## 3 Evolutionary Game Theoretical Model
### Model Calculation and Stability Analysis
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multirow{2}{*}{**Conditions**} & \multirow{2}{*}{**Determinant**} & \multicolumn{6}{c}{**Equilibrium Point**} \\ \cline{3-8}  & & & **(0, 0)** & **(1, 0)** & **(0, 1)** & **(1, 1)** & **(x\({}^{a}\), \(y^{a}\))** \\ \hline \multirow{4}{*}{1} & \(\Delta<cL_{u}\) & _det_ & \(+\) & \(-\) & \(-\) & \(+\) & \(-\) \\  & \(B<C_{2}+(c-d)L_{c}\) & _tr_ & \(-\) & \(\pm\) & \(\pm\) & \(+\) & 0 \\  & \(C_{2}+(c-d)L_{c}>0\) & Stability & ESS & Saddle point & Saddle point & Unstable & Center \\  & & & & & & & point & point \\ \hline \multirow{4}{*}{2} & \(\Delta<cL_{u}\) & _det_ & \(+\) & \(-\) & \(-\) & \(+\) & \(-\) \\  & \(B>C_{2}+(c-d)L_{c}\) & _tr_ & \(-\) & \(\pm\) & \(\pm\) & \(+\) & 0 \\  & \(C_{2}+(c-d)L_{c}>0\) & Stability & ESS & Saddle point & Saddle point & Unstable & Center \\  & & & & & & point & point \\ \hline \multirow{4}{*}{3} & \(\Delta<cL_{u}\) & _det_ & \(+\) & \(+\) & \(-\) & \(-\) & \(+\) \\  & \(B>C_{2}+(c-d)L_{c}<0\) & _tr_ & \(-\) & \(+\) & \(\pm\) & \(\pm\) & 0 \\  & \(C_{2}+(c-d)L_{c}<0\) & Stability & ESS & Unstable & Saddle point & Saddle point & Center \\  & & & & & point & point & point \\ \hline \multirow{4}{*}{4} & \(cL_{u}<\Delta<dL_{u}\) & _det_ & \(+\) & \(-\) & \(+\) & \(-\) & \(+\) \\  & \(B<C_{2}+(c-d)L_{c}\) & _tr_ & \(-\) & \(\pm\) & \(+\) & \(\pm\) & 0 \\  & \(C_{2}+(c-d)L_{c}>0\) & Stability & ESS & Saddle point & Unstable & Saddle point & Center \\  & & & & & point & point & point \\ \hline \multirow{4}{*}{5} & \(cL_{u}<\Delta<dL_{u}\) & _det_ & \(+\) & \(-\) & \(+\) & \(-\) & \(+\) \\  & \(B>C_{2}+(c-d)L_{c}\) & _tr_ & \(-\) & \(\pm\) & \(+\) & \(\pm\) & 0 \\  & \(C_{2}+(c-d)L_{c}>0\) & Stability & ESS & Saddle point & Unstable & Saddle point & Center \\  & & & & & point & point & point \\ \hline \multirow{4}{*}{6} & \(cL_{u}<\Delta<dL_{u}\) & _det_ & \(+\) & \(+\) & \(+\) & \(+\) & \(-\) \\  & \(B>C_{2}+(c-d)L_{c}\) & _tr_ & \(-\) & \(+\) & \(+\) & \(-\) & 0 \\  & \(C_{2}+(c-d)L_{c}<0\) & Stability & ESS & Unstable & Unstable & Unstable & Saddle point & Center \\  & & & & point & point & point \\ \hline \multirow{4}{*}{7} & \(\Delta>dL_{u}\) & _det_ & \(-\) & \(+\) & \(+\) & \(-\) & \(-\) \\  & \(B<C_{2}+(c-d)L_{c}\) & _tr_ & \(\pm\) & \(-\) & \(+\) & \(\pm\) & 0 \\  & \(C_{2}+(c-d)L_{c}>0\) & Stability & Saddle point & ESS & Unstable & Saddle point & Center \\  & & & & & point & point \\ \hline \multirow{4}{*}{8} & \(\Delta>dL_{u}\) & _det_ & \(-\) & \(+\) & \(+\) & \(-\) & \(-\) \\  & \(B>C_{2}+(c-d)L_{c}\) & _tr_ & \(\pm\) & \(-\) & \(+\) & \(\pm\) & 0 \\  & \(C_{2}+(c-d)L_{c}>0\) & Stability & Saddle point & ESS & Unstable & Saddle point & Center \\  & & & & point & point & point \\ \hline \multirow{4}{*}{9} & \(\Delta>dL_{u}\) & _det_ & \(-\) & \(-\) & \(+\) & \(+\) & \(+\) \\  & \(B>C_{2}+(c-d)L_{c}\) & _tr_ & \(\pm\) & \(\pm\) & \(+\) & \(-\) & 0 \\ \cline{1-1}  & \(C_{2}+(c-d)L_{c}<0\) & Stability & Saddle point & Saddle point & Unstable & ESS & Center \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Determination of potential equilibrium points in different scenarios. Among them, the proportion of the population at \(D_{1}\) (0, 0) and \(D_{4}\) (1, 1) is related to the critical point \(D_{5}\) (\(x^{*},y^{*}\)). **Proposition 4**. : _When the conditions are those in Scenarios 7 to 8, \(D_{2}\) (1, 0) is an ESS, and users and OHCs will choose (disclosure, negative protection)._  
In these scenarios, since the sum of the benefits obtained by the user disclosing private personal information is greater than the sum of the costs under the \"negative protection\" strategy, i.e., \(\Delta>dL_{u}\), the users will tend to disclose personal information (\(x\to 1\)). Moreover, no matter how much benefit users can bring to the OHCs by disclosing their private information, as long as the additional cost is greater than the reduced expected loss of the lowered privacy risk, i.e., \(C_{2}+(c-d)L_{c}>0\), the OHCs will tend to choose to implement the \"negative protection\" strategy (\(y\to 0\)).