# Unveiling the Shadows--A Framework for APT's Defense AI and Game Theory Strategy
## 5 Conceptual Framework
### Game Strategy (Stackelberg Game Model for Cyber Defense)  
To determine optimal defensive responses, the interaction between attacker and defender is formalized using a Stackelberg game framework (Table 4), where the defender commits to a strategy anticipating potential attacker moves. \begin{table}
\begin{tabular}{l} \hline \hline Isolation forest algorithm for anomaly detection \\ \hline \# Applying Isolation Forest for Anomaly Detection \\ iso\_forest \textless{}- isolation.forest(data[,1:3], \text{ntrees}=100\), sample\_size \(=256\) \\ \# Predict anomaly scores \\ data\$score \textless{}- predict(iso\_forest, \text{newdata}=\text{data[,1:3], \text{type}=\"score\")} \\ \# Flag anomalies based on threshold \\ threshold \textless{}- quantile(data\$score, 0.95) \\ data\$anomaly \textless{}- ifelse(data\$score \textgreater{}=\text{threshold},1,0) \\ \# Game Theory: Stackelberg Optimization \\ payoff\_matrix \textless{}- matrix(c(0, -10, 5, -5), \text{nrow}=2, \text{b}\text{b}\text{b}\text{b}\text{b}\text{b  
We develop a strategic payoff matrix optimization that represents the utility of the defender's strategy, denotes the effectiveness of the countermeasure, and represents the computational and resource costs. Linear programming (LP) is used to compute the optimal mixed strategy, which denotes the probability distribution over defensive actions. Machine learning techniques analyze historical user activity to construct behavioral profiles, and normal operational patterns are identified based on frequency, access patterns, and network activity. This study proposes a live case attack simulation for detecting advanced persistent threats (APTs). The simulation setup with 50 independent simulation runs was conducted to validate the framework stability, including anomaly detection performance (F1-score, precision, recall), defense strategy stability over multiple trials, and impact minimization under adversarial conditions. We evaluated the model's performance, which maintained a stable anomaly detection rate of approximately 5%, reflecting model consistency, and the attack impact reduction approach effectively reduces APT impact to \(-5.0\), as computed by the expected utility function. Anomalous deviations from baseline activity trigger alerts for potential APT activity, and time-series analysis and clustering algorithms assist in identifying stealthy, slow-moving attacks. Security feeds including Mitre ATT CK and Virus Total are queried for threat correlation, with threat hunting algorithms matching observed patterns with known APT tactics, techniques, and procedures (TTPs) [32; 33]. Our Bayesian inference models refine alert classification to reduce false positives and hybrid AI models prioritize threats based on context relevance and impact probability. Unsupervised models (e.g., isolation forest and one-class SVM) distinguish anomalous activity from legitimate traffic, and supervised classifiers (e.g., deep neural networks and SVMs) refine classification accuracy when labeled data is available. Incorporating feedback loops from confirmed incidents improves detection precision and allows models to adapt dynamically as new threats emerge. When an APT is identified, compromised systems are automatically isolated, and credentials and access tokens linked to suspicious activity are revoked. Security operations center (SOC) personnel are automatically notified with enriched contextual data to support real-time incident analysis and response. The isolation forest (IF) algorithm operates under normal points that require more partitions to be isolated and anomalous points (such as APTs) requiring fewer partitions. Given a dataset  
\[X=\{x_{1},x_{2},\ldots,x_{n}\} \tag{1}\]  
where  
\[x_{i}\in R^{d} \tag{2}\]