China
's financial system is dominated by banks, and bank credit is the primary source of corporate financing. However, there is a serious information asymmetry between banks and enterprises. According to the classic microcosmic banking theory, information asymmetry between banks and enterprises will lead to moral hazard and adverse selection problems. Therefore, in the bank credit market, when small and medium-sized enterprises need financing, they need to first transmit their own information to the bank to reduce the uncertainty of business development and improve the information asymmetry between them and financial institutions. However, for financial institutions, not only can they not fully grasp the profitability, credit level, operating conditions and other information of small and medium-sized enterprises, but also cannot fully distinguish the authenticity of the information they have obtained. Compared with the amount of loans, their risk control The cost is too high, so small and medium-sized enterprises generally have the problem of difficult and expensive financing.
1. Model background and variable setting
Due to the information asymmetry between SMEs and financial institutions, SMEs know that financial institutions will decide to grant loans to SMEs through the signals (high and low risk signals) sent by enterprises. SMEs can whitewash the type of signals sent, but However, financial institutions cannot accurately distinguish the authenticity of the signals transmitted by small and medium-sized enterprises.
Although high-risk companies may not meet the characteristics of low-risk companies, they may imitate low-risk companies to generate low-risk signals in order to obtain bank loans, and low-risk companies can easily send low-risk signals, and banks determine based on risk signals Whether to lend money. Whether an enterprise is a high-risk enterprise or a low-risk enterprise is the private information of the enterprise. The bank does not know it. It can only determine whether to lend money based on the signals sent by the enterprise. In summary, this is a dynamic game with incomplete information. Basic features of the game. Based on the theory of information asymmetry, this paper constructs a signal game model between small and medium-sized enterprises and financial institutions. Based on the theoretical basis of performance, the method of reducing adverse selection in lending is analyzed through equilibrium results. In order to study the financing decision-making game between SMEs and financial institutions more intuitively, consider the accounts receivable pledge model that does not require core enterprises to participate in the transfer of accounts receivable creditor's rights.
Suppose the financing amount of SMEs is R, the value of financing collateral is X (X>R), and the bank loan interest rate is i. The return on investment of low-risk small and medium-sized enterprises after obtaining financing from accounts receivable is r sl , and the return on investment of high-risk small and medium-sized enterprises after obtaining financing from accounts receivable is r sh . According to the no-arbitrage criterion, the risk is directly proportional to the return, so r sl < r sh . After SMEs get loans, the probability of repayment for low-risk SMEs is p sl , and that of high-risk SMEs is p sh . Since high-risk enterprises are more likely to default, p sh < p sl is set . The costs of falsifying information for low-risk enterprises and high-risk enterprises are respectively C L and CH , which include data falsification costs, penalty costs and reputation costs after being discovered afterwards. The marginal credit review cost of financial institutions is Q. The default loss of SMEs is M, the incentive for keeping promises is K, and r f is the risk-free interest rate.
2. Construction of signal game model
The signal generator of this game is a small and medium-sized enterprise, and the signal receiver is a financial institution. The time sequence of the game is as follows:
(1) According to the principle of Harsanyi conversion, enterprises are naturally divided into two categories according to the probability of enterprise distribution, the probability of low-risk enterprises is r, and the probability of high-risk enterprises is 1-r;
(2) The generator (small and medium-sized enterprises) observes its own type, and then selects a signal from the feasible signal set {high-risk information, low-risk information} to send.
(3) The receiver (financial institution) observes the information sent by the sender, and then chooses an action from the feasible action set {loan, no loan}.
The bank's income from lending to low-risk enterprises is p sl Ri+(1-p sl )(XR)-Q, and the income from not lending is Rr f ; the bank's income from loans to high-risk enterprises is p sh Ri+(1-p sh ) (XR)-Q, the benefit of not lending is Rr f . The bank's income from lending to high-risk enterprises is smaller than the income from not lending to low-risk enterprises. Equation (1):
After transforming Equation (1), Equation (2):
So when Q<p sh R(ir f ) must There is formula (3):
For a low-risk enterprise, the income of getting a loan when it sends a low-risk signal is p sl (R(r sl -i)+K)+(1-p sl )(R(1+r sl )-MX), The return of not being allowed to take out a loan is 0; the return of getting a loan when a high-risk signal occurs is p sl (R(r sl -i)+K)+(1-p sl )(R(1+r sl )-MX)-C L , the benefit of not being able to lend is -C L .
For a high-risk enterprise, the income obtained from the loan when it sends a high-risk signal is p sh (R(r sh -i)+K)+(1-p sh )(R(1+r sh )-MX), The income of not being allowed to take out a loan is 0; the income of getting a loan when a low-risk signal occurs is p sh (R(r sh -i)+K)+(1-p sh )(R(1+r sh )-MX)-C H , the disbursement not to be loaned is -C H .
Considering the determination of the optimal strategy of the participants under the equilibrium path and the non-equilibrium path, a more refined Bayesian equilibrium can be obtained. Therefore, the refined Bayesian equilibrium solution of the signal game should meet three conditions: 1) financial institutions There is an inference (belief) about the probability of the appearance of SME signals. This inference must conform to Bayesian rule, which is a posterior probability, that is, the prior probability is corrected according to the information set where it is located; 2) Under the condition of posterior probability, Financial institutions should maximize their utility; 3) Given the financial institution's strategy, SMEs should maximize their own utility. There are three types of equilibrium solutions for dynamic games with incomplete information: separation equilibrium, pooling equilibrium and quasi-separation equilibrium. The research in this section only has two signals and two types. Therefore, the refined Bayesian equilibrium does not need to consider the quasi-separation equilibrium. Therefore, this paper only analyzes Mixing Equilibrium and Separating Equilibrium.
3. Mixed Equilibrium Analysis
The mixing equilibrium of the signal game model has two situations, one is that both high-risk companies and low-risk companies are mixed with low-risk signals, and the other is that high-risk companies and low-risk companies are both mixed with high-risk signals. The latter situation lacks practical application value, that is, low-risk companies have no motivation to send high-risk signals, so this article mainly discusses that both high-risk companies and low-risk companies send low-risk signals.
However, when the game is mixed with low-risk signals, that is, high-risk companies and low-risk companies both choose to send low-risk signals. At this time, financial institutions can only choose the following two situations: 1) receiving low-risk signals for loans; 2) receiving low-risk signals No loan for low risk signal;
At the same time, in the case of confounding equilibrium, the posterior probability is equal to the prior probability. Since high-risk enterprises and low-risk enterprises both choose to send low-risk signals, that is, the signals sent by small and medium-sized enterprises are risky for financial institutions to identify financing enterprises. There is no benefit, and the signal cannot assist financial institutions to make better judgments, so the posterior probability of encountering a low-risk enterprise is still the prior probability r, and the posterior probability of encountering a high-risk enterprise is still the prior probability 1-r.
Let low-risk enterprises send low-risk signals to obtain loans. The income is A=p sl (R(r sl -i)+K)+(1-p sl )(R(1+r sl )-MX), and let high-risk enterprises The return of the enterprise to send a high-risk signal to obtain a loan is B=p sh (R(r sh -i)+K)+(1-p sh )(R(1+r sh )-MX).
(1) Both low-risk and high-risk financial institutions issue loans
In the case of the above posterior probability, the bank's strategy needs to satisfy formula (4):
The optimal strategy of a given bank is to receive both high-risk and low-risk signals to lend money. At this time, high- and low-risk companies choose to send low-risk signals, and the utility of sending low-risk signals is greater than the utility of sending high-risk signals, that is, satisfying the formula (5):
(2) Financial institutions with low-risk signals and high-risk signals do not issue loans
In the case of the above-mentioned posterior probability, the bank's strategy needs to satisfy formula (6): the
optimal strategy of a given bank is to receive high and low risk signals and not issue loans. At this time, both high and low risk companies choose to send low risk signals , it should be satisfied that the utility of sending low-risk signals is greater than the utility of sending high-risk signals, that is, satisfying formula (7):
China’s credit reporting system was gradually established in 2003. After more than ten years of continuous development, with the access to the credit reporting system The number of institutions continues to grow, and China's credit reporting system is becoming more and more perfect. At the same time, due to the characteristics of blockchain technology, the cost of default will be greatly increased. Therefore, in real life, the cost of falsifying information for low-risk enterprises and high-risk enterprises are respectively C L and C It is impossible for H to be less than 0, but it can be seen from formula (5) and formula (7) that in the first case discussed in this paper, in order to achieve the mixing equilibrium, C L >0 and CH < 0 are unrealistic, so in In today's real life, it is impossible to achieve the mixing equilibrium discussed in the first case. Confusion equilibrium can only exist in the initial stage of the construction of my country's credit reporting system. At that time, it was difficult for financial institutions to find out whether small and medium-sized enterprises forged information, and the penalty cost after the event was very low, and the information between financial institutions was not perfect.
4. Separation Equilibrium Analysis
The separation equilibrium of the signal game model has two situations. The first separation equilibrium is that low-risk enterprises choose to send low-risk information, and high-risk enterprises choose to send high-risk information; the second separation is that low-risk enterprises choose to send high-risk information. High-risk businesses choose to send low-risk messages. Obviously, the second case lacks economic rationality and practical significance. Therefore, this section only studies the conditions for the existence of the first kind of separating equilibrium.
In the case of the first separation equilibrium, since this paper discusses the financing of small and medium-sized enterprises under the supply chain finance endowed by the blockchain, the purpose is to solve the financing of small and medium-sized enterprises with various types of risks, so it is meaningful that the bank is willing to pay high Both venture companies and low-risk companies make loans, so this article only discusses this situation, and analyzes whether the empowerment of blockchain can make the decision-making of financial institutions and small and medium-sized enterprises reach Bayesian refined equilibrium.
In a meaningful separation equilibrium, when the bank receives low-risk information, the bank can judge it as a low-risk enterprise, and when it receives high-risk information, it can judge a high-risk enterprise. Therefore, at this time, banks are willing to lend to high-risk enterprises and low-risk enterprises and must satisfy formula (8) and formula (9):
Under the above-mentioned posterior probability and the strategy selected by the bank, the optimal strategy of a given bank is to receive both high-risk and low-risk signals to issue loans. At this time, low-risk companies choose to send low-risk signals, and high-risk companies choose to send high-risk signals. should satisfy formula (10):
With the development of blockchain technology, various information of enterprises can be recorded on the blockchain, and at the same time, various information transmitted by enterprises to banks can also be recorded through the blockchain. Based on the characteristics of the blockchain, the information recorded on the blockchain is difficult to tamper with and in future transactions, other financial institutions can browse the company's information on the blockchain through the public key. Therefore, the blockchain will affect the lending behavior of small and medium-sized enterprises from the dual perspectives of adverse selection and moral hazard. First, since the information published by small and medium-sized enterprises to financial institutions will be recorded on the blockchain, if companies publish false or forged information to defraud loans , based on information that is difficult to tamper with and transparent, the enterprise will suffer huge reputation costs in the future lending and financial markets; secondly, after each transaction is completed, the financial institution will record the repayment of the enterprise in the block On the chain, it will cause enterprises to be less willing or afraid to default after obtaining financing, and reduce the motivation of enterprises to default on fraudulent loans. If the enterprise defaults, the enterprise will pay a huge reputation cost. Therefore, regardless of low-risk enterprises or high-risk enterprises, the cost of falsifying or tampering information also increases significantly. Therefore, due to the increasingly perfect credit information system and blockchain empowerment, formula (8) is satisfied. At the same time, for formula (10), formula (11) can be obtained after transformation:
let f be formula (12) 
and take the derivative of f in formula (12) with respect to R, and obtain formula (13): take the derivative of 
f with p sl to get Equation (14):
After connecting to the blockchain platform, the marginal credit audit cost of financial institutions is approximately 0, that is, Q=0. Combined with formula (3), it can be seen that f '(R) is an increasing function, and f '(p sl ) is a decreasing function.
Therefore, with the empowerment of blockchain technology, the more times the accounts receivable are split and transferred in the supply chain, it just meets the "short, small, frequent, and urgent" financing needs of small and medium-sized enterprises. For many small and medium-sized enterprises at the end of the supply chain, the amount of accounts receivable split is small, and it can be seen from formula (13) that formula (8) is easier to satisfy.
From the game analysis between small and medium-sized enterprises and core enterprises in the previous section, it can be seen that the empowerment of blockchain has a positive incentive effect on SMEs’ trustworthy repayment, that is, SMEs have a higher willingness to repay. Therefore, it can be seen from formula (14) that formula ( 8) Easier to satisfy. At the same time, the smaller the loan amount R is, the greater the repayment willingness of the enterprise is. At this time, the smaller f is, the lower the loan interest rate i can also make the formula (8) valid. Therefore, in supply chain finance empowered by blockchain, it is easier for financial institutions and small and medium-sized enterprises to achieve a separation equilibrium. At this time, high-risk small and medium-sized enterprises send high-risk signals, and low-risk enterprises send low-risk signals. Banks choose to lend to both . At the same time, when banks can clearly identify SMEs with different risk types, financial institutions can conduct differentiated pricing.
Summarize
For small and medium-sized enterprises and financial institutions, this paper constructs a signal game model between small and medium-sized enterprises and financial institutions based on the theory of information asymmetry. Clearly identify SMEs with different risk types.