Modern Economy, 2013, 4, 696-705
Published Online November 2013 (http://www.scirp.org/journal/me)
http://dx.doi.org/10.4236/me.2013.411075
Open Access ME
Further Thoughts on Strategic Trade Policy under
Asymmetric Information
Chung Yuan Fu*, Shirley J. Ho
Department of Economics National Chengchi University, Taiwan
Received July 3, 2013; revised August 1, 2013; accepted August 9, 2013
Copyright © 2013 Chung Yuan Fu, Shirley J. Ho. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
We study the informational impacts of multilateral voluntary export restraints (henceforth VERs) in an international
trade model with differentiated products [1]. We first show that with competing mechanisms, the two firms’ lying in-
tentions are strategic complements and will increase with the degree of product differentiation. Next, we show that each
government will design their VERs menus to allow for only partial revelation. Contrary to the single intervention case
[2], a separating equilibrium where each country’s domestic firm truthfully reveals its private information does not exist
under multilateral policy interventions. Finally, we demonstrate that trade retaliation, when the two governments’ VERs
are positively related, will happen when the government believes that its domestic firm is more likely to be inefficient.
Keywords: Strategic Trade Policy; Voluntary Export Restraints; Partial Information Revelation
1. Introduction
It is now well known that government intervention can
shift rents by providing a strategic advantage to the do-
mestic firm. In particular, the pioneering work by Bran-
der and Spencer [3] showed that under Cournot competi-
tion, an export subsidy enables the domestic firm to be a
Stackelberg leader, and thus it increases the domestic
welfare at the expense of the foreign firm. Subsequently,
Eaton and Grossman [4] demonstrated that the optimal
policy will be an export tax, when the domestic firm
competes with a foreign firm in prices1. This indicates
that the type of export policy is sensitive to the form of
competition. In addition, the literature has also noticed
that information can also crucial in determining the ap-
propriate policy. For example, Wong [5] demonstrated
that in the Brander-Spencer model with asymmetric in-
formation (about cost), the optimal export subsidy
scheme derived from the full information case is no
longer incentive compatible. Collie and Hviid [6] and
Qiu [2] examined the use of strategic trade policy as a
signalling device when the informational asymmetry is
between domestic and foreign firms.
With incomplete information, the Principal-Agent
model can best describe the leader-follower relation be-
tween uninformed government and informed firm. By
applying the Revelation Principle, the uninformed gov-
ernment can adopt a direct mechanism by offering a
menu of policies and letting the informed domestic firm
self-select the intended policy. When domestic firm is
competing with foreign firms, this “self-selection” proc-
ess becomes more informative. In Qiu’s [2] words, “it is
a mix of screening and signalling problems”; by choos-
ing among the menu of policies, the domestic firm also
signals its private information to the rival firms [6]. The
task of the government is then to trade off between the
inefficiency from asymmetric information and the strate-
gic advantage from trade policy; whether to have the
informed domestic firm truly reveal its information, or to
hide and enjoy the strategic benefit from asymmetric
information? Qiu [2] showed that under Cournot compe-
tition the uniformed government will choose a policy
menu to truly reveal its cost information (separating
equilibrium).
*Corresponding author.
1De Meza [7] considered cost asymmetry between firms and shows that
the countries with the lowest costs provide the highest export subsidies.
Allowing a social cost of public funds that exceeds unity, Neary [8]
similarly found that non-concavity of demand is a sufficient condition
for the government to provide more subsidies to the more cost competi-
tive firm. Bandyopadhyay [9] found the conventional result in De Meza
[7] and Neary [8] is reversed for inelastic demand.
While the analysis on unilateral policy intervention has
proved to be powerful to describe the dilemma encoun-
tered by the uninformed government, in reality we often

C. Y. FU, S. J. HO 697
see bilateral or multilateral policy interventions instead
of unilateral policy. If we adopt a direct mechanism for
these multiple contracting cases, will there be a separat-
ing equilibrium? If not, how much information can be
revealed? How does the degree of information revelation
relate to the market structure? Will there be trade retalia-
tion?
In this paper, we provide answers to these questions by
studying an incomplete information VERs game in an
intra-industry trade model. The model we consider is an
international trade model with differentiated products [1].
There are two countries and each country has only one
producer, which sells its products to two countries. In
order to capture intra-industry trade of this kind, we em-
ploy the differentiated product framework by Dixit [10]
and Singh and Vives [11]. There are three reasons to
study an incomplete information VERs game of this form.
First, there have been many discussions on the informa-
tional impacts of taxes, subsidies or tariffs; we hope to
complement the literature by investigating the informa-
tional impacts of VERs, which are seen as equally im-
portant strategic tools. Second, although we are aware
that both the choice of policy instrument and the degree
of information revelation can be sensitive to the form of
competition (Cournot or Bertrand), since our focus is on
the information aspects of multilateral interventions, we
adopt a quantity competition setup to better handle the
impacts from VERs.
Third and most interestingly, we will show that in the
complete information benchmark case, each govern-
ment’s VER decision is as efficient as in the single gov-
ernment case. There is no direct interaction between the
two governments, so the policy efficiency can be retained
even with bilateral interventions. The question of con-
cern is: now that there is no game between the two gov-
ernments, can we apply the revelation principle directly
and look for a truth-telling direct mechanism in the in-
complete information VERs game? Unfortunately, the
answer is no, as we will demonstrate that the “signaling
effect” of menu selection will change the rival firm’s per-
ception about domestic firm’s private information. Con-
sequently, each firm’s intention of information revelation
will be related to the rival firm’s intention, and thus the
two governments are no longer “independent” from each
other.
Our paper starts with the complete information bench-
mark case, where we show that, by using VER each gov-
ernment gains a first mover advantage in the rival coun-
try [12-14]. However, when considering incomplete in-
formation, we first demonstrate that with competing
mechanisms, each firm’s intention to lie is positively
related to the rival firm’s lying intention. The two firms’
lying intentions are strategic complements and will in-
crease with the degree of product differentiation. Impor-
tantly, we show that each government will design their
VERs menus to allow for only partial revelation. Con-
trary to the single intervention case [2], a separating
equilibrium where each country’s domestic firm truth-
fully reveals its private information does not exist with
multilateral policy interventions. Finally, we demonstrate
that trade retaliation, when the two governments’ VERs
are positively related, will happen when the government
believes that its domestic firm is more likely to be ineffi-
cient. This result partly reflects the result by Martina and
Vergoted [15], who discussed the role of retaliation in
trade agreements and showed that retaliation is a neces-
sary feature of any efficient equilibrium.
The issues on “competing mechanisms” have received
many discussions. Peck [16] and Martimort and Stole [17]
first illustrated apparent failures of the standard revela-
tion principle with competing mechanisms. Since there is
no obvious way to deal with these problems, the litera-
ture has responded by imposing ad hoc restrictions on the
set of mechanisms from which Principals can choose
[18-22]. This is the reason why we stick to direct mecha-
nisms in this current paper. Next, our paper investigates
ex-post information revelation under bilateral govern-
ment interventions. This is different from ex-ante infor-
mation revelation such as Creane and Miyagiwa [23],
where duopoly firms make their revelation decisions be-
fore they observe their own private information. From
the information content, our model is closed to Collie
and Hviid [6] and Qiu [2], but they mainly assumed uni-
lateral policy design. Brainard and Martimort [21] con-
sidered bilateral government interventions but restricted
to truth-telling equilibria2. Finally, our results conclude
that trade retaliation happens when the government be-
lieves that its domestic firm is more likely to be ineffi-
cient. This partly coincides with Martina and Vergoted’s
[15] results. They showed that in the presence of private
information, retaliation can always be used to increase
the welfare derived from such agreements by the partici-
pating governments. In particular, it is shown that retalia-
tion is a necessary feature of any efficient equilibrium.
The remainder of the paper is organized as follows.
Section 2 discusses the complete information VERs game
as a benchmark of comparison. We demonstrate that, by
using VER, each government gains a first mover advan-
tage in the rival country. Section 3 characterizes the equi-
librium in the incomplete information VERs game. In
equilibrium, each government will only implement par-
tial revelation from its domestic firm, and there can be
trade retaliation when the government believes that its
2Brainard and Martimort [21] restricted to truth revelation equilibrium,
because Myerson [24] showed that in a bilateral principal-agent struc-
ture, truth revelation will be an equilibrium, if each agent is associated
uniquely with one principal. In our model, each firm will be related to
b
oth governments, and hence truthful revelation does not constitute an
equilibrium.
Open Access ME

C. Y. FU, S. J. HO 698
domestic firm is more likely to be inefficient. Section 4
concludes the paper with some suggestions on further re-
search.
2. The Model
Specifically, let the superscript , index the two
countries. Country ’s demand for firm 1 and firm 2’s
products are given by
1, 2k
k
11
kk
pq
2
k
q

  ,
21
kk
pq
2
k
q

  ,
where subscript ,indexes firm . and
denote firm i’s price and output in country k. The
coefficients
i1, 2,iik
i
pk
i
q

and

denote the own price effect and
cross price effects, respectively. We assume

  to
reflect that the own price effect is higher than the cross
effects. Notice that the level of

can be seen as a mea-
sure for the substitution between the two products; When

 
0
the two products are almost homogenous; when

 the two products are almost differentiated.
The reason we have considered a quantity instead of
price competition model is because we can handle the
quantity restraints easily. We are aware that the form of
competitionmight changes the policy insights [4]. Since
our focus is on the informational impacts of VERs, we
will stick to this simple framework for a neat presenta-
tion. Finally, since our focus is on the informational im-
pacts of government interventions, we assume zero
transportation cost for simplification. Each firm’s mar-
ginal production is assumed to be .
i
Each firm’s profit is thus given by
c
πi

π,1,
ij ij
iiiiii
RRcqq i 2,
ij
where i
and i denote firm ’s
revenue in domestic

and foreign countries,
respectively.
ii
ii
Rpqjj
ii
Rpq
i
i

j
We consider that the government of each country will
choose a VER , to maximize social welfare
i. Each country’s social welfare is the overall utility
deducted by foreign firm’s revenue, added by domestic
firm’s revenue in the foreign country, and minus the do-
mestic firm’s total production cost. That is,
,
j
i
qi j
SW

, for1,2,and.
ij ij
iijiiii
SWURRc qqiij 
This setup is firstly given by Singh and Vives [11],
which assumed that
 
22
2
ijiii i
iiii ijj
Uqqqqqqi 



2,.j


The advantage of this setup is: since in differentiated
product models, we cannot use the area under demand
function to measure the consumer surplus. The setup of
can help us easily measure the consumer surplus.
Also, we can easily derive the country ’s demand func-
tion by partial differentiating with respect to .
i
U
i
1
1

1
2

i
U
1

2

i
i
q
Complete Information VERs Game
As a benchmark of comparison, Section 2 discusses the
complete information VERs game where both firms’
production costs are publicly known. We will show that,
under complete information, each government’s VER
decision will be as efficient as in the single government
case. However, this policy efficiency will disappear
when we consider incomplete information in Section 3.
Not only because there is information rent in the VERs
contract, but also because the two governments’ compet-
ing mechanisms will increase firms’ strategic incentives
to lie.
The complete information VERs game proceeds as
follows. First, government 1 and government 2 set their
VERs, , and simultaneously. After observing the
VER decisions, both firm 1 and firm 2 compete in the
product markets of the two countries. By backward in-
duction, we first solve the market equilibrium, given the
two governments’ VER decisions, and then determine
each government’s optimal VER.
2
1
q1
2
q
Market Equilibrium Given the two governments’
VER decisions, and firm 1 and firm 2 maxi-
mize their profits simultaneously.
2
1
q1
2
q

1
1
12 2
111 1
max π,
q
RRcqq


2
2
12 2
222 2
max π.
q
RRcqq
Each firm’s best reply to the rival government’s VER
is given by
12
22
q



12
211 2
12
and .
qc qc
q
  

(1)
Optimal VERs Now, given the two firms’ best replies
in (1), each government chooses its VER to maximize its
social welfare. In the case of country 1, the structural
form of is:
1
SW
 



22
11111
2
22
11
qq






1
1121 2
111
12
2
2
12
1 1
.
2
SWqqqq qq
qqq
qc c q
 
 

 


 





 



1
2




1
1
22
q 
From the first order condition of maximization:
2 12
11
2
1
0
2
SWc qc
q
 



3.Therefore
3The second order condition of maximization is satisfied.
Open Access ME

C. Y. FU, S. J. HO 699

2
11
12
2
qc




2
c
(2)
Similarly, we can calculate government 2’s optimal
VER:

1
22
12
2
qc 



1
. c We will later refer 2
1
q
and 1
2
q as the efficient VERs, as each government’s
VER decision is as efficient as in the single government
case.
Accordingly, substitute ,
j
i
qi j, into firms’ best re-
plies in (1), we have 11
1
32
4
cc
q



2
and
221
2
32
.
4
cc
q




Here we make two remarks on these efficient VERs.
First, we can compare j
i
q to the outputs in the free
trade case, where each firm choose both and
to maximize
i
i
q
,
j
i
qi j,i

. The free trade outputs in
domestic and foreign markets are 2
3
ij
i
i
cc
q




 and
2
3
ij
i
i
cc
q




, respectively. A direct comparison
shows that The VER is higher than the foreign output in
the free trade case. The advantage of using VER is that,
by pre-committing to j
i
q, the government gains the po-
sition of a leader in the rival country, and in output com-
petition, there will be a first mover advantage.
This strategic advantage is first mentioned by Harris
[12], who analyzed the impacts of VERs in a Bertrand
model. Rosendorff [25] explained why governments pre-
fer VERs to tariff in a Cournot model. Also, Ishikawa
[26] studied the effect of VERs on profit, market share,
consumer surplus and welfare in a Cournot model. Berry,
et al. [27] evaluated VERs that was initially placed on
automobiles exports from Japan in 1980’s. They found
that VERs had increased both prices and the profits of
domestic firms, while leaving consumer welfare worse
off. Feenstra and Lewis [28] considered a domestic gov-
ernment with political pressure to negotiate over the
volume of trade and the transfer of rents. They charac-
terized the globally optimal, incentive-compatible trade
policies, in which the domestic government has no in-
centive to overstate (or understate) the pressure for pro-
tection. De Santis [14] studied the impact of VERs on
exporting countries. He showed that VERs at the
free-trade level would favour the concentration of indus-
try, and raise the price mark-up in the domestic market.
However, the impact on welfare is indeterminate de-
pending upon the effect on global efficiency.
Second, j
i
q in (2) tells us something about the moti-
vation of mimicking. Notice that j
i
q is decreasing in i,
and this indicates that a more efficient firm will have a
higher VER. In particular, if i has two possible values:
c
c
H
c and
L
c with
H
L
cc, then we have




jH jL
ii
qc qc. This, however, does not imply that
the less efficient firm will mimic the efficient firm. Ac-
tually, since i

is concave in , and by the definition
of maximization, the less efficient firm
j
i
q


H
c is better
off choosing


jH
qc
i than choosing

jL
i
qc
c

. In the
words of Spence [29], the inefficient firm does not envy
the efficient firm. This means that when we consider
incomplete information in a unilateral intervention case,
a separating equilibrium where each type of i chooses
its intended VER


j
ii
qc
i
might exist. Hence, our model
would suggest the same result as Qiu [2] in the unilateral
intervention case. In the next section, we will show that
with multiple mechanisms, a separating equilibrium does
not exist.
3. Incomplete Information VERs Game
Section 3 discusses the incomplete information VERs
game where i c is only privately known by firm .
Neither government nor government
i
j
or firm
j
knows this value. To simplify the analysis, we assume a
binary type set,


,
LH
ccc
i with
H
L
cc.
We have shown that with complete information, each
government’s VER decision is as efficient as in the sin-
gle government case. There is no direct interaction be-
tween the two governments, so the policy efficiency can
be retained even with bilateral interventions. With in-
complete information, we will show that the “signaling
effect” of menu selection will change the rival firm’s
perception about domestic firm’s private information.
Consequently, each firm’s intention of information reve-
lation will be related to the rival firm’s intention, and the
two governments are no longer “independent” from each
other.
The incomplete information VERs game proceeds as
follows. First, each government announces a VERs i
menu






jH
i
qc
c
,
jL
i
qc independently. Second, each
firm self selects a VER from the menu, and this
choice is publicly observed. Third, according to the ob-
served policy choices, the two firms update their beliefs
about the rival firm’s production cost, and then compete
in the product markets of the two countries. By backward
induction, we first solve the market equilibrium given the
two firms’ menu selection. Then we characterize the two
firms’ menu selection equilibrium. Finally, we determine
each government’s VERs menu.
i
Before proceeding with the derivation of market equi-
librium, we define more notations for the prior and pos-
terior beliefs on i. First, as said, we assume that


,
LH
i
ccc is only privately known by firm i. All
other players (including government , government i
j
,
and firm
j
) have common prior beliefs that the prob-
Open Access ME

C. Y. FU, S. J. HO 700
ability for
L
c is

, 01

 and the probability for
H
c is 1


j
. After observing the rival firm’s menu se-
lection strategy, each firm i can update its belief on
.
,
j
ci
Let


,
L
i
qc
H
i

 
,,
jL
ii
  denote firm i’s selection strat-
egy from the menu . It is assumed that
for . That is, in


,
jLj
i
qc qc
 
jH
i
qc

i

H

i

L H

ii

ji

,
the selection strategy for type
L
c of firm i is
, and for type

L
qc 

1

L
i
 
j H
i
qc 
Lj
ii
H
c of firm
, it is i
 
1
 
H
jL

i
H
i


1,
LH
ii
j
i
qc 
H
ii
qc . In particular,

1,
L
 0
H
ii
denotes the separating strategy where
each type of firm selects its intended VER. As an-
other example,

i


    denotes the hybrid
strategy where type
L
c of firm i selects its intended
VER, while type
H
c of firm i randomly selects be-
tween


jL
qc
i and


jH
i
qc with a probability i

.
3.1. Market Equilibrium
Belief Updating We now solve the market equilibrium
given the two firms’ menu selection. After observing
firm ’s selection strategy, firm
i
j
can update its belief
on i. That is, according to the Bayes’ rule, given the
observation
c
i

, the on-equilibrium path belief is given
by:

1
L
i
LH
ii

i





 (3)
For simplification, we assume that the off-equilibrium
path belief will be the same as the prior

.
If
L
H
ii

  then it can be calculated that i


 .
In particular, for the separating strategy
ii
, we have

1,
L
 0
H1
i



1,
. As another example,
for the hybrid strategy

LH
iii

 

, we have

1
i


L
i
ii
LH




 and 1
i


  . Finally,
given the posterior belief i


, let

i
1
ii
L
H
c


i
Ec c  

 denote firm ’s posterior
expected cost.
i
Market Competition Let


j
ii
q

denote country
’s VER associated with selection strategy i
i

. Since
each firm’s profit will be affected by their selection
strategies, we rewrite the profits as
, where

12
,, 
11

,π1,2
1
ii
ci
,, 
 






22 21
22 2
21111
1
,
Eqq
qq q

111
1
12
11 1
cq
cq q
  π


 


 

 (4)









11 1
2122122 22
22
211
12
22 22
π,,
.
cqqq
qEq q
cq q
2
2


 

 
 


(5)
In the case of


112
π,,
i
c 
, there is an expected term


1
22
Eq

. The reason for the expectation form is because
firm 1 cannot observe 2
c, and by observing 2

, firm 1
will guess firm 2’sVER as:








11
2222 2
1
22
1
111
LHL
LH
Eqq c
qc
 
 







2
.
H
Given


222
,
LH
 , the probability that type
L
c
of firm 2 takes


1
2
L
qc is 2
L

, and the probability that
type
H
c of firm 2 takes


1
2
L
qc is 2
H

. So the ex-
pected probability of taking


1
2
L
qc is


2
12
L
H

   . The expected probability of taking


2
1
H
qc can be explained similarly.
In the product market, each firm chooses to
maximize
i
i
q


12
π,,
i
c 
i
, given the selection strategy


12
,

 . Notice that


,qi  
j
ii , will be determined
by the menu selection strategy. By the first order condi-
tion of maximization4, we have
j




12
22 111 2
12
12
and .
22
EqcEq c
qq
 




(6)
This is similar to (1) in the complete information case,
except that the expected VERs will be determined in the
menu selection game.
Substitute the two best replies in (6) to (4) and (5), we
can rewrite


12
π,,
ii
c  as:
  
 
 
2
22
1
221
1121
2
112
2
11
1
221 2
11
π,, 2
2
,
2
Eq c
c
qEc
q
Eq c
cq

 

 
 







1











(7)
  
 
 
1
22
2
11 2
2122
1
221
1
22
2
1121
22
π,, 2
2
.
2
Eqc
c
qEc
q
Eq c
cq

 

 
 







2











(8)
4The second order condition of maximization is satisfied.
Open Access ME

C. Y. FU, S. J. HO
Open Access ME
701

In the case of , notice that there is a
posterior expected cost term . From (6), we know

1121
,,c 
2
E
 2
c
useful for equilibrium characterization.
Lemma 1 10
i
i
Ec





that firm 2’s best reply is

2
Eq11 2
2
c 



. But since
Proof. Since

10
iHL
i
Ec cc





 and


 
2
10
11
i
ii


 




 , we have
firm 1 cannot observe 2, it can only use the observation
of
c
2

to update its belief to be


22 2
1
2
L
H
c c

 Ec

. The similar argument ap-
plies to firm 2.
3.2. Menu Selection



 
1
2
10
11
iHL
ii
Ec cc







 .■
First, recall that in the complete information case, we
conclude that type
H
c is better off choosing


jH
i
qc
than

jL
i
qc. In the unilateral intervention case, a sepa-
rating equilibrium where each type of i chooses its
intended VER
c


jH
qc
i might exist. Hence, to simplify
the discussion, we restrict the selection strategy
to be

,
LH
iii
 
Next, we derive the equilibrium selection strategies


12
,


1, 2i
, given the best replies in (6). That is, for

and ,
L
H
i
ccc, firm i maximizes


12i
with respect to ,,c
i

i

. In the case of firm 1,
after replacing


1,
ii

 , in (7) is re-
written as (see Equation (11) ):

21
,,c 



1,
ii

 . That is, we assume
that type
L
c will take the intended VER, while type
H
c might mimic type
L
c b

H
y taking a mixed strategy
ii i i. With this restriction,

1
jL
qc  


j
qc  0
i


will indicate the separating strategy where each type
chooses its intended VER, and 1
i

 denotes the pool-
ing strategy where both types
L
c and
H
c choose


jL
i
qc.

11

In


1
1, 1

 , type
L
c will take the intended VER,
and type
H
cwill mimic type
L
c by taking a mixed
strategy





22
1
11 1 1
L
H
 qc  qc . So in (11), we have
replaced


2
11
q

in (7) by


2
1
L
qc . Also in (12), we
have replaced


2
q11

in (7) by






2
1
12
111
L
H
 qc  
c
qc . Also, we have replaced
22

and E


1
2
Eq 2

with the definitions given in (9)
and (10). The similar argument applies to firm 2.
(7) and (8) can be rewritten accordingly. 1 E

n be
written as
i
c ca
Selection Equilibrium Given the announced VERs



11,
1.
11
ii
LH
i
H
i
Ec cc
cc
 


 

 


H L
c
(9) menu






,
jL jH
ii
qc qc,


12
,


will constitute a
Bayesian equilibrium iff for
1, 2,i


12
max, ,for,.
i
L
H
iii
cccc

 
and

1
j
ii
Eq


can be rewritten as
 

 

11
11
jj
ii ii
jH
ii
Eqq c
qc

 



 

L
(10)
We need to show that for , 1, 2i1
L
i


and
i
H
i



can maximize


12
,,
ii
c  for ,
L
H
c
i
cc
1
L

,
respectively. First, from (11), if we require 1

to be
best reply for type
L
c, the intended VER must be set at
the following level
Lemma 1 concludes a preliminary result which will be








2
2 2
12
221 2
2
112 1
1
22 2
1
π,, 22
,
2
LL
L
L
L
LL
EqcqcE c
cq
Eq c
cqc

 

 












c
(11)






 






2
2 2
1
22
112
22
111 1222
111 1
1
22 22
111 1
π,, 2
1
1
2
1.
2
H
H
LH
L
H
HLH
Eq c
c
qcqcEc
qc qc
Eq c
cqcqc

 

 
 







 H














(12)

C. Y. FU, S. J. HO 702
 
2
2
1
12
2
LL
qcc Ec




2 , (13)
which is obtained by differentiating (11) with respect to


2
1
L
qc . In other words, if


2
1
L
qs set to be (13), then c
11
L


will be best reply.
Next, for type
H
c, 11
H



needs to be best reply to


2
1, 2

 . That is, given 2

, the first order condition
of maximization for (12) is:
i
 

 

 
 

2
112 22 222
111 111
1
222
1111 2
22
11
22
11
π,,
2
2
.
H
LH HLH
HLH
LH
HL H
cqc qcqcqc qc
qcqc qcEc
qc qc
cqc qc

 

 

 



 




 
Let




22
11 1
LH
Bqcqc



, firm 1’s best reply is:


2
2H
12
1
1
22
.
2
qc
B




 (14)
Similarly, we can calculate firm 2’s best reply to
H
c Ec


11
1,

 :
 
1
1
2
2
2
22
,
2
HH
qcc Ec
B





1
(15)
where




11
22 2
LH
Bqcqc



. Notice that i

is re-
lated to j

through the term j
j
E
qu
c

.
The eilibrium

12
,


s to simultaneously
sa
need
tisfy (14) and (15). r, since the structure forms
of equilibrium

12
,
Howeve

 are complicated, we derive the
following properthe menu selection equilibrium.
First, from (14), it can be calculated that
ties on




22 1
21 2
2
12
1
2
1
10.
211
HL
Ec



B
cc
B








 

A similar argument on 2

also shows that 2
1
0



.
This indicates that 1

and 2

are strategic comple-
ments. Since the level of i

denotes the degree that
type
H
c of firm i will miic type m
L
c the more that
type
H
c of firm i lies will trigger
H
c type of the
rival firm to lie more. Next, recall that the level of

measures the degree of substitution, and the smaller

indicates a higher degree of product differentiation. If we
take the partial differentiation of
1
2


 with respect to


, we know that the degree of strategic complements is
positively related to the degree of product differentiation.
Lemma 2 1

and 2

are strategic complements,
and 1
2




is decreasing in

.
Second, it is interesting to know if t he separating equi-
librium exists. That is, in the case of firm 1, we ask if
10


is a best reply to 20

 in (14). To find out,
substitute 20


in (14), so we have 22
L
Ecc


and
s best reply in (14) be firm 1’comes




2
1
1
22
2
H
HL
qcc c 


. Th
B 
e only chance for
10


is to let
 
2
1
12
2
H
HL
qcc c 


Compare this level to the efficient VER


1
2
2
2
H
cc c 


. We can conc
2
1
1
qlude that if
2
L
cc

, these two values are identical, but if 2
H
cc,
2
1
q is higher. In other words, the efficien
d
t VERs can
ly whenindeeinduce a truth-telling equilibrium but on
2
L
cc

.
More interestingly, if we consider an arbitrary positive
2

, the VER for (14) to be zero is:

level of
22
2
1
2H
HcEc
qc

 


2 
Also recall


2
1
L
qc
 from (13). We theore have the
m
ref
enu






,qc
e truth, no
words, given the
22LH
11
qc
 , which will induce each type of
m 1 to tell th matter what the rival will do. In fir
other menu




22
11
,
LH
qcqc
 , the
dominant strategy for each type of firm 1 is to tell the
truth and pick the intended VER.
Lemma 3 1) Given the menu


 
22
11
,
LH
qcqc
 , the
dominant strategy for each type of firm 1 is to tell the
2) The efficient V truth and pick the intended VER. ERs
can indeed induce a truth-telling equilibrium but only
when 2
L
cc

.
In the incomplete information VERs game, the “sig-
Open Access ME

C. Y. FU, S. J. HO 703
naling oeffect”f menu selection will change the rival
fir
ary results.
m’s perception about domestic firm’s private informa-
tion. Consequently, each firm’s intention of information
revelation will be related to the rival firm’s intention.
The question of concern is whether the government will
find it optimal to induce truthtelling, no matter how the
rival firms might lie. Will it be better off for the govern-
ment to induce a certain degree of lying in equilibrium?
How will this degree relate to the market structure? We
will provide answers to these questions shortly in next
subsection.
Finally, it can be calculated from (14) for the follow-
ing prelimin
Lemma 4

1
2H
qc
 
1
0 and 10
 


.
ed in Figur creasinAs illustrate 1, ing


2
1
H
qc will
shift the best reply of 1

inward. When


2
1
H
qc
l move
in-
creases, the menu selection equilibrium wilfrom
0
E to 1 E. Since 1

and 2

are strategple-
ments, this indicates that both 1
ic com

and 2

will de-
se.
Next,
crea
10
  indicates that th smalle
 er

is, the
m best reore theply of 1

will shift outward. In other
words, when the two pructs become more differenti-od
ated, the more likely that type
H
c will lie. Intuitively,
when the two products are more differentiated, each firm
will hope to increase their actual eport to counteract the
demand reduction from a smaller
x

. Since we are re-
stricting
 
22
11
LH
qc qc, type
H
c of each firm has
more intention to lie and hence 1

becomes higher.
3.3. Equilibrium VERs
Given the market equilibriu
tion equilibrium determined
m in (6) and the menu selec-
by (14) and (15), we now
E
0
0
2
1
2


λ
1
20
11




2
11
0, 0
H
qc  




2
121
,H qc 
E
1
λ
2
Figure 1. Increasing


2
1H
qc shifts the best replies left-
ward.
nment
e simplified the discussion by restrict the selection
determine each gover’s menu of VERs. As said,
we hav
strategy


,
LH
iii
  to be


1,
ii

 . In the case
of firm 1, according to the discussion on menu selection,
if we require 11
L


to be best type reply for
L
c, the
intended VER must be set at the following level

22
2
1
2.
2
L
LcEc
qc





 (16)
The same argument can apply to firm
left with the determination on
2. Hence we are


jL
i
qc. As mentioned in
Lemma 3 that the menu
 


22
11
,
LH
qcqc
 (from (13)
and (16)) can induce 10


folevel of 2 r any

. The
question of concern is wheent will find
it optimal to induce truth-telling from its own frm, no
matter how the rival firms might lie.
To answer the question, we first calculate the first or
der condition of maximization:
ther trnmhe gove
i


0
i
jH
i
qc  . In the
EW
case of firm 1, recall


11
SW c from Section 2:










11 111
22
iiii
SW cUcRc qq 
1
11111 1
12112 2
12 12
2111111
22
.
ij ij
j
c R
qqqqq q
RcRccqq

c








The expected social welfare is:





11 1
1
LH
EWSW cSWc  
fo f
. Since the structural
or the detailed deri- rms are complicated, we omitted
vation of

i
jH
i
qc. Then, by applying the implicit
EW5
function theorem, we can calculate



jH
i
qc
of which can tell us wether the two policies are strategic
iH
j
qc, the sign
complements or substitutes. Finally, we check whether it
is dominant for government 1 to choose






22
11
,
LH
qcqc
 , such that 10

. The same argu-
ment can apply to firm 2.
Proposition 5


2
1
H
qc and

1

2
H
qc are strategic
complements for *



, and they are strategic substi-
tutes for *

 .
Recall from Le2 and 4 that 1 mma

and 2

are
strategic m compleents and

0
i
jH
i
qc  5
 . Proposition
e strategic rsays that the key to judge thelation between


2
1
H
qc


1
2
H
qc and is the size of prior belief

. In
the case of government 1, if she thinks that the domestic
more likely to be efficient (i.e ., * firm is

 ),hen
when government 2 increases

1
2
t
H
qc , the best reply of
5Detailed derivations are available upon request.
Open Access ME

C. Y. FU, S. J. HO 704
2

will shift inward. Since 1

and 2

are strategic
complements, the equilibrium

12

,

 will both de-
ase. Now, if

cre

2
1
H
qc decreases, thethe best reply
of 2
n

will shift outward, which cuse the equilib-
rium 1
ould ca

to increer than decrease.
Ctrarily, if government 1 thinks the domestic firm is
more likely to have
ase rath
on
H
c (i.e., *

 ), then it is better
to allure the type
H
c of the rival firm to lie less. To do
so, when governmentncrease

2 is

1
2
H
qc and move the
best reply of 2

rd, government 1 must also in-
crease

inwa

2
1
H
qc and move the bef 1 st reply o

inward
to decrease bothf 1 o

and 2

in equilibrium.
MartVergoted [15] discussed the role of re-
taliation in trade agements. They showed that
ina and
re in the
presence of private information, retaliation can always be
used to increase the welfare derived from such agree-
ments by the participating governments. In particular, it
is shown that retaliation is a necessary feature of any ef-
ficient equilibrium. Our results show that retaliation can
only happen when *

 .
Proposition 6 Given any level of j

, it is optimal for
the government to ienmplemt 0
i

.
eIn the case of firm 1, to see wheth it is optimal for
government 1 to choose
r





22
11
q


(from (13) ,
LH
qcc
0 and (15)) to implement 1

, we substitute


2
1
L
qc

and


2
1
H
qc
 into the first order condition

i
H
qc . In
j
EW

i
the Appendix, we show that

0
jH
i
qc
i
EW
VERs menu

 under the




22
,
LH
qcqc
 6oncavity of
i
EW , we can conce optimal

11
lude t
. Due c to the
hat th

2
1
H
qc must
smaller than

be

2
1
H
qc . By Lemmsince

a 2,
1
20
H
qc
 
, we cade that givenany level of
1
2
n conclu

, it is optimal for government 1 to implement 1

.
Concluding Remarksss 4.
We study the informational impa
untary export restraints in a he
cts oltilateral vol-
teroges version of
sms, the two firms’ lying intentions are stra-
te
-industry trade model, for both
an
ENCES
[1] H. H. Wang, Ciffication and Wel-
fare in a Diffe World Economy,
f mu
nou
Brander and Krugman’s [30] international trade model.
Similar to the unilateral intervention case such as Qiu [2]
and Collie and Hviid [6], we ask if separating equilib-
rium where each country’s domestic firm truthfully re-
veals its private information still exists. If not, how much
information can be revealed? How does information
revelation relate to market structure? Will there be trade
retaliation?
To these questions, we first showed that with compet-
ing mechani
gic complements and will increase with the degree of
product differentiation. Next, we showed that each gov-
ernment will design their VERs menus to allow for only
partial revelation. Contrary to the single intervention case
[2], a separating equilibrium where each country’s do-
mestic firm truthfully reveals its private information does
not exist with multilateral interventions. Finally, we
demonstrated that trade retaliation, when the two gov-
ernments’ VERs are positively related, will happen when
the government believes that its domestic firm is more
likely to be inefficient.
As mentioned, we have restricted our discussion on the
VERs game to an intra
alytical convenience and for complementation to the
literature. It is also interesting to extend our model to dis-
cuss other policy instruments such as subsidies or taxes,
and in another form of competition such as Cournot and
Bertrand models. The literature has shown that the type
of export policy is sensitive to the form of competition.
In the case of subsidies or taxes, the informational im-
pacts will not be as surprising as in VERs game, as the
two governments are already related to each other with
complete information. We will leave these interesting
issues for further research.
REFER
. Peng and H. Wu, “Tar
erentiated Duopoly,” Th
Vol. 36, No. 7, 2013, pp. 899-911.
http://dx.doi.org/10.1016/0022-1996(94)90007-8
[2] L. D. Qiu, “Optimal Strategic Trade
metric Information,” Journal of International Eco
Policy under Asym-
nomics,
Interna-
Vol. 36, No. 3-4, 1994, pp. 333-354.
[3] J. A. Brander and B. J. Spencer, “Export Subsidies and
International Market Share Rivalry,” Journal of
tional Economics, Vol. 18, No. 1-2, 1985, pp. 83-100.
http://dx.doi.org/10.1016/0022-1996(85)90006-6
[4] J. Eaton, and G. Grossman, “Optimal Trade and Industri
Policy under Oligopoly,” Quarterly Journal of Econo
al
mics,
Vol. 101, No. 2, 1986, pp. 383-406.
http://dx.doi.org/10.2307/1891121
[5] K. Wong, “Incentive Incompatible, Im
Subsidies,” University of Washing
miserizing Export
ton Discussion Paper
ss,” Scandinavian Journal of Economics,
No. 9020, 1990.
[6] D. R. Collie and M. Hviid, “Export Subsidies as Signals
of Competitivene
Vol. 95, No. 3, 1993, pp. 327-339.
http://dx.doi.org/10.2307/3440359
[7] D. De Meza, “Export Subsidies an
Cause or Effect,” Canadian Journa
d High Productivity:
l of Economics, Vol.
19, No. 2, 1986, pp. 347-350.
http://dx.doi.org/10.2307/135289
[8] J. P. Neary, “Cost Asymmetries in International Subsidy
6Detailed derivations are available upon request.
Open Access ME

C. Y. FU, S. J. HO
Open Access ME
705
p Winners or Losers?”Games: Should Governments Hel
Journal of International Economics, Vol. 37, No. 3-4,
1994, pp. 197-218.
http://dx.doi.org/10.1016/0022-1996(94)90045-0
[9] S. Bandyopadhyay, “Dema
and Strategic Trade Policy,” Journal of Internation
nd Elasticities, Asymmetry
al Eco-
nomics, Vol. 42, No. 1-2, 1997, pp. 167-177.
http://dx.doi.org/10.1016/S0022-1996(96)01453-5
[10] A. Dixit, “A Model of Duopoly Suggesting a
Entry Barriers,” Bell Journal of Economics, Vol. 1
Theory of
0, No.
1, 1979, pp. 20-32. http://dx.doi.org/10.2307/3003317
[11] N. Singh and X. Vives, “Price and Quantity Competition
in a Differentiated Duopoly,” The RAND Journal of Eco-
nomics, Vol. 15, No. 4, 1984, pp. 546-554.
http://dx.doi.org/10.2307/2555525
[12] R. Harris, “Why Voluntary Export Restraints
tary’,” The Canadian Journal of Ec
Are ‘Volun-
onomics, Vol. 18, No.
4, 1985, pp. 799-809.
http://dx.doi.org/10.2307/135091
[13] C. C. Mai and H. H. W
straints Are Voluntary: An Extensi
ang, “Why Voluntary Export Re-
on,” The Canadian Jou-
rnal of Economics, Vol. 21, No. 4, 1988, pp. 877-882.
http://dx.doi.org/10.2307/135273
[14] R. A. De Santis, “Why Exporting Countries Agree t
Voluntary Export Restraints: The
o
Oligopolistic Power of
the Foreign Supplier,” Scottish Journal of Political
Economy, Vol. 50, No. 3, 2003, pp. 247-263.
http://dx.doi.org/10.1111/1467-9485.5003009
[15] A. Martina and W. Vergoted, “On the Role of
in Trade Agreements,” Journal of Internationa
Retaliation
l Econom-
ics, Vol. 76, No. 1, 2008, pp. 61-77.
http://dx.doi.org/10.1016/j.jinteco.2008.03.009
[16] J. Peck, “A Note on Competing Mech
velation Principle,” Ohio State University, Mime
anisms and the Re-
o, 1
281-1312.
995.
[17] D. Martimort and L. Stole, “Communication Spaces, Equi-
libria Sets and the Revelation Principle under Common
Agency,” University of Chicago Graduate School of Bu-
siness, Discussion Paper STE019, 1997.
[18] P. McAfee, “Mechanism Design by Competing Sellers,”
Econometrica, Vol. 61, No. 6, 1993, pp. 1
http://dx.doi.org/10.2307/2951643
[19] M. Peters, “On the Equivalence of Walrasian and N
Walrasian Equilibria in Contract Ma
on-
rkets,” Review of Eco-
nomic Studies, Vol. 64, No. 2, 1997, pp. 241-265.
http://dx.doi.org/10.2307/2971711
[20] M. Peters and S. Severinov, “Competition among Sellers
Who Offer Auctions Instead of Prices,” Journal of Eco-
nomic Theory, Vol. 75, No. 1, 1997, pp. 141-179.
http://dx.doi.org/10.1006/jeth.1997.2278
[21] S. L. Brainard and D. Martimort, “Strategic Trade Policy
with Incomplete Informed Policymakers,” Journal of In-
ternational Economics, Vol. 42, No. 1-2, 1997, pp. 33-65.
http://dx.doi.org/10.1016/S0022-1996(96)01446-8
[22] L. G. Epstein and M. Peters, “A Revelation Principle for
542
Competing Mechanisms,” Journal of Economic Theory,
Vol. 88, No. 1, 1999, pp. 119-160.
http://dx.doi.org/10.1006/jeth.1999.2
and Disclosure
2
[23] A. Creane and K. Miyagiwa, “Information
in Strategic Trade Policy,” Journal of International Eco-
nomics, Vol. 75, No. 1, 2008, pp. 229-244.
http://dx.doi.org/10.1016/j.jinteco.2007.11.00
s in Gen-[24] R. Myerson, “Optimal Coordination Mechanism
eralized Principal-Agent Problems,” Journal of Mathe-
matical Economics, Vol. 10, No. 1, 1982, pp. 67-81.
http://dx.doi.org/10.1016/0304-4068(82)90006-4
[25] B. P. Rosendorff, “Voluntary Export Restraints, Antidum-
ort Re-
1/1467-9396.00092
ping Procedure, and Domestic Politics,” American Eco-
nomic Review, Vol. 86, No. 3, 1996, pp. 544-561.
[26] J. Ishikawa, “Who Benefits from Voluntary Exp
straints?” Review of International Economics, Vol. 6, No.
1, 1998, pp. 129-141.
http://dx.doi.org/10.111
ntary Export [27] S. Berry, J. Levinsohn and A. Pakes, “Volu
Restraints on Automobiles: Evaluating a Trade Policy,”
American Economic Review, Vol. 89, No. 3, 1999, pp.
400-430. http://dx.doi.org/10.1257/aer.89.3.400
[28] R. C. Feenstra and T. R., Lewis, “Negotiated Trade Re-
g/10.2307/2937965
strictions with Private Political Pressure,” Quarterly
Journal of Economics, Vol. 106, No. 4, 1991, pp.
1287-1307.
http://dx.doi.or
Quarterly Journal of [29] M. Spence, “Job Market Signaling,”
Economics, Vol. 87, No. 3, 1973, pp. 355-374.
http://dx.doi.org/10.2307/1882010
[30] J. A. Brander and P. Krugman, “A Reciprocal Dumping
Model of International Trade,” Journal of International
Economics, Vol. 15, No. 3-4, 1983, pp. 313-321.
http://dx.doi.org/10.1016/S0022-1996(83)80008-7