Game Analysis of SME Financing

doi:10.4236/jfrm.2012.14011

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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

Game Analysis of SME Financing

Pingzhong Lin

School of Finance and Economics, Jimei University, Xiamen, China

Email: [email protected]

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:









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









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

National Inf ormation Shari n g Mechanism Must Be

rnments should promote the establishment of a national

Credibility Restraint Mechanisms Must Be Built

many

tim

siness relationship between

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-

P. Z. LIN

Perfecting the Judicial System and Improving

ic game between banks and enterprises

e of sound legal system and efficient

Strengthenin g Information E xchange and Prom oting

inancial system must be established and improved in

REFERENCES

Chen, Y., & Tang, Z. of commercial bank

Gijing: Renmin Uni-

tion database if the company defaults. When the defaulter reap-

plies for credit, he would face up to higher interest rate to make

up the cost of default, or even be rejected from financing. In the

long term, to be faithful is conductive to reduce the cost of

borrowing, maintain a good relationship between banks and

enterprises, and promote the company’s long-term development.

Banks can assess the borrower’s credit situation from historical

records and regulate the requirements on collateral accordingly.

Judicial Efficiency

The pattern of dynam

ill be changed by high transaction costs and inefficient judi-

cial process. This kind of allocation of resources is not effective.

Influenced by relatively minor loans and more expensive trans-

action costs, SMEs are more likely face credit crunch. Only by

being aware of the legal knowledge and judicial procedures,

adopting a proper attitude to the threat of bank can enterprises

make sensible decision.

Under the circumstanc

dicial process, the threat of honoring liability becomes more

credible for the SMEs. Thus, the result of game may turn out to

be a win-win state (Ghatak, 1999). In other words, enterprise

tends to fulfill the obligation. Both parties have benefit and

there is a Pareto Optimality.

the Long-Term Cooperation between Banks and

SMEs

The f

terprises to ensure financial information is truthful, accurate

and complete, enhance the transparency of financial informa-

tion. A good image should be established by means of passing

real and complete information to the bank through effective

way. From long-term perspective, cooperative relationship be-

tween banks and enterprises should be established. This rela-

tionship is helpful to reduce financing costs, increase credit

profits, evade credit risks, and enhance the competitiveness of

SMEs in China.

Y. (2001). Game analysis

credit. Studies of International Finance, 4, 23-28.

ao, H. Y. (2011). Western economics micropart. Be

versity of China Press.

Ghatak, M., & Timothy, G. (1999). The economics of lending with

joint liability: Theory and practice. Journal of Development Econo-

mics, 60, 195-228. doi:10.1016/S0304-3878(99)00041-3

off, K., & Joseph, E. S. (1990). Imperfect information andH rural credit

markets: Puzzles and policy. World Bank Economic Review, 4, 235-

250. doi:10.1093/wber/4.3.235

eps, M. R., & Wilson, R. (1982Kr). Reputation and imperfect informa-

tion. Economic Theory, 27, 253-279.

doi:10.1016/0022-0531(82)90030-8

u, L. X., Wang, J. T., & Yu, Z. W. (2005)L. Banks and SMEs credit

Zormation costs and informa-

game analysis. Jinan Finance, 3, 36-37.

hao, G. X. (2009). Bank and the game, inf

tion production efforts of commercial banks. Productivity Research,

22, 58-60.