# Risk Assessment of UAV Cyber Range Based on Bayesian-Nash Equilibrium
## 3 Application of Attack-Defense Tree Model in UAV Cyber Range
### Quantification of Strategic Benefits of Both Sides
#### 3.2.2 Defense Payoff Function  
An important attribute is assigned to each defense measure of the attack-defense tree, defense payoff function (_DPF_), which represents the expected income after spending a certain cost on a specific attack event and deploying corresponding defense measures during the offensive and defense game in the UAV cyber range, as shown in the following formula.  
\[DPF=\frac{ALE_{uw}\times RM-C}{C} \tag{2}\]  
where \(ALE_{uw}\) indicates the economic loss that may be caused by the potential information security risk of the UAV cyber range, which is related to the asset value, the percentage of asset value loss after the threat is generated, and other factors. The rate \(RM\) at which the risk of an attack on a UAV system is reduced due to the deployment of a defensive measure at a UAV range ranges from 0 to 1. \(C\) represents the cost of deploying a defensive measure. Specifically, the formula symbols are expressed in Table 1.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Content** \\ \hline _APF_ & Attack payoff function \\ \hline \(G\) & The gain an attacker expects from a successful attack \\ \hline \(cost_{a}\) & The cost to the attacker to carry out the attack \\ \hline \(RM\) & The rate at which the risk of an attack on a drone system is reduced due to the deployment of a defensive measure at the drone range \\ \hline \hline \end{tabular}
\end{table}
Table 1: Meaning of offensive and defensive strategy formula.  
Construct the Game Model of Attack and Defense of UAV Cyber Range with Incomplete Information Static  
Game theory [54] is an important mathematical theory for the study of confrontation or competition in the economic field. Based on game model analysis, it can infer the strategic choices of participants. In the UAV cyber range, the attacker attacks the risk of the UAV, and the defender deploys defense strategies for the possible threats of the UAV, forming an offensive and defensive game between the two. Based on the attack and defense game of UAV cyber range, this paper constructs a static game model of incomplete information to evaluate UAV security, considering the uncertainty of information between attack and defense. The content expressed by the formula symbol is shown in Table 2.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Content** \\ \hline \(A\) & Attacker atomic attack set \\ \hline \(D\) & Defense behavior set \\ \hline \(N_{A}\) & Attackers at the UAV range \\ \hline \(N_{D}\) & Defenders at the UAV range \\ \hline \(T_{A}\) & A collection of attack types, such as internal attacks, external attacks, and espionage \\ \hline \(T_{D}\) & A collection of defense types, such as security experts, security analysts, and security operations personnel \\ \hline \(B_{A}\) & Aggressive behavior of game players, such as DoS, backdoors, fuzzers \\ \hline \(B_{D}\) & Defensive behavior of game participants, such as identity authentication, transmission encryption, intrusion detection \\ \hline \(P_{A}\) & In the case of type \(t_{A}\), the attacker determines the probability of the defender’s type \(t_{D}\) \\ \hline \(P_{D}\) & In the case of type \(t_{D}\), the defender determines the probability of the attacker’s type \(t_{A}\) \\ \hline \(U_{A}\) & The attacker’s payoff function \\ \hline \(U_{D}\) & The defender’s revenue function \\ \hline \(S_{A}(t_{A})\) & The attacker’s pure policy set under the type \(t_{A}\in T_{A}\) \\ \hline \(F_{D}(t_{D})\) & Defender mixed strategy probability distribution \\ \hline \(F_{A}(t_{A})\) & Probability distribution of attacker mixed strategy \\ \hline \(S_{m}^{A}(t_{A})\) & The attacker’s pure strategy \\ \hline \(R_{i}\) & The threat value of unmanned aerial systems inside the UAV range \\ \hline \(R_{all}\) & The overall security risk value of drones \\ \hline \(W\) & Weight vector \\ \hline \hline \end{tabular}
\end{table}
Table 2: The meaning of game strategy model formula.