Policy-oriented financing guarantee schemes are widely adopted in the world to alleviate the financing difficulties of small and medium-sized enterprises. However, the development level of policy-oriented financing guarantee market in China has not reached the desired high-level equilibrium target, even though governments have issued a series of guiding policies. Accordingly, based on the evolutionary game theory, this study establishes and analyzes the game model between local governments, guarantee institutions, and banks. Then, the breakthrough effects of different paths on the low-level equilibrium of the guarantee market are simulated. The results show that strengthening superior government's performance appraisal intensity can only partially delay the “window period” of the low-level equilibrium, while adjusting local governments' compensation coefficients or increasing banks' risk sharing ratio have further synergistic effects on the realization of the high-level equilibrium. Additionally, dynamic reward and penalty mechanism of the local governments can effectively restrain the unbalanced state of financing guarantee market caused by banks' excess compensation risk, and finally impel the stabilization of the high-level equilibrium state.

Although local governments have issued relevant reward and penalty policies, there are still problems of medical waste disposal in China, particularly in light of the special situation of the COVID-19 pandemic. Furthermore, these problems are generated in the game between local governments and disposal enterprises. Accordingly, based on the evolutionary game theory, this paper establishes and analyzes the game system between local governments and disposal enterprises under four modes: static reward and static penalty, dynamic reward and static penalty, static reward and dynamic penalty, and dynamic reward and dynamic penalty. The theoretical analysis is verified through numerical simulation of a medical waste disposal case in China. The results showed that when local governments choose the static reward and static penalty mode, the game system hardly always has an evolutionary stable state, and the dynamic reward or dynamic penalty mode can make up for the shortcomings of the static reward and static penalty mode. The static reward and dynamic penalty mode is considerably better than the other two dynamic reward and penalty modes, which has the best effect on improving the quality of medical waste disposal. Additionally, if the reward or penalty increases dynamically, local governments tend to implement a “relaxed supervision” strategy, and disposal enterprises will still improve the disposal quality of medical waste. The suggestions proposed based on the research conclusions offer some enlightenment for policymakers to formulate reasonable reward and penalty measures.

Financing guarantee is an important means and key link to solve the financing difficulties of small- and medium-size enterprises (SMEs). However, while financial guarantees alleviate the financing difficulties of SMEs, the complex guarantee relationships also constitute a new channel for credit risk contagion in the financial guarantee network. In this paper, we construct a model of credit risk contagion process of guarantee network based on SEIR and analyse the equilibrium point and stability of the model. Then, we find the threshold value of risk contagion and further simulate the SEIR model dynamically to analyse the influence of each parameter of the model. The results show that the risk of the financing guarantee network begins to be widely contagious only when risk contagion threshold is greater than 1, and the conversion rate of exposed enterprises, removal rate of infected enterprises, nodal enterprises degree, and risk contagion rate have significant effects on the changes of individual density of susceptible, exposed, infected, and recovered enterprises. Combining the above findings, it is of great theoretical and practical significance to propose relevant countermeasures for credit risk control of financial guarantee network.