Gamified Security Tactics Through Digital Card Game Models

Cybersecurity threats are becoming increasingly sophisticated, often exploiting vulnerabilities in system protocols to compromise integrity and resilience. This study introduces a novel framework that combines gamification, automata theory, and modal logic to advance system security engineering. Specifically, it models cyber card games using Kleene's theorem and Kripke modal logic (KTKL) to provide a structured mechanism for analysing security protocols. The KTKL framework integrates attackers (A), defenders (D), possible worlds (W), and accessibility relations (R) to systematically represent state transitions and strategic interactions in cybersecurity scenarios. The methodology involves an experimental study with 163 participants acting as defenders attempting to counteract simulated cyber attacks in the proposed framework. This interactive process generates a rich dataset of real-world gameplay, which is analyse using machine learning (ML) to extract actionable insights. Key performance metrics, including Precision, Recall, ROC, Accuracy, and computational time, were evaluated. Among the models tested, the Perceptron demonstrated superior performance, achieving an Area Under the Curve (AUC) of 65%, outperforming the Quadratic Discriminant Analysis (QDA). The results demonstrate the utility of the KTKL framework in studying and maintaining system integrity and fostering resilience against diverse attack vectors. The study highlights the potential of gamified approaches to bridge theoretical and practical aspects of system security engineering, offering a promising direction for future research and applications in combating advanced cyber threats.