## 4 Verification and Validation
### Verification of the Proposed Models  
One way to verify a mathematical model is to perform empirical analysis using actual data. In this study, the actual data required to verify the model are the details of a previous cyber incident involving malicious insiders. However, organizations usually prefer not to publish insider attack incidents for various reasons, such as reputation damage, loss of trust, legal and regulatory concerns, competitive disadvantage, and contractual considerations. Therefore, the unavailability of actual data necessitated using the Monte Carlo simulation to verify our proposed model. In fact, in the absence of actual data, simulation is a valuable tool to analyze mathematical models, as demonstrated by [PERSON] et al. [13] and [PERSON] et al. [15]. The authors [15] used Monte Carlo simulations to analyze their game models. [PERSON] et al. [13] also performed simulations to analyze their game model due to the challenges in obtaining actual data for input parameters. Similarly, in this research, we used the Monte Carlo simulation to verify our proposed model. For each game model, we analyzed the basic parameters \(\beta,\omega,C_{cyb}\) and the probabilities \(p_{1}\), \(p_{2}\), and \(\delta\) for both the simultaneous move and sequential move game models. In this experiment, we employed a Monte Carlo simulation, generating multiple parameter combinations to identify those that satisfied the constraints for each game model, where each parameter was normalized and, hence, randomized from \((0,1)\). Regarding sampling techniques, we employed random sampling to generate parameter combinations across the defined parameter space. Each parameter was sampled from a uniform distribution within theoretically justified bounds, ensuring a comprehensive exploration of the game's strategic landscape. This approach was chosen for its simplicity and effectiveness in covering a wide range of scenarios without prior assumptions about parameter distributions. The ranges for each parameter were determined based on theoretical considerations within the construction cybersecurity field. For instance, the parameter \(\delta\), which is the probability that an insider is malicious, was varied between 0 and 1 to cover all possible weights, reflecting a wide spectrum of game dynamics; \(p_{1}\) (the probability that the identity of the malicious insider and his/her activity is discovered in the case of proper authentication) needed to be greater than \(p_{2}\) (the probability that the identity of the malicious insider and his/her activity is discovered in the case of a cyberattack). We conducted many simulation runs for each parameter set to ensure the robustness and reliability of our results. This large number of runs leveraged the law of large numbers, allowing us to approximate the expected outcomes of strategies with high confidence. The decision to randomize and normalize parameters within the 0 to 1 range is grounded in both theoretical considerations and practical assumptions. Specifically, pa rameters such as \(p_{1},p_{2},\) and \(\delta\) represent probabilities, inherently necessitating their values to fall within the 0 to 1 interval. This ensures that their interpretation remains consistent with probabilistic theory. For parameters like \(C_{cyb},\omega,\) and \(\beta\), which are related to costs and payoffs, normalizing their values to a 0 to 1 scale is a strategic choice aimed at establishing a universal and consistent framework for comparison. In real-world scenarios, absolute values of costs and payoffs can vary significantly across different contexts, such as varying scales of projects or financial capacities of companies. Normalizing these values facilitates a more generalized and adaptable model application. For each parameter exploration, we conducted numerous simulations, approximately 10,000, which leveraged the law of large numbers to ensure the robustness of our model. Therefore, the simulation process adhered to the law of large numbers.