# Risk Assessment of UAV Cyber Range Based on Bayesian-Nash Equilibrium
## 6 Application and Analysis
According to \(R_{all}\), the calculation of the overall threat value of UAV \(R_{all}=0.729\), the threat level is divided into five levels according to [57], and the threat level of this system is judged to be level 4. Similarly, you can obtain the threat value when deploying other defense strategies. At the same time, this paper takes the absolute value of the revenue of the defense strategy and calculates the average value of the revenue of each defense strategy. In this case, the strategy with a small value is better, as shown in Figure 5.  
It is evident that when UAV range administrators choose \(b_{2}^{D}\) for strategic defenses, the resultant security risk value is notably minimized, concurrently aligning with a relatively equitable defense income function. This confluence enables managers to judiciously select and enact the optimal defense strategy by comparing threat values against the income function, thereby fortifying the UAV's security posture and curtailing potential security risks. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Mixed Strategy** & **Type of Attacker/Defender** &
\begin{tabular}{c} **Mixed Strategy Bayesian-Nash** \\ **Equilibrium Probability Distribution** \\ \end{tabular} \\ \hline \multirow{2}{*}{\(F_{A}^{*}(t_{A})\)} & Adventurous attacker & \(\{F_{1}^{A^{*}}(t_{A}),F_{2}^{A^{*}}(t_{A})\}=\{0.475,0.524\}\) \\ \cline{2-3}  & Conservative attacker & \(\{F_{3}^{A^{*}}(t_{A}),F_{4}^{A^{*}}(t_{A})\}=\{0.256,0.648\}\) \\ \hline \multirow{2}{*}{\(F_{D}^{*}(t_{D})\)} & High-level defender & \(\{F_{1}^{D^{*}}(t_{D}),F_{2}^{D^{*}}(t_{D})\}=\{0.603,0.327\}\) \\ \cline{2-3}  & Primary defender & \(\{F_{3}^{D^{*}}(t_{D}),F_{4}^{D^{*}}(t_{D})\}=\{0.421,0.583\}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Mixed strategy Bayesian Nash equilibrium. The methodology proposed herein demonstrates its practicality and efficacy through this analysis. Notably, we incorporate the principles of static game theory under conditions of incomplete information, meticulously accounting for the dynamic interplay between offensive and defensive maneuvers, alongside the inherent uncertainties that pervade their interactions. This approach yields a more authentic reflection of real-world applications, as it encapsulates the complexity and unpredictability intrinsic to risk landscapes. Considering the influence of different risk evaluation methods on the results, this paper analyzes the FAHP, Minimax Theorem, Nash equilibrium and Bayesian equilibrium. In the experimental environment, the Intel Xeon Gold 6230 20 core CPU is selected, Ubuntu 18.04 version is selected as the operating system, Pycharm is used as the development tool, and Python 3.6 version is adopted. The specific comparison of cyber security assessment in the UAV cyber range is shown in Figure 6, where (a) is the method of this paper, (b) FAHP [58], (c) Minimax Theorem [59], and (d) Nash equilibrium [60]. K indicates the change in information requirements of both sides. K = 4 indicates that an attacker and a defender possess 100% of each other's information. Similarly, K = 1 indicates that an attacker and a defender possess 25% of each other's information. It can be seen that in the scenario of random protection of security targets, in the Bayesian equilibrium method of the incomplete-information game introduced in this paper, when the information demand of both sides expands to 4, the security benefit can be maintained at a high level close to 1 when the attack benefit is lower than the investment cost. Different from the conservative and adventurous attackers of FAHP, the change in security benefit is less than 0.1 with the increase in information requirements of both sides. In the case of a system completely without Minimax Theorem and Nash equilibrium of information, the increase in security benefit is about 0.2 with the increase in information requirements of both sides.