Journal of Financial Risk Management
2012. Vol.1, No.4, 64-67
Published
Online December 2012 in SciRes (http://www.SciRP.org/journal/jfrm) http://dx.doi.org/10.4236/jfrm.2012.14011
64
Game Analysis of SME Financing
Pingzhong Lin
School of Finance and Economics, Jimei University, Xiamen, China
Received July 31st, 2012; revised September 26th, accepted October 15th, 2012
The SMEs (small and medium-sized enterprises) play important role in the economy. However, the fi-
nancing problem is a big difficulty, which has plagued the SMEs’ development. Information asymmetry
is the main reason for the SMEs’ gaining funds so hard. The information asymmetry between banks and
enterprises is that banks do not know the operating conditions and credit situation of SMEs. Then, to
some extent, the banks are reluctant to support credit for businesses under the circumstance of lacking
appropriate information, resulting in a “credit crunch” behavior. Therefore, the main measures of solving
SMEs’ financing difficulty are to overcome the information asymmetry in the process of SME financing
by establishing effective information mechanisms, the credibility and restraint mechanisms, strengthening
the construction of credit rating agencies, and promoting the mutual exchange of information.
Keywords: Credit Crunch; Game; Information Asymmetry; Adverse Selection
Introduction
In financing activities, information asymmetry between
SMEs and investors is widespread. SMEs own relatively com-
plete information about their future profitability. Whereas, the
investors are often difficult to fully grasp the future profitability
of SMEs, which means that they have incomplete information
(Gao, 2011). This paper analyzes SMEs’ financing problem
from two perspectives: dynamic game of complete information
and dynamic game of incomplete information. On the basis of
the above analysis, it tries to identify the main reasons and vi-
able solutions to change the status quo in SME financing.
A Dynamic Game of Complete Information
The Game’s Basic Assumptions
1) The players: banks, small and medium enterprises. Both
banks and SMEs are rational “economic man”, whose pursuits
are maximizing their own interests;
2) If there were enterprises in default on a loan, an efficient
judicial system would safeguard the lender’s normal interests,
and the investigation cost of bank would be low and counted as
zero;
3) Both sides of the players conduct dynamic game. It means
that one party may act on camera according to the other party’s
action;
4) The players have the entire information about their own
possible benefit in each state during the game. In other words,
we are talking about a dynamic game of complete information.
The Process of Game Development
1) First, we assume credit market with complete information
is the ideal state. If borrowers were in debt default, an efficient
judicial system would solve the problem quickly. Meantime,
the investigation cost of bank is low and counted as zero.
The payoff matrix of bank and enterprise is:
a) If bank did not provide capital for SME, then both sides’
interests would be zero. The revenue collection is (0,0);
b) If bank provided capital for SME and the enterprise re-
turned the loan repayment in time, then the situation would be
win-win cooperation. The revenue collection is (+1,+1);
c) If bank provided capital for SME, the enterprise refused to
return the loan repayment and bank borne loss. Then the en-
terprise obtained interests exclusively and bank lost its principal.
The revenue collection is (+2,−1);
d) If bank provided capital for SME, the enterprise refused to
return the loan repayment and bank dun to enterprise. At this
point, the profit of company would be zero for its punishment,
because it did not fulfill its responsibilities. And bank’s in-
terests would be protected. The revenue collection is (0,+1).
We get the following Nash equilibrium: Bank provides ca-
pital to SME and the enterprise returns the loan repayment. The
revenue collection is (+1,+1), both participants in the develop-
ment process are beneficiaries, and the situation would be
win-win cooperation.
2) Due to information asymmetry, the above ideal state is
difficult to meet in our real life. Owing to SMEs with the char-
acteristics of lacking assets and collateral, banks cannot obtain
sufficient income by means of auction of mortgaged property
(Chen & Tang, 2001). Therefore, the only solution is to resort
to the judicial system. However, judicial system in China is
inefficient and expensive at present. The inefficient judicial
system is likely to make the bank cannot recover costs or pay
higher costs when the bank recourse to law after company de-
faults.
Therefore, we make the second assumption: we assume that
banks should pay high transaction costs when it resorts to the
judicial system after enterprise defaults. The transaction cost is
set to 0.5. So the bank’s interests is 0.5, the company’s interests
is 1.5 when the enterprise refused to return the loan repayment
and bank dun to the enterprise.
The payoff matrix of bank and enterprise is:
a) If bank did not provide capital for SME, then both sides’
interests would be zero. The revenue collection is (0,0);

P. Z. LIN
b) If bank provided capital for SME and the enterprise re-
turned the loan repayment in time, then the situation would be
win-win cooperation. The revenue collection is (+1,+1);
c) If bank provided capital for SME, the enterprise refused to
return the loan repayment and bank borne loss. Then the enter-
prise obtained interests exclusively and bank lost its principal.
The revenue collection is (+2,−1);
d) If bank provided capital for SME, the enterprise refused to
return the loan repayment and bank dun to enterprise. At this
point, the inefficient judicial system would make the company
still gain interests of 1.5, and the bank’s interests would be
protected to some extent as 0.5. The revenue collection is (+1.5,
+0.5).
Examine the pattern of this game between the bank and the
enterprise, we will find that the original equilibrium is broken.
The new Nash equilibrium should be (0,0). That is the banks
refused to offer money from the very beginning.
This phenomenon is not uncommon in real life. As a result of
Chinese judicial system’s inefficiency when it duns for ar-
rearage, bank can get back little money but pays high transac-
tion cost. In other words, the desired effect cannot be achieved
when bank pursuits debt recovery through the judicial system.
The expected return of dunning to enterprise, for the bank, is
less than debt recovery cost in this case. Then the bank tends to
not pursue the matter, and make its threat become incredible.
Therefore, when the company knows the bank's rational choice,
its best option is “deadbeat”. Thus, in order to avoid losses (−1),
banks would choose not to trust SMEs and retain principal
when they know the company would refuse to repay the debts.
The best choice of banks is not offer capital to SMEs. It is the
so called “credit crunch” when banks expected to lose their prin-
cipal. In this circumstance, Nash equilibrium of the dynamic
game between the bank and the SME becomes (0,0). At this
time, in order to guarantee its principal safe, the bank would
like to invest in large enterprises, who own less credit risk,
instead of SME (Lu, 2005). This is why SME loans accounted
for a relatively small proportion in total corporate loans.
Equilibrium Analysis
Through the above analysis of game, we know that bank
could not recover its lost totally in time when the enterprise
chose to break the contract. The bank inclined to select “credit
crunch”. Thus, SMEs cannot gain enough funds to obtain their
own development. At the meantime, standard financial system
has not been set up generally in SMEs, which makes banks face
extremely high costs of searching for business information of
SMEs. The small scale of most SMEs financing creates the
small income of bank. The bank’s cost-profit ratio (profits/costs,
costs include the cost of searching for information and the am-
ortized cost of non-performing loans of SMEs) from SMEs is
much lower than the one from large enterprises. Therefore,
bank credit funds flow to the large enterprises eventually.
Thence, standard financial system should be set up in SMEs to
overcome the information asymmetry in the process of SME
financing on the one side, and effective judicial system should
be established in society to increase the costs of breaking con-
tract on the other hand. Increasing bank’s cost-profit ratio from
SMEs would make part of bank credit funds flow from the
large enterprises to the SMEs. This process would not stop until
the two cost-profit ratios are equal. That is capital liquidity
maintains a balanced state.
A Dynamic Game of Incomplete Information
The Game’s Basic Assumptions
1) The players: banks, small and medium-sized enterprises.
SMEs are divided into two types: enterprises with good eco-
nomic efficiency and ones with poor economic efficiency. The
good ones can repay all the bank loans on time, whereas the
poor ones would make banks suffer losses.
2) The revenue of bank from offering capital is set to Rg, and
. The revenue of bank from offering capital to enter-
prises with good economic efficiency is set to R1, ; the
interests of enterprises who choose repudiation is set to R2,
; the revenue of bank from offering capital to enter-
prises with poor economic efficiency is set to Rb,
Rg 0
R2 0
R1 0
Rb 0

.
The Process of Game Development
1) Whether the SMEs apply for loans from banks or not in
this game.
Game tree can be used to represent this incomplete informa-
tion game. The second layer of this decision tree contains two
decision nodes, which means that information of business
situation owned by bank is incomplete. In other words, the
bank does not know which path reflects the true operating
situation of the SMEs. Then banks cannot make decision sepa-
rately according to the two different cases. There are three pos-
sibilities for the banks on the promise of the enterprises apply
for a loan. If banks choose to accept the application, they may
get a profit (enterprises with good economic efficiency) and
may suffer a loss (enterprises with bad economic efficiency). If
the banks choose not to accept the application, they would miss
the opportunity of gain. As a result, the banks need to assess the
probabilities of enterprises’ efficiency before they make the
decision.
R2 0
, means that enterprises with poor economic effi-
ciency can gain benefits through defrauding banks of funds.
Therefore, it is easy to know that enterprises will apply for a
loan whether they are in good or poor management state.
Whether the banks accept the SMEs’ application for loans or
not in this game.
On the promise of enterprises apply for a loan, we use


PGA stands for the conditional probability of enterprises
with good economic efficiency and

PBA

stands for the
conditional probability of the ones with bad economic effi-
ciency.


PG and


PB stand for the probabilities of enter-
prises in good and in bad management state respectively (both
probabilities only can be estimated by empirical data or general
knowledge from the average case).

PAG

and


PAB
stand for the conditional probabilities of enterprises in good and
in bad management state respectively when they apply for loans.
Based on the above analysis, we know:


PAGPAB 1


According to Bayes’ rule:
















PG|APGPA|G PGPA|G PBPA|B
From




PBA1 PGA , it is easy to find


PBA .


     

 



PGA
PGPAGPGPAG PBPAB
PG PG PBPG



P. Z. LIN
Similarly:




PBAPB
This means that the probability of enterprises in good ma-
nagement state on the market is equal to the one on the credit
market, and so do the probability of ones in bad management.
Since banks cannot know accurately the status of the busi-
ness application, they can only make decisions by calculating
the expected return E(R) based on the applicant’s probability of
management situation.
According to the banks’ experience and judgment, we set up:

PG p
So, on the promise of the banks accept the application, the
expected payment is:






ERpRg 1pRbRgRbpRb 
Conditions of banks choose to lend:




E RRgRbpRb0
Namely:




p
RbRg Rb
Accordingly, Conditions of banks choose not to lend:




E RRgRbpRb0
Namely:




PRbRgRb
This is a pooling equilibrium, means that banks would not
like to offer credit until there is an overwhelming majority of
enterprises with good economic efficiency. As a result, when
the probability that




PRbRgRb on the circumstance
of economic downturn and the overall social credit deteriora-
tion, the bank will refuse to provide capital to evade risks. This
“credit crunch” behavior makes the SMEs raise funds with
great difficulty.
Since it is difficult to see the




p
RbRg Rb con-
ditions on the average in reality, the banks mistrust the SMEs
even if
 
RbRg Rb is indeed smaller than p. That is, as
long as the banks think
 
PRbRgRb , they would
refuse the SMEs application for loans. This is a complete mar-
ket failure. Of course, market efficiency can be achieved par-
tially if the bank still takes mixed strategy (make decision with
a certain probability randomly) under the circumstance of lack-
ing confidence in the SMEs. In this case, the market is lack of
efficiency. This explains why SME loans accounted for a rela-
tively small proportion in total corporate loans, even there are
so many documents issued by the State Council and the CBRC
(China Banking Regulatory Commission) requiring banking
institutions to increase more loans for the SMEs. Apparently,
the incomplete information, under certain circumstances, in-
deed brings about a significant impact on the market efficiency.
In addition, in the case of asymmetric information, bank
needs to pay costs in the process of searching information. The
direct costs of information production include manpower cost,
fund cost, generating from the process of information searching,
screening, treating and processing, which directly affect the
economic efficiency of commercial banks credit activities. The
indirect costs of information production include the loss of
declining efficiency, the loss of decreasing service level and the
loss of reducing market share (Zhao, 2009). The level of infor-
mation costs is correlated positively with the degree of infor-
mation asymmetry. The higher degree of information asymme-
try is, the higher information cost is produced. Investors must
be requiring a higher return on investment as compensation.
The Way of Easing “Credit Crunch” from the
National Cr e Built
cy
is
National Inf ormation Shari n g Mechanism Must Be
rnments should promote the establishment of a national
in
Credibility Restraint Mechanisms Must Be Built
many
tim
siness relationship between
bu
above Analysis of Game
dit Rating Agencies Must Be
Nowadays, the development of Chinese credit rating agen
not standard. Banks can only search for SMEs’ information
from within, as a result of disbelieving rating results from credit
rating agency, which increases lending costs. In fact, rating by
professional credit rating agencies is much cost-effective than
establishing the credibility on the bank’s own. Therefore, go-
vernment should support the establishment of national profes-
sional rating agencies. Meantime, foreign large-scale rating agen-
cies should be introduced timely as well. These behaviors would
reduce the financial institutions’ high costs of organizing their
own rating of SMEs. Rational bank is willing to cooperate with
professional rating agencies to reduce its information costs for
SMEs. After the text edit has been completed, the paper is
ready for the template. Duplicate the template file by using the
Save As command, and use the naming convention prescribed
by your journal for the name of your paper. In this newly cre-
ated file, highlight all of the contents and import your prepared
text file. You are now ready to style your paper.
Built
Gove
formation sharing system of SMEs. This can increase the
SMEs’ loss of corporate defaults and cut financial institutions’
high costs of building their own information systems for SMEs,
and promote the development of the socioeconomic. Estab-
lishing and maintaining expenses of information systems can be
sponsored by banks, guarantee agencies, trusts, and private
equity funds. Financial institutions can identify the borrower’s
credit more effectively by taking advantage of shared informa-
tion systems. On the one hand, the contract breaching cost of
defaulter has been increased and the financing cost of trustwor-
thy person has been reduced; on the other hand, the selecting
costs of the bank before lending money has been cut down as
well. Then, the bank’s credit assets quality will increase as the
structure of information between banks and enterprises im-
proved. Credit risk can be controlled effectively and financial
stability can be maintained (Hoff, 1990).
Most SMEs hope they can obtain loans from bank
es in reality. According to reputation model of Kreps Mil-
grom and Wilson Roberts (1982), incomplete information can
lead to cooperative effects in finite repeated games. Because
both parties, in order to obtain long-term benefits from cooper-
ating, do not want to prematurely reveal their nature. Therefore,
only those enterprises, who do not want long-term development
will break contract prematurely.
In modern society, long-term bu
sinesses and banks should be constituted, especially for the
SMEs who pursue long-term development. In the case of re-
peated games, the poor credit record will be entered in informa-
66

P. Z. LIN
Perfecting the Judicial System and Improving
ic game between banks and enterprises
w
e of sound legal system and efficient
ju
Strengthenin g Information E xchange and Prom oting
inancial system must be established and improved in
en
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