## 4 Analysis of the Stability Strategy of Each Game Subject
### Stability Analysis of Equilibrium Point of Tripartite Evolutionary Game System

Table 4: Stability analysis of equilibrium points. In Scenario 1: When \(-C_{G}^{G}-R_{-U}\)>\(C_{S}^{G}-C_{G}\), it means that the loss of the local government choosing to negatively respond is less than the loss of choosing to actively respond. At this point, the local government's strategy is to respond negatively, and the system only has a stable point, \(O_{3}(0,1,0)\). When \(-C_{G}^{G}-R_{-U}\)>\(C_{S}^{G}-C_{G}\), there are \(C_{G}\)>\(R_{G}+R_{U}+C_{S}^{G}\), \(R_{S}^{G}+C_{G}\)>\(R_{G}+R_{U}\) and \(R_{S}^{G}+C_{G}\)>\(C_{G}^{G}+R_{-U}\). According to Table 4, it can be seen that Condition 1 is satisfied, while Conditions 2, 3, 4 and 5 are not satisfied. \(\square\)  
It can be seen from Scenario 1 that when the central government's punishment and the negative effects of the deterioration of the situation are small, or when the local government's punishment on green smart supply chain enterprises is small and the local government's active response cost is large, the local government actively responds and negatively responds. The returns of all are negative, and the strategy portfolio evolution is stable at (0, 1, 0). It can be seen that if the emergency response rules and regulations of the central government are not perfect, the local governments will choose to respond negatively, which will lead to the deterioration of the situation. The central government can prevent local governments from choosing to respond negatively by increasing penalties and incentives, which will be reflected in Scenarios 2 and 3. Based on China's governance during the COVID-19 pandemic, we can find that for local governments, the damage of poor governance is huge and irreversible. In reality, the local government does not choose to respond negatively, so the equilibrium point \(O_{3}(0,1,0)\) in Scenario 1 has no research value. In Scenario 2: When \(-R_{S}^{G}-C_{G}\)> \(-C_{G}^{G}-R_{-U}\) and \(C_{P}\)<\((1-\omega_{1})V_{AB}\), it means that the loss of the local government choosing to negatively respond is greater than the loss of choosing to actively respond. While local government's strategy is to respond negatively, and the public's strategy is to panic buy, the reason for this is the lack of credibility of the local government due to its weak response, and the system may have two stable points \(O_{7}(0,1,1)\) and \(O_{8}(1,1,1)\). (a) If the condition \(R_{S}^{G}-C_{S}\)<\(R_{SS}-C_{S}^{G}\) is added, the system achieves a unique stable point, \(O_{7}(0,1,1)\); (b) If the condition \(R_{S}^{G}-C_{S}\)>\(R_{SS}-C_{S}^{G}\) is added, the system realizes a unique stable point, \(O_{8}(1,1,1)\). When \(-R_{S}^{G}-C_{G}\)> \(-C_{G}^{G}-R_{-U}\) and \(C_{P}\)<\((1-\omega_{1})V_{AB}\), there are \(-C_{G}^{G}-R_{-U}\)<\(C_{S}^{G}-C_{G}\) and \(C_{P}\)<\((1-\omega_{1})V_{PB}\). According to Table 4, it can be seen that Conditions 1, 2 and 3 are not satisfied. If condition \(R_{S}^{G}-C_{S}\)<\(R_{SS}-C_{S}^{G}\) is added, Condition 4 is satisfied; if condition \(R_{S}^{G}-C_{S}\)>\(R_{SS}-C_{S}^{G}\) is added, Condition 5 is satisfied. \(\square\)  
From Scenario 2, it can be seen that when the central government's punishment and negative effects are large and the local government's coping cost and subsidies to green smart supply chain enterprises are small, it can effectively prevent the local government in Scenario 1 from choosing a negative coping strategy. Since the public's perceived benefits outweigh its panic buying costs, in the stable strategy combination of Scenario 2(a) and (b), the public will choose to panic buy. Scenario 2(a) is manifested in the fact that it often occurs in the misallocation of limited resources and funds of local governments, resulting in a strategic combination (0, 1, 1). Scenario 2(b) is quite different from reality, when local governments and green smart supply chain enterprises choose to actively respond. According to China's experience, the public's panic buying has been effectively suppressed at this time. Therefore, the equilibrium point, \(O_{8}(1,1,1)\) in Scenario 2(b) should be discarded.