For IE675
Zhao Wu
Department of Industrial Engineering
University At Buffalo
The Interplay Between Anti-Smuggling Measures taken by
Collaborative Countries
Abstract
The game depiction of anti-smuggling measures is presented, emphasizing the interaction
between two collaborative countries. I investigate two factors that would affect the defensive
measures taken by two countries. The goal of this article is to find the optimal way for each
countries to defend themselves from smuggling.
I.
Introduction
Smuggling has a long and controversial history, probably dating back to the first time at
which duties were imposed in any form, or any attempt was made to prohibit a form of traffic.
Smuggling is the clandestine transportation of goods or persons, such as out of a building,
into a prison, or across an international border, in violation of applicable laws or other
regulations. People smuggle for different reasons. These include the participation in illegal trade,
such as in the drug trade, in illegal immigration or illegal emigration, tax evasion,
providing contraband to a prison inmate, or the theft of the items being smuggled. Examples of
non-financial motivations include bringing banned items past a security checkpoint (such
as airline security) or the removal of classified documents from a government or corporate
office.
Research on smuggling as economic phenomenon is scanty. Jagdish Bhagwati and Bent
Hansen first forwarded a theory of smuggling in which they saw smuggling essentially as an
import-substituting economic activity1. Their main consideration, however, was the welfare
implications of smuggling. Against common belief that the private sector is more efficient than
the public sector, they showed that, smuggling might not enhance social welfare though it may
divert resources from government to private sector. In contrast, Faizul Latif Chowdhury, in 1999,
suggested a production-substituting model of smuggling in which price disparity due to cost of
supply is critically important as an incentive for smuggling. This price disparity is caused by
domestic consumption taxes as well as import duties. Drawing attention to the case of cigarettes,
Chowdhury suggested that, in Bangladesh, smuggling of cigarettes reduced the level of domestic
production. Domestic production of cigarettes is subject to value added tax and
other consumption tax. Reduction of domestic taxes enables the local producer to supply at a
lower cost and bring down the price disparity that encourages smuggling. However, Chowdhury
suggested that there is a limit beyond which reducing domestic taxes on production cannot
Bhagwati, J. and B. Hansen: ‘A Theoretical Analysis of Smuggling’, Quarterly Journal of Economics,
1973, p.172.
1
For IE675
Zhao Wu
Department of Industrial Engineering
University At Buffalo
confer a competitive advantage versus smuggled cigarettes2. Therefore, government needs to
upscale its anti-smuggling drive so that seizures (the taking possession of person or property by
legal process) can add to the cost of smuggling and thus render smuggling uncompetitive.
Notably, Chowdhury modelled the relationship of the smuggler to the local producer as one of
antagonistic duopoly.
For a single country, the problem is described in the area of resource allocation. There are
already many mature theories, which are very helpful on solving this kind of problem. And since
the international smuggling is from one country to another country, it’s not a one-way action.
Considering the smuggling between America and Mexico or Canada, we would obviously find
that smuggling brought loss to all countries involved not just the country who is exported. When
countries are mutually targeted by a group of smugglers, their anti-smuggling measures imply
transnational externalities and associated market failures. Anti-smuggling measures taken by
either country would provide benefits for all involved countries; thus anti-smuggling measures
represents a public good with strong free-rider incentives(Sandler and Siqueira 2006). With the
formation of widely flung smuggling networks, transnational smuggling has become a crucial
security concern worldwide. The enhanced movement of people, resources and goods tied to
globalization provides smugglers with greater cover.
The primary purpose of this article is to investigate how two countries would collaborate in
order to protect one’s own profit.
II.
MODEL PRELIMINARIES
Smuggling could be divided by different types, such as goods smuggling, human smuggling,
wildlife smuggling, etc. Here we assume the smuggling discussed in this article to be goods
smuggling because it is the most prevalent case.
We assume that two nations-Homeland (H) and Foreign Country (F)-are two countries
troubled by smuggling. In this two- country world, the damage from smugglers is captured by T,
which can be reduced by anti-smuggling measures:
T H  T (m H , m F )
(1)
T F  T (m F , m H )
(2)
T H denotes the damage to Homeland and T F denotes the damage to Foreign Country.
2
Chowdhury, F. L. 'Smuggling, Tax Structure and The Need for Anti-Smuggling Drive', Fiscal Frontier,
Vol VI, 2000, Dhaka.
For IE675
Zhao Wu
Department of Industrial Engineering
University At Buffalo
T H
T H

0,
0
m H
m F
(3)
T F
T F

0,
0
m H
m F
(4)
The expression in (3) and (4) indicates that level of anti-smuggling measures would decrease
damages at a diminishing rate. Also level of anti-smuggling measures is public good which means
anti-smuggling measures taken by either H or F would benefit the other country as well. As a
public good, anti-smuggling measures imply strong free-rider incentives.
When two countries are involved, the decision-maker in each country independently
H
F
decides level of anti-smuggling measures, that is m and m . In this article, I assume the two
decision-makers simultaneously make their decision. To capture the decision-process, I firstly
H
F
introduce possible expressions for T , T .
III.
FORMULATE THE DAMAGE FUNCTION
H
F
The damage function T , T must have following properties:
a. Each has two variables m and m .
H
F
b. Must satisfy expression (3) and (4) ,which means level of anti-smuggling measures
would decreases damages at a diminishing rate.
c.
Reveal the property of free-rider incentives.
d.
T H , T F should have similar expressions.
e.
m H would be more important in T H
f.
m F would be more important in T F
The following damage function captures these properties:
T H  T (1  m H )(1  m F )  T (1  m H );
(5)
T F  T (1  m H )(1  m F )   T (1  m F );
For IE675
Zhao Wu
Department of Industrial Engineering
University At Buffalo
IV.
THE TOTAL LOSS FUNCTION
H
If country H faces a constant marginal cost c for its defensive measures, then its total loss
V H is given by:
V H  T H  c H mH  T (1  m H )(1  m F )  T (1  m H )  c H m H
(6)
F
Similarly, if country F faces a constant marginal cost c for its defensive measures, then
V F  T F  c F mF  T (1  mH )(1  mF )   T (1  m F )  c F m F
V.
(7)
Find the Nash Equilibrium
Now we already have the total loss function and what we need is the Nash Equilibrium.
Denote m
H*
and m
F*
H
F
be the best response respectively to V , V .
Thus,
m H *  arg min(V H )  arg min(T  Tm H  Tm F  Tm H m F  T  Tm H  c H m H )
mH *(0,1)
=
mH *(0,1)
if m  1   
F
0
cH
T
(8)
cH
if m  1   
T
F
1
Similarly,
m F *  arg min(V F )  arg min(T  Tm H  Tm F  Tm H m F  T  Tm F  c F m F )
mF *(0,1)
=
0
mF *(0,1)
if
mH  1   
cF
T
(9)
1
cF
if m  1   
T
H
For IE675
Zhao Wu
Department of Industrial Engineering
University At Buffalo
In order to find the Nash Equilibrium, we want to get the intersection of m
H*
and m
F*
.
Following are some graphs of different value of  ,  .
i)
mH
1  
mF*
cF
T
mH *
mF
1  
Figure 1 1   
cH
T
cH
cF
 1,1   
 1 . As shown in the graph, there is only
T
T
one NE existed that is ( m
F*
,m
H*
)=(1,0)
For IE675
Zhao Wu
Department of Industrial Engineering
University At Buffalo
ii)
mH
mF*
1  
cF
T
mH *
mF
cH
1  
T
Figure 2 1   
cH
cF
 1,1   
 1 . As shown in the graph, there are three
T
T
NE existed that is ( m
F*
,m
H*
cH
cF
( 1  
,1   
)
T
T
)=(1,0) or (0,1) or
For IE675
Zhao Wu
Department of Industrial Engineering
University At Buffalo
iii)
mH
mF*
1  
cF
T
mH *
mF
1  
cH
T
cH
cF
 1,1   
 1 . As shown in the graph, there is only
Figure 3 1   
T
T
one NE existed that is ( m
F*
,m
H*
)= ( 1 , 1 )
For IE675
Zhao Wu
Department of Industrial Engineering
University At Buffalo
iv)
mH
1  
cF
T
mH *
mF*
mF
1  
Figure 4 1   
cH
T
cH
cF
 1,1   
 1 . As shown in the graph, there is only
T
T
one NE existed that is ( m
F*
,m
H*
)= ( 0,1)
For IE675
Zhao Wu
Department of Industrial Engineering
University At Buffalo
VI.
ANALYSE NE
As we could see in part V, the NE of this game is influenced by two parameters  ,  . But
what’s the real meaning of them? Looking back into the part III (e) and (f),  ,  come from
these two assumptions.
T represents the extra damage other than the common damage T to
H and similarly  T represents the extra damage other than the common damage T to F. Thus
 ,  could be regarded as proportion. Let’s see an extreme case. We would assume  ,  <<1,
which means the damage to these two countries could be regarded as equal.
Now we got four cases:
i)
If

(m
ii)
If
If
If
F*
F*
(m
F*
)=(1,0)
H*
)=(1,0) or (0,1) or( 1   
cH
cF
, 
T
T
,m

H*
cH
cF
, 
T
T
,m

(m
iv)
,m

(m
iii)
F*
cH
cF
.
, 
T
T
H*
)= ( 1 , 1 )
cH
cF
, 
T
T
,m
H*
)= ( 0,1)
cH
cF
,1   
)
T
T
For IE675
Zhao Wu
Department of Industrial Engineering
University At Buffalo
In case i),
we could see that

cH
cF
F
,which means c <<T. Thus Country F would choose to
, 
T
T
take a full defensive level which would make T
F
 T (1  mH )(1  mF )   T (1  mF ) =0 and
Country H , on the other hand, would like to take a free ride. The final loss of these two countries
would be
V H  T ,V F  c F
In case ii),

cH
cF
F
H
, which means c and c couldn’t be ignored. In this case, there would be
, 
T
T
three NE.
(m
F*
,m
H*
H
F
(V ,V )
)
(0,1)
( T , c )
(1,0)
( c , T )
H
F
( c  2 T , c  2 T )
F
cH
cF
( 1  
,1   
)
T
T
H
In case iii)

(m
cH
cF
F
H
, 
, which means c <<T, c <<T.
T
T
F*
,m
H*
F
H
F
H
)= ( 1 , 1 )and ( V , V )=( c , c ).
H
F
We could see that when the marginal cost c , c is relatively small compared to the damage T,
then ( m
F*
,m
H*
)= (1,1) , which means each country would prefer to take a full level of
F
H
F
H
anti-smuggling measures. And their total loss would be ( V , V )= (c , c ) , which is the cost
of defensive resources.
For IE675
Zhao Wu
Department of Industrial Engineering
University At Buffalo
In case iv),
We could see that
(m
F*
VII.
,m
H*

cH
cF
. This case is symmetric to case I and we could find that
, 
T
T
)= ( 0,1) is also symmetric to that in case i). ( V , V )=(  T , c )
F
H
H
CONCLUSIONS
The goal of this paper is try to find the Nash Equilibrium of two collaborative countries
endangered by smugglings. The analysis identifies two key determinants: proportion of extra
damage(  ,  ) and cost of defensive resource ( c , c ). Under the extreme case that  ,  <<1,
H
F
the game representation shows that the country with low cost of defensive resource would
prefer to take a full level of anti-smuggling measures and if the cost of both countries isn’t that
low then there would be three pure Nash Equilibriums.
VIII. FUTURE WORK
Though we succeed in finding the Nash Equilibrium of the model, however, the total four
cases are divided by comparing
 and
cH
cF
,  and
so that we have to first know how
T
T
to quantify  ,  then we would be able to apply this method.
Also, the game model established in this article is a very simple one. In the real world, with
the formation of widely flung smuggling networks, transnational smuggling usually would involve
several countries and would across several borders. The enhanced movement of people,
resources and goods tied to globalization provides smugglers with greater cover and much more
chances. The future work would be establishing a more accurate model with more key
parameters considered.
For IE675
Zhao Wu
Department of Industrial Engineering
University At Buffalo
REFERENCES
1.
SUBHAYU BANDYOPADHYAY and TODD SANDLER. The Interplay Between Preemptive
and Defensive Counterterrorism Measures: A Two-stage Game. Economica(2011)
78,546-564
2.
DAVID P.MORTON, FENG PAN, KEVIN J.SAEGER. Models for nuclear smuggling
interdiction. IIE Transactions, 39(1), 3-14
3.
VICKI M.BIER, NARAPHORN HAPHURIWAT, Analytical method to identify the number of
containers to inspect at U.S. ports to deter terrorist attacks, Ann Oper Res(2011)
187:137-158