## 3 Methods  
### Game Design and Description  
The three elements of the game system are as follows: (1) Players: The model only includes two interested subjects. A\({}_{1}\) represents the coal mining enterprises and A\({}_{2}\) represents local governments. Both players in the game are limited rational players and they choose their respective strategies based on the maximization of their respective safety perception benefits. (2) Strategy: The strategy space that coal mining enterprises can choose is A\({}_{1}=\) {full implementation, no implementation}, with probabilities \(p\) and \(1-p\), respectively. The strategy space that the local government can choose is A\({}_{2}=\) {strict regulation, deregulation}, with probabilities \(q\) and \(1-q\), respectively. (3) Income: This is determined by local government departments and coal mining enterprises to meet the valence account function \(V(x)\) and cost account function \(C(x)\) constructed based on the psychological account theory, which is expressed as follows:  
\[V(x)=\left\{ \begin{aligned} &\left(x-U_{0}\right)^{\theta},x\geq U _{0}\\ &-\lambda\left(U_{0}-x\right)^{\beta},x<U_{0}\end{aligned} \right. \tag{1}\]  
\[C(x)=\left\{ \begin{aligned} &\delta(x-U_{1})^{\varphi},x\geq U _{1}\\ &-\left(U_{1}-x\right)^{\sigma},x<U_{1}\end{aligned} \right. \tag{2}\]  
In the equations, \(U_{0}\) and \(U_{1}\) represent reference points of the value perception; \(\lambda\) represents valence loss avoidance sensitivity; and \(\beta\) and \(\theta\) represent the risk preference index of valence. \(\varphi\) and \(\sigma\) represent the risk preference index of cost, and \(\delta\) represents the sensitivity of cost loss avoidance. The greater the risk preference index, the more sensitive the risk perception. According to the random test results for the relevant parameters, it is found that the values of \(U_{0}\) and \(U_{1}\) are between 0.5 and 1.4. In order to ensure the accuracy of the calculations, we referred to the value of Tversky and used the median interval of 0.9 [41]. To calculate the mental account decision weight function \(\omega(\varepsilon)\), we used the following equations:\[\omega^{+}(\epsilon) =\frac{\epsilon^{r}}{\left[\epsilon^{r}+\left(1-\epsilon\right)^{r} \right]^{\frac{1}{r}}} \tag{3}\] \[\omega^{-}(\epsilon) =\frac{\epsilon^{i}}{\left[\epsilon^{i}+\left(1-\epsilon\right)^{ i}\right]^{\frac{1}{i}}} \tag{4}\]  
In Equations (3) and (4), \(\omega^{+}(\epsilon)\) represents the decision weight when there is a gain; \(\omega^{-}(\epsilon)\) represents the decision weight when there is a loss; \(r\) and \(i\) represent the decision influence coefficients; and the function is a monotone increasing function. In order to facilitate the subsequent equation derivation and calculation, according to the research of [PERSON], the unified \(\omega(\epsilon)\) was used instead; the parameter is denoted as r and we set its value at 0.75 [42]. The following model assumptions are proposed, based on the above three elements. **Hypothesis 1:**_Since the coal mining enterprise and the government mechanism take the obtained value function as the income target, all parameters involved in the value function are more significant than zero and are fixed [43]._  
**Hypothesis 2:**_The two sides of the game are mainly local government departments and coal mining enterprise groups, which have only limited rationality in the game process and conform to the value perception function \(E\) constructed based on the combination of prospect theory and mental accounting theory, i.e., the form of \(E=T(\Delta x)\)\(\omega(\epsilon)\)[44]._  
In addition, it is worth noting that only when the coal mining enterprises fully implement the intelligent mine construction, and the local government strictly supervises it, can the overall safety state be ensured, i.e., the safety risk cost is 0. Otherwise, there will be a risk, which is linear and transfers from one party to the other, and the transfer coefficient will vary from subject to subject [45].