American Journal of Industrial and Business Management, 2013, 3, 610-613
Published Online November 2013 (http://www.scirp.org/journal/ajibm)
http://dx.doi.org/10.4236/ajibm.2013.37071
Open Access AJIBM
CSR Based on Game Theory
Weixiao Zhu, Hongyan Li
College of Management, Shanghai University of Engineering Science, Shanghai, China.
Received October 10th, 2103; revised November 10th, 2013; accepted November 15th, 2013
Copyright © 2013 Weixiao Zhu, Hongyan Li. 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
In recent years, Corporate Social Responsibility (CSR) has gradually become a hot topic with the public’s increasing
concern. In th is stud y, authors br ief ly in troduce so me rev iews and concepts of CSR, and then combine the idea of Game
Theory and Matrix linear equations method to conduct an empirical analysis between enterprises with enterprises and
enterprises with government. By analysis, we find that it is very important for the development of enterprises in these
two parts: the fulfillment of social responsibility and the supervision of government. Finally, the authors also put for-
ward some suggestions to the fulfillment of CSR and hope to improve the poor sense of presence.
Keywords: Corporate Social Responsibility; Game Theory; Linear Equations Method
1. Introduction
Corporate Social Responsibility (CSR) doesn’t appear
very long, but it has caused an extensive attention in the
academic and practical field, which makes domestic and
foreign scholars study diligent. This fully shows that
CSR is of significant value in researching. By studying
the existed literature, we find that the formers’ research
from the perspective of game theory is not very much
and also not very comprehensive. This article intends to
introduce game theory into the study of CSR, and it uses
the relevant content to analyze the relationship between
enterprises with other enterprises and enterprises with
government in the process of fulfilling CSR. We can find
the intrinsic link among them, then deeply excavate fac-
tors that affect enterprise to fulfill the social responsibili-
ties. We find the underlying reasons for the low level of
CSR in China. Eventually we can propose the appropri-
ate measures. It is of great theoretical significance in
China’s enterprises actively fu lfilling the social responsi-
bility, building a harmonious society and implementing
the concept of scientific development.
From the point of enterprise’s own survival and de-
velopment, we introduce the fulfillment of CSR into the
framework of game theory. The concept of CSR is wide,
whether it is implemented or not and the extent of it all
are influenced by various stakeholders in making deci-
sions. Whether the government supervises CSR or not
and the intensity of it, as well as whether the staff is loyal
to the enterprise or not, whether the competitor fu lfills its
social responsibility or not and whether the consumer
buys the products of company or not, all have direct im-
pacts on the fulfillment of CSR.
2. Literature Review
2.1. CSR
Since 1924, Oliver Sheldon proposed the concept of CSR
for the first time; it has been widely concern ed b y all sec-
tors of society. He believed that enterprises do not only
have the economic ob ligations and legalities, but also as-
sume the social responsibility which beyond these obli-
gations. Y. Li et al. [1] proposed “the model of three le-
vels and four cores”, which gave a more complete, rigo-
rous and dynamic definition of CSR. Namely, “in a parti-
cular period of social development, the enterprise should
assume the economic, regulatory, ethical, voluntary chari-
table and other related responsibilities for its stakehol-
ders.” D. Lu [2] thought the connotation of CSR was that
“enterprise is a commercial org an ization and its go al is to
maximize shareholders’ interests, CSR assumes the res-
ponsibility of preserving and enhancing social welfare
value while in the pursuit of maximizing shareholders’
interests for the purpose.
In the aspect of method and model, L. Zhang et al. [3]
used Analytic Hierarchy Process study CSR; F. Wei et al.
[4] used Solow model; S. Mai et al. [5] used TOPSIS and
so on. But the research of it by game theory is less. This
paper tries to use the game theory to analyze the impor-

CSR Based on Game Theory 611
tance of fulfilling CSR.
2.2. Game Theory
Game theory studies how rational people choose the tac-
tics. Nash established the classic story of game theory
which called “Prisoner’s Dilemma”, this described the
establishment of non-cooperative game and equilibrium
solution, this is why it called “Nash equilibrium”. In this
story, the two prisoners chose to admit committing mur-
der, then two people all won the intermediate results of
pronounce judgment. If one of them confessed the mur-
der, and the other don’t, then the one who admitted would
be commuted a sentence, and another would be senten-
ced to ten years in prison.
In the game, if all participants have a dominant strat-
egy, it proves that the game will reach equilibrium on the
basis of the dominant strategy of all participants; this
equilibrium is called dominant strategy equilibrium. The
prisoner’s dilemma above mentioned “prisoner A confes-
ses, B confesses” is the dominant strategy equilibrium.
Prisoner’s dilemma reflects a profound problem: the
conflicts between individual ratio nality and group ration-
ality. Then you will need to introduce Nash equilibrium.
Nash equilibrium points that each participant in the game
convinces that in a given case of other participants’ cho-
sen strategy, the participant chooses the optimal strategy
in response to the opponent’s strategy.
3. The Analysis of CSR That Based on Game
Theory
3.1. Prisoner’s Dilemma of Two Enterprises with
No Government Involvement
The assumptions of basic model:
First: there are only Companies 1 and 2 in the market,
Companies 1 and 2 are “rational economic man”, they
are in pursuit of profit maximization, excluding emotional
factors;
Second: Companies 1 and 2 all faced incomplete and
asymmetric information, namely is any one firm does not
know another firm’s strategy in choosing;
Third: in the market, Companies 1 and 2 have two choi-
ces: bear the social responsibility or not;
Fourth: once Companies 1 and 2 make a decision, it
can not be changed. Therefore, we establish a payoff
matrix shown in the following Table 1, the first number
is the benefit of selecting Company 1, the second number
is the benefit of selecting Company 2.
If and , the benefits that companies not
fulfilling their CSR is greater than that companies do,
then two companies trap into Prisoner’s Dilemma. They
achieves Nash equilibrium in

(each party of
game gets the equilibrium in the strategy of game),
namely both of them do not fulfill their social responsi-
bility.
acbd
Table 1. The payoff matrix of the two companies.
Company 2
Fulfill Not fulfilling
Fulfill


,aa

,bc
Company 1Not fulfilling

,cb

,dd
Company’s behavior will produce external effects, in-
cluding external economies and external diseconomies.
External influence can be here and there, various activi-
ties of companies will produce external influence. The
effect produced by certain acts of CSR has the nature of
public product, and can not be ruled out by the circum-
stance that other enterprises, consumers or organizations
share their benefits without paying the cost, which is
called “free rider”. Thus we say, “It is the public goods’
nature of CSR activities that restricts companies from
undertaking their social responsibilities actively.”
3.2. The Analysis of Tactics’ Selection between
Government and Company in the
Disposable Game
The assumptions of basic model:
First: there are two participants in the model: company
and government;
Second: company is regarded as a “rational economic
man”, in pursuit of profit maximization; there is no in-
herent enthusiasm in undertaking social responsibility.
Government is regarded as a representative on behalf of
interests of the public. On the one hand government can
promote economic growth, on the other hand, it can bear
pressure from the public, and be required to supervise
companies to undertake CSR, such as improve the envi-
ronment in order to boost the quality of life;
Third: As shown in Table 2, companies are facing
with two choice: “bear social responsibility” or “not bear-
ing” during the game.
M
is the required cost of com-
pany’s undertaking CSR, assuming that if company un-
dertakes CSR, the government will get profits from this
part; is the cost of the government supervision,
N
F
is the fine, and
F
N; the first number is the benefit of
selecting the government, the second number is the bene-
fit of selecting the company.
We assume is the probability of government su-
pervision, is the probability of company’s undertak-
ing CSR, for a given “q”, the expected benefit of gov-
ernment supervision
p
q


1p

or without supervision


0p

are respectively as follows:

,dd If the government supervising, its expected benefit is





 
11, 1Wq MNqMFNq

 .
If the government does not supervise, its expected
benefit is


20,0 1WqMq q


 .
Open Access AJIBM

CSR Based on Game Theory
612
Table 2. The payoff matrix with the government’s involve-
ment.
Company
Fulfill

qNot fulfilling


1q

Supervise 
p
 ,
M
NM  , 
M
FNFM 
Government Without
supervision

1
p


,
M
M


0,0
If the benefit of whether the government supervises or
not is same, namely is , so
 
12
1, 0,WqW q

*qMFNMF

. If the probability of com-
pany’s undertaking social responsibility is greater than

M
FN MF , the government will choose not
to supervise; if the probability is less than

M
FN MF , the government will choose to
supervise; if the probability is exactly equal to

M
FN MF , the government can randomly
choose whether supervise or not.
For a given “p”, the expected benefits of company’s
undertaking social responsibility or not under-
taking are as follows:

1q


0q
If companies chose to undertake, its expected benefit
is
 


3,1 1WpMp Mp .
If companies chose not to undertake, its expected ben-
efit is .
 
4,00 1Wp FMpp 



If the benefit of whether the company undertakes or
not is same, namely is , so
 
34
,1 ,0Wp Wp

*pMMF. If the probability of government su-
pervision is less than

M
MF, the company will
choose not to undertake social responsibility; if the
probability of government’s supervision is greater than

M
MF, then the company will choose to undertake
social responsibility; if the prob ability is exactly equal to

M
MF, the company can randomly select whether
undertake or not. .
Therefore, the Nash equilibrium of mixed strategy is:
 
*, *,pqMM FM FNM F


,
namely the government is willing to supervise by the
probability of

M
MF, and company willing to
undertake the social responsibility by the probability of

M
FN MF . Through analyzing Nash equi-
librium, we find that game equilibrium solutions are
closely related with the cost of supervision, management
and fine. Visibly, the more the cost of supervision, the
lower the probability of company’s undertaking social
responsibility. Because company knows the government
will carry out a cost-effectiveness analysis rationa lly and
reduce the strength of supervision. The higher the cost of
management, the greater probability of company’s un-
dertaking social responsibility. If companies do not take
social responsibility they will bring bad social influence,
because they may be afraid of affecting reputation and
taking more social responsibility. The higher the fines,
the greater probability of company’s undertaking social
responsibility. Because the government thinks that com-
panies would be afraid of large fines, and be willing to
take social responsibility. So, in the disposable game,
companies and government choose not to supervise or
undertaking in a large extent, the two sides do not
achieve their optimal choice or profits maximization as a
whole. So Prisoner’s dilemma is still existed. The best
way to solve Prisoner’s dilemma is gaming repeatedly.
4. Empirical Study
4.1. Two Companies’ Prisoner’s Dilemma with
No Government Involvement
There are only Company 1 and Company 2 in the market,
and the payoff matrix of whether fulfill the responsibility
they face as follows (see Table 3):
Matrix


1
,,GSDA, is the strategy of Com-
pany 1, is the strategy of Company 2,
S
D1
A
is the pay
of the armor. 1
51
93
A






，taking a minimum from each
row and a maximum from each line, we can find there
exists the saddle point





22
*, *,3,3
ij
Sd Sd, the
game value *3
G
V

.
From Table 3, we know that the benefit that com-
pany’s not fulfilling the social responsibility is greater
than they do, so the two companies trap into Prisoner’s
Dilemma. They reached Nash equilibrium in, na-
mely both of them do not undertake their social respon-
sibilities.
)3,3(
4.2. The Analysis of Tactics’ Selection between
Government and Company in the
Disposable Game
We have surveyed a company and find that if company
undertakes CSR, then they should pay ten units, the cost
of government’s supervision is two units, the cost of
fines is three units. The payoff matrix with the govern-
ment’s involvement is as follows (see Table 4):
Matrix


2
,,GSDA，, taking a mini-
2
811
10 0
A 


mum from each row and a maximum from each line. We
can find there is no saddle point, namely, there is no so-
lution in the sense of pure strategy. At this time, we in-
troduce 22

matrix linear equations.
Suppose that the mixed strategy of government is


,1
x
x

,


0, 1x; the mixed strategy of company is


,1
y
y

,


0, 1y; the equations are as follows:


8101
x
xv



8111
y
yv


110 1
x
xv



100 1
y
yv
Open Access AJIBM

CSR Based on Game Theory
Open Access AJIBM
613
Table 3. Prisoner’s dilemma of two companies’ CSR.
Company 2
Fulfill Not fulfilling
Fulfill

5,5

1, 9
Company 1 Not fulfilling

9,1


3,3
Table 4. The payoff matrix with the government’s involve-
ment.
Company
Fulfill

qNot Fulfilling

1q

Supervise 
p
 8, 10  11,13
Government Without
supervision 
1
p


10, 10

0,0
We can solve that: 1013,11 13xy.
Therefore, the mixed strategy of government is

1013,313

, the mixed strategy of company is

11 13,213.
So, we can find that the government is willing to su-
pervise by probability of 10/13, and company willing to
fulfill the social responsibility by probability of 11/13.
This shows that it is still likely for government to super-
vise and company to und ertake the social responsibility.
5. Conclusions
From the perspective of game theory, undertaking social
responsibility for a long time is the optimal strategy of
company. But in the sho rt time, companies will choose a
low-cost way to get more profits, so the construction of
CSR must be based on the sustainable development. At
the same time, the government should strengthen the
supervision and improve the investment of social respon-
sibility by economic, regulatory and ethical means.
It is significant for company to undertake the social
responsibility, because it can implement the scientific
development concept of our country and build a harmo-
nious society. Combined with China’s current situation,
if we want to make enterprises much better, we should
fulfill our social responsibilities. It is the key to change
the idea of corporate and enable itself to realize that ful-
filling their social responsibility is not only the benefit
for society, but also for their rapid development. By do-
ing it, we can fundamentally solve the problems of ful-
fillment of CSR that is not in place. In the course of im-
plementation of CSR, the government should play a
watchdog role, and regulate corporate behavior through a
variety of proactive measures. Throughout the course of
the game, the government should grasp the performance
of company’s CSR and conduct mechanism innovation,
as well as encourage companies to undertake their social
responsibility conscientiously. While the enterprises are
in the pursuit of getting more benefits, they should also
have the courage to undertake the social responsibility,
establish a social responsibility-oriented corporate cul-
ture and a good corporate image, improve the moral con-
struction and transparency of the company, and strive to
be good company citizens. From the long-term perspec-
tive, the more social responsibility companies undertake,
the more benefits they will have. It is good for its devel-
opment if companies undertake more social responsibil-
ity.
6. Acknowledgements
This work is supported by the National Natural Science
Foundation of China under Grant 11101265 and 61075115,
Innovation Program of Shanghai Education Commission
under Gra nt 14ZZ157.
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