
DE
L
OU
T
OF
M
F
ANY
MM
P
Y

OSSIBLE
A
E
L
TERNATI
V
E
S
61
A
ss
i
gne
d
A
mount
s
M
AC
C
ountr
y
B
’
s
M
A
C
Demander’
s

S
urp
l
us
S
u
pp
lier’s
Sur
p
lu
s
A’s Status Quo
B
’s Status
Q
uo
A
mount o
f
E
missions
+
−
P*
P
*
:
com
p

etitive e
q
uilibrium
p
ric
e
C
ountry A
’
s
M
A
C
F
igure
6
. Initial Points of Transactions and Emissions Trading in Hizen an
d
S
aijo’s Experiment
P
ri
ce
P
r
i
c
e
Pr
i

cePr
i
ce
P
r
i
c
e
P
r
i
ce
You
r P
os
i
t
i
on
N
o Transact
i
o
n
Y
ou
r P
os
i
t

i
on
Your Pos
i
t
i
o
n
N
o Transactio
n
You
r P
os
i
t
i
o
n
Your Pos
i
t
i
on
Y
our Pos
i
t
i
on

B
B
B
A
A
A
Pa
y
in
g
Price
P
ay
i
ng Pr
i
c
e
Bu
y
in
g
Pric
e
B
uy
i
ng Pr
i
ce

B
ene
fit
B
ene
fit
Profit
Pro
fit
B
u
y!
Buy!
S
ell!
S
ell
!
F
igure 7. Benefits and Profits of Subject
s
6
2Ex
p
erimental Business Research Vol. I
I
T
able 2. Controls in Hizen and Sai
j
o’s Experimen

t
M
ar
g
inal Abatement Cos
t
C
ur
v
e Information
Disclosure
(
O
)
Closure
(
X
)
D
i
sc
l
osu
r
e
B
il
a
t
e

r
a
l
C
ontract
(
O
)
OO O
X
T
radin
g
I
nf
o
rm
at
i
o
n
C
l
osure
(
X
)
XO
XX
D

i
sc
l
osure (O) C
l
osure (X
)
Doub
l
e
A
uc
ti
o
n
O
X
m
ar
g
inal cost curve and the price line, he/she could obtain the benefit correspondin
g
t
o
t
h
e
b
ene
fi

t area
i
n F
i
gure 7. A
f
ter t
h
e transact
i
on, t
h
e pos
i
t
i
on o
f
t
h
e su
bj
ect moves.
A new transact
i
on starts
f
rom t
hi
s new pos

i
t
i
on. F
ig
ure 7 s
h
ows a
ll
t
h
e poss
ibl
e cases
.
C
onsider next the controls in Hizen and Sai
j
o’s experiment. In the bilateral
tra
di
ng sett
i
ng, two contro
l
s were use
d
. T
h
e

fi
rst was t
h
e marg
i
na
l
cost curve
i
n
f
orma
-
t
i
on
d
epen
di
n
g
on
if
t
h
e su
bj
ects
k
new a

ll
t
h
e mar
gi
na
l
cost curves. T
h
e secon
d
was the contract information depending on the concealment or disclosure of the
c
ontracte
d
pr
i
ce. A
l
t
h
oug
h
t
h
e assumpt
i
on t
h
at eac

h
country
k
nows a
ll
t
h
e marg
i
na
l
ab
atement cost curves
i
s unrea
li
st
i
c, we emp
l
o
y
e
d

i
t
b
ecause Bo
h

m (1997) o
b
serve
d
h
igh efficiency under the condition that every country knows the curves fairly well.
B
y compar
i
ng t
h
e resu
l
ts w
i
t
h

f
u
ll

i
n
f
ormat
i
on o
f
marg

i
na
l
a
b
atement cost curves
to t
h
e ones w
i
t
h
on
ly
pr
i
vate mar
gi
na
l
a
b
atement cost
i
n
f
ormat
i
on, we can measure
the effect of the information disclosure. In the case of the double auction, only

t
h
e marg
i
na
l
a
b
atement cost
i
n
f
ormat
i
on contro
l

i
s emp
l
oye
d
s
i
nce t
h
e contract
i
n
f

ormat
i
on
i
s ava
il
a
bl
e to ever
y
countr
y
. For eac
h
ce
ll

i
n Ta
bl
e 2, at
l
east two
sessions were conducted with different sets of subjects.
C
ons
id
er H
i
zen an

d
Sa
ij
o’s (2001) exper
i
menta
l
resu
l
ts
f
rom t
h
e v
i
ewpo
i
nt o
f
effi
c
i
enc
y
. As Propos
i
t
i
on 1-(4) s
h

ows, t
h
e tota
l
surp
l
us
i
s max
i
m
i
ze
d
at t
h
e com-
petitive equilibrium. That is, the total surplus accruing from any trading rule cannot
e
xcee
d
t
h
e tota
l
surp
l
us o
f
t

h
e compet
i
t
i
ve equ
ilib
r
i
um. T
h
ere
f
ore,
d
e
fi
ne a measure
o
f
e
ffi
c
i
enc
y
as
f
o
ll

ows:
The sum of the surplus of all subjects
The total surplus of the competitive equilibrium
sum of the surplus of all
total su plus of the competitive
T
herefore, the maximum efficienc
y
is one or 100%. In the Hizen and Sai
j
o’s (2001)
e
x
p
eriment, the com
p
etitive e
q
uilibrium
p
rice is between 118 and 120. Therefore,
C
HOOS
IN
G
C
C
A
M
O

DE
L
OU
T
OF
M
F
ANY
MM
P
Y
OSSIBLE
A
E
L
TERNATI
V
E
S
6
3
we ta
k
e t
h
e average 119 as t
h
e compet
i
t

i
ve equ
ilib
r
i
um pr
i
ce. W
h
en t
h
e transact
i
on
i
s conducted under this price, the total sum of the surplus is
6
990. The first row in
T
able 3 shows the tradin
g
rule, and the second shows the names of the sessions.
For examp
l
e, “OX2” un
d
er
bil
atera
l

tra
di
ng
i
n
di
cates t
h
e
di
sc
l
osure o
f
contract
pr
i
ces, t
h
e c
l
osure o
f
marg
i
na
l
cost curve
i
n

f
ormat
i
on, an
d
t
h
e secon
d
sess
i
on o
f
t
hi
s
c
ondition. That is, “O” indicates “disclosure” and “X” indicates “concealment.” The
fi
rst
di
g
i
t
i
n
di
cates t
h
e contract

i
n
f
ormat
i
on; t
h
e secon
d
one
i
n
di
cates t
h
e marg
i
na
l
c
ost curve
i
n
f
ormat
i
on; an
d
t
h

e
l
ast
di
g
i
t
i
n
di
cates t
h
e sess
i
on num
b
er. S
i
nce t
h
e
c
ontract information is disclosed in the double auction, “X1” indicates the concealmen
t
of
t
h
e marg
i
na

l
cost curve
i
n
f
ormat
i
on an
d
t
h
e
fi
rst sess
i
on o
f
t
hi
s contro
l
. T
h
e
n
um
b
er
i
n t

h
e
l
e
f
tmost co
l
umn
i
n
di
cates t
h
e su
bj
ect num
b
er; t
h
e num
b
er
i
n paren-
theses indicates the surplus obtained b
y
the sub
j
ect at the competitive equilibrium.
I

n eac
h
ce
ll
, t
h
e upper num
b
er
i
s t
h
e surp
l
us t
h
at t
h
e su
bj
ect actua
ll
y o
b
ta
i
ne
d

in

t
h
e exper
i
ment, w
hil
e t
h
e
l
ower num
b
er
i
s t
h
e
i
n
di
v
id
ua
l
e
ffi
c
i
ency. For examp
l

e,
the individual efficienc
y
of sub
j
ect 1 is 0.732, which is obtained b
y
the ratio of the
surplus at the competitive equilibrium (2555) to the actual surplus (1870). The
i
n
di
v
id
ua
l
e
ffi
c
i
ency
i
s
diff
erent
f
rom t
h
e sess
i

on e
ffi
c
i
ency.
The former ma
y
exceed one since the distribution of total surplus depends on
h
ow t
h
e transact
i
ons are carr
i
e
d
out a
l
t
h
oug
h
t
h
e tota
l
sum o
f
t

h
e surp
l
us cannot
e
xceed
6
990. Some subjects might have low efficiency since they sell their emission
s
permits for less than the competitive price. On the other hand, some mi
g
ht attain
hi
g
h
e
ffi
c
i
ency
b
y
b
uy
i
ng perm
i
ts at
l
ow pr

i
ces. In t
h
e exper
i
ment, t
h
e max
i
mum
m
onetary reward was 7600 yen, the minimum 2000 yen, and the average 3459 yen.
As Table 3 shows, the efficienc
y
of each session was quite hi
g
h except for the
“
XO1” session. Subject 5 in this session traded even though he/she suffered consid-
e
ra
bl
e
l
osses. On t
h
e ot
h
er
h

an
d
,
i
n
di
v
id
ua
l
e
ffi
c
i
enc
i
es var
i
e
d
even
i
n su
bj
ects w
h
o
h
ad the same i.d. number. In bilateral tradin
g

, Russia’s efficiencies were lower than
t
h
ose o
f
t
h
e compet
i
t
i
ve equ
ilib
r
i
um, an
d
Po
l
an
d
’s e
ffi
c
i
enc
i
es were
hi
g

h
er t
h
an
t
h
ose o
f
t
h
e compet
i
t
i
ve equ
ilib
r
i
um. We cannot say t
h
at t
h
e e
ffi
c
i
enc
i
es o
f

t
h
e ot
h
er
c
ountries were statisticall
y
different from one another. On the other hand, under the
d
ou
bl
e auct
i
on, t
h
e e
ffi
c
i
enc
i
es o
f
t
h
e US were
hi
g
h

er t
h
an t
h
ose o
f
t
h
e compet
i
t
i
ve
e
qu
ilib
r
i
um, Po
l
an
d
’ e
ffi
c
i
enc
i
es were
hi

g
h
er t
h
an t
h
ose o
f
t
h
e compet
i
t
i
ve equ
ilib
-
rium, and the efficiencies of the others were statisticall
y
close to one.
C
ons
id
er now t
h
e e
ffi
c
i
ency

d
ynam
i
cs over t
i
me. Un
d
er
bil
atera
l
tra
di
ng, t
h
e
effi
c
i
enc
i
es o
f
a
ll
sess
i
ons, except
f
or sess

i
on XX2, excee
d
e
d
80%, an
d
t
h
e e
ffi
c
i
-
e
ncies immediatel
y
after 2
5
minutes exceeded 90% in six out of ei
g
ht sessions. The
effi
c
i
enc
i
es
i
ncrease

d
monoton
i
ca
ll
y,
b
ut t
h
e e
ffi
c
i
ency o
f
sess
i
on OX2
fl
uctuate
d
s
i
nce one su
bj
ect
b
oug
h
t perm

i
ts at a
l
oss an
d
t
h
en so
ld
some o
f
t
h
em at a re
l
at
i
ve
l
y
h
i
g
h price. Under the double auction, the efficiencies of all sessions, except for
sess
i
on X2, excee
d
e
d

70%
i
mme
di
ate
l
y a
f
ter 17 m
i
nutes an
d
excee
d
e
d
90% a
f
ter
44 m
i
nutes. T
h
ey
i
ncrease
d
monoton
i
ca

ll
y,
b
ut we o
b
serve
d
a
d
ecrease
i
n t
h
e X
sessions after achievin
g
100%. For example, in session X2, one sub
j
ect sold permits
a
t a
l
oss w
hil
e expect
i
ng to
b
uy t
h

em at a re
l
at
i
ve
l
y
l
ow pr
i
ce,
b
ut cou
ld
not. Suc
h
l
osses were not o
b
serve
d
w
h
en t
h
e marg
i
na
l
cost curve

i
n
f
ormat
i
on was
di
sc
l
ose
d
.
T
hese results led to the followin
g
observation:
6
4Ex
p
erimental Business Research Vol. I
I
Table 3. E
ffi
ciencies in Hizen and –Sai
j
o’s experimen
t
Bilateral Trading Double Auction
Subject No. OO1 OO2 OX1 OX2 XO1 XO2 XX1 XX2 O1 O2 O3 X1 X2
1 (2555) 1420 1870 960 1710 1510 1100 1460 1600 2410 2410 1981 2260 2865

(Russia) 0.556 0.732 0.376 0.669 0.591 0.431 0.571 0.626 0.943 0.943 0.775 0.885 1.121
2 (1290) 1140 914 360 1665 1320 940 1536 2370 1320 1320 520 1770 1120
(Ukraine) 0.884 0.709 0.279 1.291 1.023 0.729 1.191 1.837 1.023 1.023 0.403 1.372 0.868
3 (610) 685 683 2060 372 1846 615 583 550 850 865 1144 681 1270
(U.S.A.) 1.123 1.120 3.377 0.610 3.026 1.008 0.956 0.902 1.393 1.418 1.875 1.116 2.082
4 (390) 520 570 850 530 500 555 910 500 200 350 230 209 355
(Poland) 1.333 1.462 2.179 1.359 1.282 1.423 2.333 1.282 0.513 0.897 0.590 0.536 0.910
5 (620) 800 1105 1300 755
−
1
5
0 1080 81 1
5
07
5
0
5
00 1380 700
0
(EU) 1.290 1.782 2.097 1.218
−
0
.242 1.742 0.131 0.242 1.210 0.80
6
2.22
6
1.129 0.000
6 (1525) 2425 1800 1450 1844 1400 2700 2390 1800 1430 1515 1695 1350 1360
(Japan) 1.590 1.180 0.951 1.209 0.918 1.770 1.567 1.180 0.938 0.993 1.111 0.885 0.892
S

um 6990 6942 6980 6876 6426 6990 6960 6970 6960 6960 69
5
0 6970 697
0
(
6
990) 1 0.993 0.999 0.984 0.919 1 0.99
6
0.997 0.99
6
0.99
6
0.994 0.997 0.99
7