Game Analysis of Government Subsidy Mechanism for WEEE Recycling in China

■2012 JSPS Asian CORE Program, Nagoya University and VNU University of Economics and Business

Game Analysis of Government Subsidy Mechanism for WEEE Recycling in
China

Southwest Jiaotong University

Zu-Jun MA*, Shu HU**, Yu-Sen YE**

ABSTRACT: Electrical and electronic equipment closed-loop supply chains consisting of manufacturers, sellers, and
consumers under government regulation was investigated in this paper. Based on Cobweb theorem, we analyzed the
repeated game process between government and manufacturers, and obtained the equilibrium solution for stage game. On
this basis, we discussed the impact of government subsidy for WEEE recycling on social welfare, as well as the mutual
response strategies of manufacturers and government. By the results of our study, we have discovered that, if
manufacturers recycle WEEE with the possible maximum recycling rate attained without loss of own revenue after
receiving government subsidies, it will cause the loss of social welfare, and that the degree of loss will increase with the
increase of unit subsidy for recycling WEEE. Therefore, to promote the recycling of WEEE, we should maximize the rate
of recycling WEEE without loss of social welfare, and government should enhance as far as possible the degree of
sensitivity to the recycling rate adopted by manufacturers, as well as the upper bound of unit subsidy for recycling
WEEE.
KEYWORDS: closed-loop supply chains, government subsidies, WEEE, repeated game, Cobweb theory

that recycler should be subsidized with a certain range

1. INTRODUCTION

in accordance with the real amounts of finished

There are more than 200 millions of Waste
Electrical

and

Electronic

Equipment

dismantling WEEEs. The subsidization criteria are ¥85

(WEEE)

per TV set, ¥80 per refrigerator, ¥35 per washing

produced every year in China, which has become one

machine, ¥35 per room air conditioner and ¥85 per

of the major sources of solid waste. The Regulation on

microcomputer. On December 2010, the Ministry of

the Administration of the Recovery and Disposal of

Industry and Information Technology of China (MIIT)

Waste Electrical and Electronic Products came into

drafted the Access Conditions of China Comprehensive

effect on January 1, 2011, and the Administrative

Utilization of Waste Electrical and Electronic Products,

Provisions on the Collection of the Fund for Disposing

stipulating the limit and target value of recycling rate

Waste Electrical and Electronic Products carried into

for seven types of WEEE, among which the values for

execution from July 1, 2012, which is an important

televisions, refrigerators, washing machines, air

supporting regulation to the former one. It is proposed

conditioners,

computers

*Southwest Jiaotong University, School of Economics and Management
**Southwest Jiaotong University, School of Transportation and Logistics

were

65%

and

75%

respectively. The formulation and implementation of

Hammond and Beullens(2007) established a model

relevant regulations for WEEE recycling must have

consisting of manufacturers and consumer markets

significant effect on manufacturers or retailers in

engaged in a Cournot pricing game with perfect

closed-loop supply chains (CLSC). The question is

information, which is formulated with the intent of

whether the mechanism for WEEE recycling is proper,

examining issues surrounding the WEEE directive.

and how it can effectively promote the WEEE

Mitra and Webster(2008) examined the effects of

recycling.

government subsidies as a means to promote

There are few studies considering the influence of

remanufacturing activity, finding that subsidy sharing

governmental financial regulation. Atasu et al.(2009)

creates incentives for the manufacturer to design a

considered the impact of take-back legislation on the

product that is more suitable for remanufacturing, and

economy and look at the efficiency of existing policies

to be more open to efforts to increase the return rate of

such as the WEEE directive of the European

end-of-life products. Aksen et al.(2009) presented and

Commission. They argued that the weight based

solved two bi-level programming (BP) models

directives and the weight-based categorization of

describing the subsidization agreement between the

products may not necessarily be efficient (neither

government and a company engaged in collection and

economically nor ecologically). A better categorization

recovery operations. They introduced a supportive and

of products and the selection of targets would consider:

a legislative BP model to tackle this comprehensive

(i) the treatment cost or the benefit from recycling, (ii)

collection system design problem. The results showed

the environmental impact of the product, (iii) the

that for the same collection rate and profitaility ratio

willingness-to-pay of customers for the decrease in the

the government has to grant a higher subsidy in the

environmental impact, and (iv) the competition

supportive model than in the legislative model. Sheu et

intensity of the specific market. Atasu et al.(2008)

al.(2005) presented an optimization-based model to

pointed out that there exists a contradiction between

deal with integrated logistics operational problems of

the regenerating of materials and reusing of products in

green-supply chain management (G-SCM). Results of

the WEEE Directive, causing competitions when

numerical studies indicate that the reverse chain-based

pursing the goal of recycling. Chen and Sheu (2009)

net profits increase significantly with the increase of

demonstrated that a proper design of environmental

the value of the governmental subsidy, and increase

regulation pricing strategies can promote EPR for the

proportionally with the increase of the return ratio

firms in supply chains. They established a differential

subject to the certain range of the return ratio, and then

game model comprising Vidale–Wolfe equation. They

decline as the return ratio continues to increase. Li et

found

the

al.(2011) developed a CLSC network equilibrium

effectiveness of environmental policy on the premise

model, analyzing the behavior of the various decision-

that it is nature for business to pursue maximal profits.

makers by using network equilibrium theory and

Georgiadis and Besiou(2010) used an extension of a

variational inequality. The results showed that the

System Dynamics-based model to investigate the

collection rate will increase with the growth of

significance of the factors that comprise the

subsidies, and that heterogeneous products always

environmental

the

compete in sale and recovery processes. Hong and

operational features of CLSC, their interactions and the

Ke(2011) presented a Stackelberg-type model to

type of their impact on the environmental and

determine Advanced recycling fees and socially

economical sustainability of a WEEE CLSC.

optimal subsidy fees in decentralized reverse supply

that

governments

sustainability

should

consider

strategies

and

chains where each entity independently acts according

WEEE processing enterprises, not including WEEE

to its own interests. They found that the two fees

collecting ones. It is obvious that the researches above

achieve the maximum of social welfare at the

could not reflect the main features of government

equilibrium status, while both MISs (manufacturers,

regulation tools for WEEE recycling in China.

importers, and sellers) and recyclers gain the maximum

To encourage and promote the recycling of WEEE,

of profits. Wang and Shen(2011) studied the incentive

the government will develop subsidy criteria and

mechanism of RSC under government regulation,

related policies in accordance with the situation of

resulting that taking both subsidies and punishment is

WEEE recycling, regulating and controlling the

the optimal program. Wang et al.(2010) established

recycling

variational inequality models considering the penalty

manufacturers will adjust the recycling rate based on

policy to manufacturers and the allowance policy to

its operation situations and the published subsidy

collectors by the government. The result showed that

criteria, to maximize his own profits. Thus, there exists

the equilibrium quantity results increase with the

a dynamic process of repeated game between the

increase of the allowance given by the government

government and manufacturers. In this paper, the

whereas they decrease with the increase of the penalty

Cobweb model was used to analyze the repeated game

to manufacturers.

process. We try to answer the following questions:

market.

As

a

recycler

of

WEEE,

Most of the literatures above are on the basis of the

How to come to an equilibrium state in repeated game?

European WEEE Directive or extended producer

How do WEEE recycling subsidies have any effect on

responsibility (EPR)-type policies, which set up a

social welfare? What kind of response strategies should

minimum collecting rate and recycling rate to design

be taken by manufacturers and the government to

the incentive and punishment mechanism considering

maximize the recycling rate on the premise of suffering

the real finished situation of enterprises. However,

no loss of both manufacturer’s benefit and social

copying existing WEEE-type legislation may not lead

welfare?

to improved welfare outcomes, as different regions of
the world may face different cost structures,
environmental consciousness levels, and competition

2. MODEL ASSUMPTIONS

(Atasu et al., 2009). For example, now there is no

Consider an electrical and electronic equipment

requirement about minimum recycling rate in China,

(EEE) CLSC consisting of manufacturers, retailers and

nor punishment for not completing. The Administrative

consumers (as shown in Figure 1). New products are

Provisions on the Collection of the Fund for Disposing

produced by manufacturers and sold by retailers.

Waste Electrical and Electronic Products only

Manufacturers are also in charge of the processing and

provided the limit value and target value for different

reuse of WEEE, which are collected from consumers

types of WEEE recycling rate. It also stipulated that a

by retailers. The government encourages the recycling

certain processing fee should be levied in accordance

of WEEE by subsidizing manufacturers.

with the amounts of production enterprises, import
production, imports of electrical and electronic

p

w

manufacturers

retailers
bm

consumers
br

products separately. Also it will subsidize the recycling
enterprises in accordance with the real finished
amounts of WEEE, nor the finished recovery or
recycling rate. The subsidized objects are limited to

Figure 1 The structure of EEE CLSC
To facilitate problem formulation, we make the
following assumptions.


(1)

The unit production cost of the original

appliances is denoted by cm , and the unit cost of

3. MODEL FOMULATION
We introduce the Cobweb theory to characterize the
game: When the government sets up a subsidy criterion

producing remanufactured products by the components

s1 , manufacturers will choose his recycling rate u1 ,

cr ,

which generates a new subsidy criterion s2 . It will

the

lead to a new recycling rate u2 determined by

remanufactured cost per unit when the recycling rate of

manufacturer. Then again and again, the continuous

WEEE

adjustment will finally reach to an equilibrium state sn

and

parts

with

cr

of
cm

WEEE

u (cm

equals

g)

to

is

denoted

,

where

100%.

Both

by
g

is

original

and

and un , as shown in Figure 2.

remanufactured products are selling at a same price.
The unit processing fee for WEEE is denoted

by ch , which is a quadratic function of recycling
rate u , i.e. ch

e

fu 2 , where e and f

are both

nonnegative constants.

Unit subsidy s

(2)

Manufacturers' strategy

s2

u2
s4

We denote the wholesale price by w and the

(3)

selling price by p .
(4)

u4

sn
s5

The selling amount of the appliances D p

u3

s3

has a linear relationship with the selling price p , i.e.
D p

a bp , where a and b are both nonnegative

constants.
(5)

Government's strategy

u1

s1
un

The price of collecting a unit WEEE from

Recycling Rate u

consumers is denoted by br , while the transaction

Figure 2 The Cobweb model

price of per unit paid by manufacturers to retailers is

3.1 Stage game between the government and

denoted by bm .

manufacturers

(6)

The collecting amounts G br

proportional
i.e. G br

to

the

transaction

of WEEE is
,

stage game, which reflects the interactions among the

are both

government, manufacturers and retailers. In fact, the

D p .

process can be constructed as a three phase game with

Government charges a certain processing fee

the following decision-making orders: The first stage is

c dbr , where

price

c and d

nonnegative constants and restricted by G br
(7)

br

for per unit of WEEE, which is denoted by h .
(8)

Each game in the repeated game process is called a

set for environmental policy making. The government

Government subsidy fees for manufacturers

will take the maximization of social welfare as a goal,

recycling of per WEEE are denoted by s . It is

determining the recycling subsidy criterion s of

stipulated that manufacturers’ processing rate of

WEEE, which is given to manufacturers. In the second

WEEE should not be lower than the lowest recycling

stage, manufacturers will maximize its own profits in

rate u ( 0 u 1 ).

accordance with the subsidy criterion to determine the

(9)

The environmental cost for consuming per

wholesale price w, the transaction price paid to

appliance is denoted by C , as the environmental

retailers bm and the recycling rate u . In the final stage,

benefits from collecting and processing per unit can be

retailers will determine the selling price p of the

denoted by V .

appliances and the collecting price br under a given w
and bm , to make its own profits maximum.
We assume that the decisions are made with perfect


information and backward induction can be used to
solve the problem.
We solve retailers’ optimal operation decision in the
third stage first. The total cost of purchasing appliances
from manufacturer is denoted by D p w , while the
total revenue is D p p . The total processing fees paid
to the consumers are denoted by G br br , while the
total transaction fees are G br bm . Retailers try to

(
u

R

p ,br

G br

bm

br

D p

)

cm g
2f

(7)

Eq. (3), and obtain
3a bcm bh
p*
4b

(8)

fu 2 ucm ug
4

s e

br

(1)

p w

*

c
2d

By putting Eq. (5) into Eq. (2), putting Eq. (6) into

maximize its own profits, that is
max

fu 2 ucm ug
2
6

s e

bm

3c
4d

(9)

Finally, we solve the optimal economy policy of the
From the first-order conditions

R

p

0,

R

br

0,

we can get that

determines the recycling subsidy for the purpose of

a bw
2b
dbm c
2d

p
br

government in the first stage. The government

(2)
(3)

encouraging manufacturers to promote the recycling
rate of WEEE and achieving the maximum social

welfare. Social welfare is equals to the sum of

Then move to manufacturers’ optimal production
decision in the second stage. The total cost of

D p

customer surplus denoted by

2b

2

, manufacturer’s

, retailer’s profits denoted by

producing remanufactured products by the components
and parts of WEEE is denoted by G br cr . The total

profits denoted by

production cost of the original ones is denoted by

by D p h , subsidy fees from government denoted by

D p

G br

cm .

stands

D p h

for

the

R

, processing fees charged by government denoted

G br s , the environmental cost for consuming new

appliances

processing fees charged by the government. The total
revenue of manufacturer is D p w , while the total
transaction fees are G br bm and the total processing
fees of WEEE are G br ch . G br s stands for the

G br

s bm

cm

D p

w cm

h

ch

cr

=

( D p )2
2b
+D p

M

0 , and

bm
w*

(

M

u

the

G br
p cm

V

br +cm

cr

ch

(10)

C

By putting Eqs. (5)-(9) into Eq. (10). According to
(4)

the first-order condition

By combining Eqs. (2) and (3) with Eq. (4).
According to the first-order conditions

and

D p C

M
R +D p h
2b

G br s D p C G br V

s

characterized by
M

by

( D p )2

max

Manufacturers’ maximizing its own profits can be

w,bm ,u

denoted

environmental benefits of collecting and processing
WEEE denoted by G br V , that is

recycling subsidy fees provided by the government.

max

M

M

w

0,

0 , we can get that

s

cm g
4f

2

c
d

s

0 , we can get that

e +2V

(11)

By putting Eqs. (7) and (11) into Eqs. (6) and (9)
respectively, we can obtain

a bcm bh
2b

5

)

bm

cm

g
4f

2

e +V

(12)


br =

cm

g

2

c
2d

8f

e V
+
2 2

(13)

The equilibrium solution is achieved in the situation
when the government, manufacturers and retailers set
their goals to maximize their own profits respectively.

To

improve

the

processing

enthusiasm

of

manufacturer, the government subsidies should be no
less than the loss when performing the lowest recycling
rate, i.e.

However, it will be usually affected by some

cm

s

constraints in practice, such as the lowest recycling rate

*
M

M

. The recycling subsidy fees can be

2

g

u cm

4f

fu 2

g

(16)

u of WEEE in China as mentioned above. That is to

On the contrary, when setting up a certain subsidy

say, manufacturers must set his recycling rate above u

criterion s , the upper bound of recycling rate achieving

so as to engage in WEEE recycling business, as well as

at no loss of manufacturer’s profits is

enjoy government subsidies.

cm

u

g + 4 fs
2f

3.2 Manufacturers’ response strategy to the

(17)

It seems that the government should give incentive

government’s subsidy criterion
3.2.1 The upper bound of recycling rate at no loss of

to manufacturers to collect and process at the upper

manufacturers’ profits

bound of recycling rate. Is it a reasonable practice?

When there is no recycling subsidy from the
government,

the

profits

of

manufacturer

is

Under this circumstance, we can get the social
welfare as follows

characterized by
max
w,bm ,u

d

G br

M

bm

cm

D p w cm

ch

his

( 14)

h

condition

'M
u

u*

cm g
2f

profits.

3d

From

the

2

g

16 f

a bcm

u*

cm

(15)

2

e
4

bh 7 a 7bcm

bh 8bC

(18)

production decision at the recycling rate u* to
maximize his profits. Social welfare can be denoted by

g

e+

recycling rate u . If u

cm

d

g

c
d

D p

w cm

h

+

16 f

*

u , the optimal decision of

cm

3d

g

c
4d

e
V
4
2

2

c
+
4d

16 f

a bcm

bh 7 a 7bcm

*

ds

cm

cm

g

w cm

h

e

fu

2

g

16 f

ds
cm
4

be denoted by
c
d

bh 8bC

(19)

Using Eqs. (18) and (19), we can obtain that

subsidies. Otherwise, the profits of manufacturer can

2

e
4

32b

manufacturer will not be affected by government

s u

2

2

2

4f

D p

s

Without subsidies, manufacturers will make the
0 , we can obtain that

it is required for manufacturers to process at the lowest

d

e
V
4

32b

When the government provides recycling subsidies,

M

c
4d

c
+
4d

first-order

The profit of manufacturer is
d

+

16 f

cm

*

*
M

2

g

cr

Manufacturers will choose the recycling rate to
maximize

cm

ch

2

+
cr

c
4d

e
4

c
d

The profits of manufacturer should be nonnegative,
i.e.

bm

cm

ch

cr

0 . Thus, we can get

*

,


as social welfare

is linear decreasing with the

3
s u cm
4

government subsidy.

Remark 1 When the government providing a

s u cm

g

certain recycling subsidy, if manufacturers performs at
3
=
4

the upper bound of recycling rate on the premise of
achieving no loss of his own profits, the social welfare

g
4f

2

fu 2 +

e
e

fu 2 +

c
d

c

d

2

+
V

s

2

c
+
d

e

+

cm

g
4f

2

+

c
d

e V

(21)

It needs to be analyzed through simulation on

is linear decreasing with the unit recycling subsidy of
WEEE and lower than that without government

cm

g

account of being unable to get a closed-form
expression.

subsidy.
It is because that when adding the unit recycling
subsidy of WEEE, the upper bound of recycling rate at

3.2.3 Government’s response strategy to the
manufacturers’ recycling rate
Government regulation policies are characterized by

no loss of manufacturers’ profit will increase as well
(from Eq. (17)). If performing at this rate, it will add
processing and remanufacturing cost to manufacturers’
operation, decreasing social welfare (from Eq. (10)).
Thus, it will make no benefit to social welfare when

relative stability and adaptable readjustment when
necessary. If manufacturers’ recycling rate is not up to
the expectation of the government, the government will
adjust WEEE recycling subsidy criteria: when the
recycling rate is low, he should improve the unit

pursuing the maximum of recycling rate.
How to choose a right recycling rate? It is
reasonable to maximize the recycling rate at no loss of

WEEE recycling subsidy fee to encourage WEEE
recycling. Conversely, he should reduce the subsidy fee
to a proper level to reduce the burden of government.

social welfare.
3.2.2 The WEEE recycling rate on the condition of
no loss of social welfare
Assume u '' as the recycling rate chosen by
manufacturers with a certain subsidy fee s . The social

That is to say, the unit WEEE recycling subsidy fee of
next stage si 1 has a negatively correlation with
manufacturers’ recycling rate at this stage ui . Assume
a linear relationship, namely
si

welfare can be characterized by

1

ui，

i 1, 2, , n

(22)

Where the sensitive degree of government is denoted
d
s u cm
4
3d
s u cm
4
a bcm

g
g

e
e

bh 7a 7bcm
32b

c
fu +
d
2

c
fu +
d

V

s

by

subsidy fee is denoted by . They are both optimally

2

2

determined through simulation analysis.

bh 8bC

(20)

4. NUMERICAL EXAMPLE

As the post-subsidizing social welfare should not be
less than that before subsidizing, the critical solution
goes to

=

*

We can get the relationship between u '' and s on the
condition of performing no loss of social welfare,
which is

and the upper bound of unit WEEE recycling

Take the production, recovery and processing of
refrigerators as an example. We assume that
a

7 107 , b

2.5 104 , c

7 105 , d

2 105 , e =23

0，f =1000，g =1200，h =6，cm =2300，C =40，V =0.6.
The initial recycling subsidy fee of WEEE for
manufacturer is that s1 =80, where ,

[100,150] .

4.1 Determine the optimal parameters of the
government response strategy

According to Eqs. (21) and (22), we simulate the
repeated game process between the government and
manufacturers in Matlab 7.0. When reaching an
equilibrium, i.e.
(
=0.01),
un un 1
manufacturers’ recycling rate un
parameter

and

changing with

is shown as Figure 3.

Figure 4 The repeated game process between the
government and manufacturers
Remark 3 When considering the condition that the
post-subsidizing social welfare should be no less than
that before subsidizing, there is a nonlinear relationship
between manufacturers' recycling rate and unit subsidy
Figure 3 The variation of recycling rate un with
parameter

and

for WEEE recycling. The recycling rate is fluctuating
in a certain interval (here is [45%, 65%]) with the

Remark 2 Along with the increasing of the sensitive

increasing of unit recycling subsidy. When the game

degree of government imposing on manufacturer's

achieving a convergence after dynamic adjustment, it

recycling rate, or adding the upper bound of unit

reaches the peak of the recycling rate (here is 65.01%),

WEEE

that is what we need.

recycling

subsidy

(subsidy

ceiling),

manufacturer's recycling rate performs as an oscillation
increasing trend when reaching the equilibrium in the
repeated game. Therefore, considering the condition

5. CONCLUSION

that the post-subsidizing social welfare should be no

We establish a WEEE CLSC consisting with a

less than that before subsidizing, the government

manufacturer, a retailer and a consumer group under

should choose a higher sensitive degree as far as

the government regulation, analyzing the repeated

possible, as well as the subsidy ceiling, to promote the

game

WEEE recycling.

manufacturers based on the cobweb theory. The main

4.2 The repeated game process between the

conclusion is summarized as follows.

process

between

the

government

and

(1) If manufacturers perform at the upper bound of

government and manufacturers
When =150and =150, manufacturers' recycling

recycling rate on the premise of achieving no loss of its

rate under an equilibrium reaches the peak, equals to

own profits, it will make no benefit to social welfare.

65.01%. According to Eqs. (21) and (22), we can

The loss of social welfare is increasing with the unit

obtain a repeated game process shown in Figure 4.

recycling subsidy of WEEE. It is resulted from adding
processing and remanufacturing cost to manufacturers’
operation and decreasing the social welfare. Therefore,
it is reasonable to maximize the recycling rate at no
loss of social welfare.


(2)

Considering

the

condition

that

the

economical sustainability of WEEE closed-loop supply

post-subsidizing social welfare should be no less than

chains with recycling: a system dynamics analysis”,

that before subsidizing, higher sensitive degree and

International Journal of Advanced Manufacturing

subsidy ceiling should be chosen by the government in

Technology, Vol.47, No.5-8, pp. 475-493.

the equilibrium of the repeated game to promote the

Hammond, D. and Beullens, P. (2007) “Closed-loop supply
chain network equilibrium under legislation”, European

WEEE recycling.

Journal of Operational Research, Vol.183, No.2,
pp.895-908.

ACKNOWLEDGMENTS

Hong, I.-H. and Ke, J.-S. (2011) “Determining Advanced

This research was supported by National Natural Science

Recycling Fees and Subsidies in “E-scrap” Reverse

Foundation of China (No.71103149), National Social

Supply Chains”, Journal of Environmental Management,

Science Foundation of China (No.07CJY019), Program for
New

Century

Excellent

Talents

in

University

(No.NCET-10-0706), Fund for Cultivating Academic and

Technological Leaders in Sichuan Province (No.2011-441),
Fundamental Research Funds for the Central Universities
(No.SWJTU11CX152), and the Grant-in-Aid for Asian
CORE

Program

"Manufacturing

and

Environmental

Management in East Asia" of Japan Society for the
Promotion of Science (JSPS).

Vol.92, No.6, pp.1495-1502.
Jen, S. T. (2007) The Optimal Economic Policy of
Governmental Involvement on the Performance of Green
Supply Chain, Master’s Thesis, National Chiao Tung
University.
Li, X. Q., Wu, Q. M., and Zhu, D. L. (2011) “A Multicommodity

Flow

Closed-

loop

Supply

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Equilibrium Model with Stochastic Demand” Systems
Engineering, Vol.29, No.10, pp. 51-57.
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