Download Environmental Regulation Strategy Analysis of Local Government

2014 International Conference on Management Science & Engineering (21th)
August 17-19, 2014
Helsinki, Finland
Environmental Regulation Strategy Analysis of Local Government
Based on Evolutionary Game Theory
PAN Feng1，XI Bao2，WANG Lin1
1 School of Management, Harbin Institute of Technology, Harbin 150001, P.R.China
2 School of Public Administration and Law, Dalian University of Technology, Dalian 116024, P.R.China
Abstract: The environmental regulation is
formulated by central government and implemented by
local government in China, and the environmental
quality of whole nation is directly affected by the
environmental regulation strategy of local government.
For the implementation of environmental regulation,
evolutionary process of strategy among local government,
enterprise and central government from the perspective
of evolutionary game theory is discussed. The
evolutionary game model between local government and
enterprise is established, and the evolutionary game
model between local government and central government
as well. The behavioral evolutionary law and
evolutionarily stable strategies are given according to
replicator dynamics equation. The influencing factors of
environmental regulation strategy of local government
are analyzed. The results show that the environmental
regulation strategy of the local government is affected by
the weight coefficient of environmental quality index and
economic development index in achievement assessment
system, the cost of implementation of environmental
regulation, the punishment of central government to local
government, the rate of pollution discharge, the cost and
the emission reductions of controlling pollution. Finally
some policy suggestions for the implementation of
environmental regulation are proposed.
Keywords: bounded rationality, evolutionary game,
environmental regulation, evolutionarily stable strategy,
local government
1 Introduction
The ecological environment suffered serious
destruction with the economic rapidly growth since
reform and opening up in China. The living conditions of
public and the sustainable development of economy is
endangered by environmental pollution. The cause of
environmental pollution is negative externality of
enterprise’s productive behavior, thus the formulation
and implementation of environmental regulation are
Supported by the Key Project of National Social Science Fund
(12AGL010) and the National Natural Science Foundation of
China (61074133)
needed to rectify the market failure. A series of
environmental policies have been formulated since the
environmental protection law was promulgated by
central government in 1979, however environmental
pollution has not been effectively controlled. The
environmental regulation is implemented by local
government in China, the environmental issues can be
solved or not, depends on the implementation degree of
environmental regulation to a large extent.
Environmental regulation refers to the limitation
and adjustment to the polluting behavior of enterprise
from governments or regulatory organizations. The
process of implementing environmental regulation is also
the process of game. Many domestic and foreign scholars
have studied the strategic behavior of related bodies in
the process of environmental regulation. In the aspect of
behavior interaction between regulatory subject and
regulatory object, Moledina established a dynamic game
model under asymmetric information and found that the
enterprise will choose different strategies with different
environmental policy instruments[1], Deng Feng also got
a similar conclusion through analyzing the interactive
relationship between government and enterprise[2]. Meng
Xiaolian proposed that the enterprise can be rationally
controlled through encouraging pollution treatment or
minimizing pollution on the spot[3]. Yang Lin studied the
relationship between environmental degradation and
game of enterprise and supervision department based on
complete rationality[4]. Some scholars thought that
strengthening the supervision and punishment to
enterprises will contribute to the improvement of
environmental quality[5-6], however Zhang Qian
discovered that the pollution emission of enterprise
cannot be influenced by the supervision of government
directly[7]. In the aspect of behavior interaction between
regulatory subjects, Barrett and Kennedy analyzed the
Noncooperative game of environmental decision making
between governments under imperfect competition
market[8-9]. Dungumaro discussed the role of public
participation in environmental protection based on game
theory[10]. Akihiko Yanase studied game behavior
between oligarchs countries in pollution treatment using
differential game model[11]. Fujiwara studied the
relationship between cross border pollution and foreign
trade through building dynamic game model[12]. Cui
- 1957 978-1-4799-5376-9/14/$31.00 ©2014 IEEE
Yafei studied the strategies of pollution treatment
between local governments in China, and Liu Yang
analyzed the game process between local governments in
cross regional pollution treatment further[13-14]. In
addition, the influence of competition between local
governments on environmental governance was also
studied by some scholars [15-17].
Based on the literature review above we can find
that, in the aspect of research content, the foreign
research puts more emphasis on the method of pollution
treatment and cross border pollution treatment, the
domestic research focuses more on the strategic behavior
of enterprise under environmental regulation and the
interaction between local governments, ignoring the
environmental regulation strategy of local government
and related factors in the implementation of
environmental regulation. In the aspect of research
method, most of existing research is on the premise of
complete rationality, but in reality, the game players are
bounded rational. The behavioral evolutionary law and
evolutionarily stable strategy of game players who are
bounded rational can be systematically analyzed using
evolutionary game model, however there are only a few
scholars have analyzed environmental problems based on
evolutionary game theory, and also lack of attention to
the regulatory behavior of local government[18-19].
The local government gradually has his own interest
and action ability with the deepening of fiscal
decentralization in China. In the implementation of
environmental regulation, there is game relationship not
only between local government and enterprise but also
between local government and central government.
Considering the repeatability of environmental regulation
strategic game, this paper tries to construct evolutionary
game model between local government and enterprise,
and evolutionary game model between local government
and central government, analyze the influencing factors
of environmental regulation strategy of local government,
propose the policy suggestions to promote the
implementation of environmental regulation.
2
Evolutionary
game
analysis
on
environmental regulation strategy of local
government
2.1 Basic assumptions of model
(1) Game players and behavior strategy. Assume
that the game players include local government,
enterprise and central government. They have incomplete
information and are bounded rational. The local
government can choose to implement environmental
regulation, such as levying pollution charge from
enterprise, and can also choose not to implement
environmental regulation, the action set is {implement,
not implement}. The central government can choose to
monitor local government, such as monitoring whether
or not environmental regulation has been implemented,
and can also choose not to monitor local government, the
action set is {monitor, not monitor}. The enterprise can
choose to control pollution, and can also choose not to
control pollution, the action set is {control, not control}.
(2) Variable declaration. Assume that C1 indicates
the cost of implementation of environmental regulation;
C2 indicates the cost of monitoring; C3 indicates the
cost of controlling pollution; h indicates the quantity of
pollution emission when enterprise controls pollution,
q ( q  h ) indicates the quantity of pollution emission
when enterprise does not control pollution; H indicates
the quantity of pollution emission when local
government chooses “implement”, and Q indicates the
quantity of pollution emission when local government
chooses “not implement” within his jurisdictions; G
indicates the local economic losses caused by the
implementation of environmental regulation. F
indicates the punishment of central government to local
government when the environmental regulation has not
been implemented.  indicates the rate of pollution
discharge.  ( 0    1 ) indicates the influencing
coefficient of local economic on national economic.
 ( 0    1 ) indicates the influencing coefficient of
local environmental quality on national environmental
quality.  1 ( 0  1  1 ) indicates the weight coefficient of
environmental quality index in achievement assessment
system.  2 ( 0   2  1 ) indicates the weight coefficient of
economic development index in achievement assessment
system. The income and cost of local government from
environmental quality is determined both by the quantity
of pollution emission within his jurisdictions and the
weight coefficient of environmental quality index. Local
economic growth is mainly the result of enterprise’s
production value, therefore the local economic
development level can be substituted by the profit of
enterprise. The income and cost of local government
from economic development is determined both by the
profit of enterprise and the weight coefficient of
economic development index.
(3) Evolutionary game model. In the condition of
incomplete information and bounded rationality, it is
difficult for game players in environmental regulation
system to ensure that their strategies are optimal. The
players’ ability to find mistakes and adjust strategy is
fairly low, and their behavior change is mainly not rapid
learn and adjustment, but a slow evolution. Therefore,
we can imitate the game process of environmental
regulation by replicator dynamics mechanism. The
replicator dynamics is dynamic differential equations
describing the proportion of the strategy used by a
population. If the income of the strategy were better than
the average, the proportion of the strategy would rise. In
repeated game, the individual constantly adjusts his
strategy to improve his income and reach into a dynamic
equilibrium. In the equilibrium state, any individual
doesn’t want to change his strategy and the proportion of
the strategy is constant. The strategy in the equilibrium
state is evolutionarily stable strategy (ESS)[20].
- 1958 -
2.2 Evolutionary game model between local
government and enterprise
In the 2  2 asymmetry repeated game, we assume
that local government can choose “implement” and “not
implement”
strategies
stochastic
independently,
enterprise can also choose “control” and “not control”
strategies stochastic independently. The payoff matrix of
stage game between local government and enterprise is
shown as Tab.1.
Assume that the enterprise chooses the strategy
“control” with a proportion x , and chooses the strategy
“not control” with a proportion 1  x ; the local
government chooses the strategy “implement” with a
proportion y , and chooses the strategy “not implement”
with a proportion 1  y .
When enterprise chooses “control” strategy, his
fitness is:
f1  y (C3   h)  (1  y )(C3 )
When enterprise chooses “not control” strategy, his
fitness is:
f 2   y q
Then the average fitness of enterprise is:
f12  xf1  (1  x ) f 2
According to the Malthusian equation[21], the growth rate
of “control” strategy is:
x / x  f1  f12  (1  x)[ y (q  h)  C3 ]
(1)
When local government chooses “implement”
strategy, his fitness is:
f3  x[C1   2 (C3   h)  1h   h]  (1  x)
(C1   2 q  1q   q)
When local government chooses “not implement”
strategy, his fitness is:
f 4  x( 2C3  1h)  (1  x)(1q)
Then the average fitness of local government is:
f 34  yf 3  (1  y ) f 4
Similarly the growth rate of “implement” strategy is:
y / y  (1  y )[ q(1   2 )  C1  x (q  h)(1   2 )] (2)
The replicator dynamics system of local
government and enterprise is:
 x  x(1  x)[ y (q  h)  C3 ]
(3)

 y  y (1  y )[ q(1   2 )  C1  x (q  h)(1   2 )]
According to the method Friedman put forward in
1991, we can get the stability of equilibrium point in
evolution system through analyzing the local stability of
Jacobian matrix of system. The Jacobian matrix of
system is[22]:
Tab.1 The payoff matrix of stage game
between local government and enterprise
Local government
Implement
Not implement
Enterprise
Control
Not control
 C3   h
C3
C1   2 (C3   h)  1h   h
 2 C3   1h
 q
0
C1   2 q   1q   q
1q
Tab.2 DetJ and trJ numerical expression of system (3)
EP
det J
trJ
(0, 0)
C3[ q(1   2 )  C1 ]
C3   q(1   2 )  C1
(1, 0)
C3[ h(1   2 )  C1 ]
C3   h(1   2 )  C1
(1,1)
( e  C3 )[ h(1   2 )  C1 ]
 e  C3   h(1   2 )  C1
(0,1)
( e  C3 )[ q(1   2 )  C1 ]
 e  C3   q(1   2 )  C1
(“EP” denotes “equilibrium points”)
 (1  2 x )[ y ( q  h )  C 3 ]

J 
 y ( y  1) ( q  h )(1   2 )
x (1  x ) ( q  h ) 

(1  2 y )[ q (1   2 )  
C1  x ( q  h )(1   2 )] 
Then the determinant of J is:
det J  ( y e  C3 )(1  2 x)(1  2 y )[ q(1   2 )  C1  x e(1   2 )] 
xy (1  x)( y  1)(1   2 ) 2e 2
The trace of J is:
trJ  ( y e  C3 )(1  2 x)  (1  2 y )[ q(1   2 )  C1  x e(1   2 )]
Where e ( e  q  h ) indicates the emission reductions
when enterprise chooses “control”, that is the emission
reductions of controlling pollution.
Let x  0 and y  0 in the replicator dynamics
system of local government and enterprise, we can get 4
equilibrium points include: O (0,0) , A(1,0) , B (1,1) ,
C (0,1) . The determinant and trace of J with 4
equilibrium points are shown as Tab.2.
Let  1   q (1   2 )  C1 ,  2   h(1   2 )  C1 ,  3   e  C3
in Tab.2. Then  1 indicates the net income of local
government implementing environmental regulation
when enterprise chooses “not control”,  2 indicates the
net income of local government implementing
environmental regulation when enterprise chooses
“control”,  3 indicates the net income of enterprise
controlling pollution under environmental regulation.
According to the theory of evolutionary game, the
equilibrium point is the stable point of system when
det J  0 and trJ  0 . The evolutionarily stable
strategies under different situations are shown as Tab.3.
In situation 6, let x  F ( x )  x (1  x )( y e  C3 )  0 ,
then the game is stable when x  0 or x  1 . If
y  C3 /  e , that is F ( x )  0 , F '(0)  0 , F '(1)  0 .
Evolutionarily stable strategy is achieved when
dF ( x ) / dx  0 according to the stability theorem of
differential equation. Thus, the evolutionarily stable
strategy will be achieved when x  1 . If y  C3 /  e , that
is F ( x )  0 , F '(0)  0 , F '(1)  0 . Thus, evolutionarily
stable strategy will be achieved when x  0 . Similarly,
let y  F ( y )  y (1  y )[ q (1   2 )  C1  x e(1   2 )]  0 , then
the game is stable when y  0 or y  1 . If
x  [ q(1   2 )  C1 ] /  e(1   2 ) , evolutionarily stable
y0 .
strategy
will
be
achieved
when
If x  [ q(1   2 )  C1 ] /  e(1   2 ) , evolutionarily stable
strategy will be achieved when y  1 . Evolutionary game
phase diagram is divided into four fields Ⅰ, Ⅱ, Ⅲ,
- 1959 -
y
Tab.3 Local stability analysis results of system (3)
C(0,1)
Situation 1: 1  0 ,  3  0
EP
det J
(0, 0)
+
+
(1, 0)
(1,1)
(0,1)
EP
(0, 0)
(1, 0)
(1,1)
(0,1)
EP
trJ
stability
ESS
saddle point
saddle point
instability
~
~
+
Situation 2: 1  0 ,  3  0
C3
e
stability
ESS
saddle point
instability
saddle point
Situation 3: 1  0 ,  2  0 ,  3  0
det J
trJ
+
+
-
~
+
~
O(0,0)
(0, 0)
(1, 0)
(1,1)
(0,1)
EP
(1, 0)
(1,1)
(0,1)
EP
(0, 0)
(1, 0)
(1,1)
(0,1)
EP
(0, 0)
(1, 0)
(1,1)
(0,1)
trJ
stability
saddle point
instability
ESS
saddle point
Situation 6: 1  0 ,  2  0 ,  3  0
det J
trJ
+
+
-
~
+
~
det J
trJ
-
~
~
~
~
stability
saddle point
saddle point
saddle point
saddle point
(“~” denotes “indeterminacy”)
value
y1*  C3 /  e
and
*
x  [ q(1   2 )  C1 ] /  e(1   2 ) . When initial state of game
is in field Ⅰ, the game will converge into point B (1,1) ,
which means that “control” and “implement” are the
final choices of two players. When initial state of game is
in field Ⅱ, the game will converge into point A(1,0) ,
which means that “control” and “not implement” are the
final choices of two players. When initial state of game is
in field Ⅲ, the game will converge into point C (0,1) ,
which means that “not control” and “implement” are the
final choices of two players. When initial state of game is
in field Ⅳ, the game will converge into point O (0,0) ,
Ⅳ
by
critical
Ⅱ
Ⅲ
Ⅳ
 q(1   2 )  C1
 e(1   2 )
A(1,0)
x
which means that “not control” and “not implement” are
the final choices of two players. The probability of local
government choosing “implement” will increase with the
increase of area Ⅰand Ⅲ in Fig.1 The probability of
enterprise choosing “control” will increase with the
increase of area Ⅰand Ⅱ in Fig.1.
From Tab.3 we can find that the local government
tends to choose “not implement” when 1  0 in
situation 1(ESS is (0,0)) and situation 2(ESS is (0,0)).
When 1  0 , the local government tends to choose
“implement” in situation 3(ESS is (0,1)), situation 4(ESS
is (0,1)) and situation 5(ESS is (1,1)); the probability of
local government choosing “implement” will increase
with the increase of area Ⅰ and Ⅲ in situation 6. We
assume that the probability of different situations in the
game are same, then increasing  1 , and increasing x*
trJ
stability
~
saddle point
+
+
instability
~
saddle point
+
ESS
Situation 5: 1  0 ,  2  0 ,  3  0
det J
(0, 0)
Ⅰ
Fig.1 Evolutionary game phase diagram (situation 6)
stability
instability
+
instability
+
+
instability
+
ESS
Situation 4: 1  0 ,  2  0 ,  3  0
det J
B(1,1)
to expand area Ⅰ and Ⅲ, both which will increase the
proportion of choosing “implement” strategy in local
government.
Based on the analysis of situation 1, situation 5
and situation 6, we can find that the enterprise may
choose “control” only if 1  0 and  3  0 . That is the
local government choosing “implement” and the net
income of controlling pollution under environmental
regulation is positive are the essential conditions of
enterprise choosing “control”. The probability of
enterprise choosing “control” will increase with the
increase of area Ⅰand Ⅱ in situation 6. Thus we can
get the Proposition 1:
Increasing  3 , and increasing y1* to expand area
ⅠandⅡ, both which can increase the proportion of
choosing “control” strategy in enterprise under
environmental regulation. The enterprise will choose
“not control” without environmental regulation.
2.3 Evolutionary game model between local
government and central government
We assume that central government is able to find
out whether or not the environmental regulation has been
implemented. The local government will be punished
- 1960 -
when environmental regulation has not been
implemented. In the 2  2 asymmetry repeated game,
local government can choose “implement” and “not
implement” strategies stochastic independently, central
government can also choose “monitor” and “not
monitor” strategies stochastic independently. The payoff
matrix of stage game between local government and
central government is shown as Tab.4.
Assume that the local government chooses the
strategy “implement” with a proportion y , and chooses
the strategy “not implement” with a proportion 1  y ;
the central government chooses the strategy “monitor”
with a proportion z , and chooses the strategy “not
monitor” with a proportion 1  z .
When local government chooses “implement”
strategy, his fitness is:
f1  z (C1   H  1H   2G )  (1  z )
(C1   H  1H   2G )
When local government chooses “not implement”
strategy, his fitness is:
f 2  z ( F  1Q)  (1  z )(1Q)
Then the average fitness of local government is:
f12  yf1  (1  y ) f 2
The growth rate of “implement” strategy is:
y / y  f1  f12  (1  y )[ zF   H  1 (Q  H ) 
(4)
C1   2G ]
When central government chooses “monitor”
strategy, his fitness is:
f3  y (C2   G   H )  (1  y )(C2  F   Q)
When central government chooses “not monitor”
strategy, his fitness is:
f 4  y (  G   H )  (1  y )(   Q )
Then the average fitness of central government is:
f 34  zf 3  (1  z ) f 4
The growth rate of “monitor” strategy is:
z / z  f 3  f 34  (1  z )( F  C2  yF )
The replicator dynamics system of
government and central government is:
 y  y (1  y )[ zF   H  1 (Q  H )  C1   2G ]
(5)
local

 z  z (1  z )( F  C2  yF )
(6)
Tab.4 The payoff matrix of stage game
between local government and central government
Central government
Monitor
Not monitor
Local
government
C1   H  1 H   2G
C1   H  1 H   2G
C 2   G   H
 G   H
 F  1Q
 1Q
C 2  F   Q
 Q
Implement
Not
implement
The
Jacobian
matrix
of
system
(1  2 y)[ zF   H  1(Q  H )  C1   2G] y(1  y)F 
is: J  

(1  2z)(F  C2  yF )
( z  1) zF
Tab.5 DetJ and trJ numerical expression of system (6)
EP
(0, 0)
(1, 0)
(1,1)
(0,1)
det J
trJ
( H  1E  C1   2G)
 H  1 E  C1   2G  F 
( F  C2 )
C2
( H  1E  C1   2G)C2
 H  1 E  C1   2G  C2
( F   H  1E  C1   2G )
 H  1E  C1   2G  F 
(C2 )
C2
( F   H  1E  C1   2G)
( F  C2 )
 H  1E  C1   2G  C2
Then the determinant of J is:
det J  ( zF   H  1E  C1   2G )(1  2 y ) (1  2 z )( F  C2  yF ) 
y (1  y )( z  1) zF 2
The trace of J is:
trJ  ( zF   H  1E  C1   2G)(1  2 y )  (1  2 z )( F  C2  yF )
Where E ( E  Q  H ) indicates the emission reductions
within his jurisdictions when local government chooses
“implement”.
Let y  0 and z  0 in the replicator dynamics
system of local government and central government, we
can get 4 equilibrium points include: O(0,0) , A(1,0) ,
B(1,1) , C(0,1) .The determinant and trace of J with 4
equilibrium points are shown as Tab.5.
Let  4 = H  1E  C1   2G in Tab.5. Then  4
indicates the net income of local government
implementing environmental regulation. The equilibrium
point is the stable point of system when det J  0 and
trJ  0 .The evolutionarily stable strategies under
different situations are shown as Tab.6.
In situation 12, let
y  F ( y )  y (1  y )[ zF   H  1 E  C1   2G ]  0 , then
the game is stable when y  0 or y  1 .
If z  (C1   2G   H  1E ) / F , that is F ( y )  0 ,
F '(0)  0 , F '(1)  0 . Thus, evolutionarily stable strategy
y 1
will
be
achieved
when
.
If
that is
F ( y)  0 ,
z  (C1   2G   H   1 E ) / F ,
F '(0)  0 , F '(1)  0 . Thus, evolutionarily stable strategy
y0 .
will be achieved when
Similarly,
let z  F ( z )  z (1  z )( F  C2  yF )  0 , then the game is
stable when z  0 or z  1 . If y  ( F  C2 ) / F ,
evolutionarily stable strategy will be achieved when
z  0 . If y  ( F  C 2 ) / F , evolutionarily stable strategy
will be achieved when z  1 . Evolutionary game phase
diagram is divided into four fields Ⅰ, Ⅱ, Ⅲ, Ⅳ by
critical
value
z *  (C1   2G   H  1E ) / F
and
*
y2  ( F  C2 ) / F . When initial state of game is in field
Ⅰ, the game will converge into point B(1,1) , which
means that “implement” and “monitor” are the final
choices of two players. When initial state of game is in
field Ⅱ, the game will converge into point A(1,0) ,
which means that “implement” and “not monitor” are the
final choices of two players. When initial state of game is
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Tab.6 Local stability analysis results of system (6)
EP
(0, 0)
(1, 0)
(1,1)
(0,1)
EP
(0, 0)
(1, 0)
(1,1)
(0,1)
EP
(0, 0)
(1, 0)
(1,1)
(0,1)
EP
(0, 0)
(1, 0)
(1,1)
(0,1)
EP
(0, 0)
(1, 0)
(1,1)
(0,1)
EP
(0, 0)
(1, 0)
(1,1)
(0,1)
z
Situation 7:  4  0 , F  C2  0
det J
+
+
-
C(0,1)
stability
instability
ESS
instability
instability
trJ
+
+
Situation 8:  4  0 , F  C2  0
C1   2G   H  1E
F
stability
~
saddle point
+
ESS
~
saddle point
+
+
instability
Situation 9:  4  0 , F  C2  0 , F   4  0
det J
det J
trJ
Ⅱ
Ⅲ
Ⅳ
trJ
trJ
+
+
+
+
Situation 12:  4  0 , F  C2  0 ,
det J
trJ
-
~
~
~
~
A(1,0) y
F  C2
F
Fig.2 Evolutionary game phase diagram (situation 12)
O(0,0)
stability
ESS
saddle point
instability
saddle point
F  C2  0 , F   4  0
+
+
+
+
Situation 11:  4  0 , F  C2  0 ,
det J
Ⅰ
trJ
+
~
+
+
~
Situation 10:  4  0 ,
det J
B(1,1)
“implement” will increase with the increase of area Ⅰ
and Ⅱ in situation 12. We still assume that the
probability of different situations in the game are same,
then increasing  4 , and reducing z * to expand area Ⅰ
and Ⅱ , both which will increase the proportion of
choosing “implement” strategy in local government.
stability
instability
instability
instability
ESS
F  4  0
3 Discussion of parameter variation
In the game between local government and
enterprise,  1 and x* can be increased by increasing
 , reducing C1 and reducing  2 , both which can
increase the proportion of choosing “implement” strategy
in local government. Whereas x* will be reduced by
increasing e , thus the proportion of choosing
“implement” strategy in local government will be
reduced by increasing e .
In the game between local government and central
government,  4 can be increased and z * can be
reduced by reducing C1 , increasing 1 and reducing
stability
ESS
instability
instability
instability
F  4  0
stability
saddle point
saddle point
saddle point
saddle point
 2 . z * also can be reduced by increasing F . Thus, the
in field Ⅲ, the game will converge into point C(0,1) ,
which means that “not implement” and “monitor” are the
final choices of two players. When initial state of game is
in field Ⅳ, the game will converge into point O(0,0) ,
which means that “not implement” and “not monitor” are
the final choices of two players. The probability of local
government choosing “implement” will increase with the
increase of area Ⅰ and Ⅱ in Fig.2.
From Tab.6 we can find that the local government
tends to choose “implement” when  4  0 in situation
7(ESS is (1,0)) and situation 8(ESS is (1,0)). When
 4  0 , the local government may choose “implement”
in situation 12 only if F  C2  0 , F   4  0 and z  z* .
The probability of local government choosing
proportion of choosing “implement” strategy in local
government will be increased by reducing C1 ,
increasing 1 , reducing  2 and increasing F .
According to Proposition 1,  3 can be increased and
y1* can be reduced by increasing  , reducing C3 and
increasing e , both which can increase the proportion of
choosing “control” strategy in enterprise under
environmental regulation. Thus the proportion of
choosing “control” strategy in enterprise under
environmental
regulation
can
be
represented
as x  x ( , C3 , e) . The quantity of pollution emission and
the emission reductions within his jurisdictions when
local government chooses “implement”, and the local
economic losses caused by implementation of
environmental regulation can be respectively represented
as:
H  xh  (1  x ) q , E  xe , G  xC3  xh  (1  x ) q
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Then the net income of implementing environmental
regulation can be represented as:
 4   [ xh  (1  x ) q ]  1 xe  C1   2 [ xC3  xh  (1  x ) q ]
That is:
4 Conclusions
 4  x[1e   2C3  (1   2 ) e]  q (1   2 )  C1
Then  4 can be increased and z * can be reduced by
reducing C3 and increasing e , both which can increase
the proportion of choosing “implement” strategy in local
government when 1  ( 2C3 / e)  (1   2 ) .  4 can be
↑ or ↓ ↑ or ↓ ↑ or ↓
1  ( 2C3 / e)  (1   2 )
This paper studied the evolutionary process of
strategy among local government, enterprise and central
government from the perspective of evolutionary game
in the condition of bounded rationality. The purpose of
this paper is to analyze the influencing factors of
environmental regulation strategy of local government.
The analysis results show that the environmental
regulation strategy of local government is affected by the
weight coefficient of environmental quality index in
achievement assessment system, the weight coefficient
of economic development index in achievement
assessment system, the cost of implementation of
environmental regulation, the punishment of central
government to local government when the environmental
regulation has not been implemented, the rate of
pollution discharge, the emission reductions of
controlling pollution and the cost of controlling
pollution.
The net income of controlling pollution under
environmental regulation can be increased by increasing
the rate of pollution discharge, increasing the emission
reductions of controlling pollution and reducing the cost
of controlling pollution. These measures will encourage
enterprise to control pollution theoretically, however, the
proportion of choosing “implement” strategy in local
government may reduce.
Increasing the weight coefficient of environmental
quality index and reducing weight coefficient of
economic development index in achievement assessment
system can not only promote local government to
implement environmental regulation, but also reduce the
negative impact of environmental policy on choosing
“implement” of local government, such as increasing the
rate of pollution discharge and reducing the cost of
controlling pollution.
In addition, the central government can strengthen
the punishment to local government, reduce the cost of
implementation of environmental regulation by
implementing fiscal transfer payment to promote the
implementation of environmental regulation in the local
government, which will contribute to the improvement of
environmental quality.
↑
↓
↑
1  ( 2C3 / e)  (1   2 )
References
reduced and z * can be increased by reducing C3 and
increasing e , both which can reduce the proportion of
choosing “implement” strategy in local government
when 1  ( 2C3 / e)  (1   2 ) .The net income of
implementing environmental regulation can also be
represented as:
 4   (1   2 )( q  ex )  x (1e   2C3 )  C1
Then  4 can be increased and z * can be reduced by
increasing  , both which can increase the proportion of
choosing “implement” strategy in local government
when 1   2C3 / e . It is not able to determine the
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Tab.7 The influence of parameter variation on
environmental regulation strategy of local government
Parameter
variation
Game between local
government and
enterprise
Game between local
government and central
government
1
x*
y
4
z*
y
1 ↑
—
—
—
↑
↓
↑
2 ↓
↑
↑
↑
↑
↓
↑
C1 ↓
↑
↑
↑
↑
↓
↑
F↑
—
—
—
—
↓
↑
1   2C3 / e
↑
e↑
↑
—
↑
↓
↑
↓
↑
↓
1   2C3 / e
↑
↓
↑
↓
1  ( 2C3 / e)  (1   2 )
C3 ↓
—
—
—
The influence of parameters on environmental
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Tab.7.
↑
↓
↑
1  ( 2C3 / e)  (1   2 )
↓
↑
↓
(“↑” denotes “increasing”, “↓” denotes “reducing”, “—”
denotes “no effect”)
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