  In recent times deep learning has been widely used for automating various
security tasks in Cyber Domains. However, adversaries manipulate data in many
situations and diminish the deployed deep learning model's accuracy. One
notable example is fooling CAPTCHA data to access the CAPTCHA-based Classifier
leading to the critical system being vulnerable to cybersecurity attacks. To
alleviate this, we propose a computational framework of game theory to analyze
the CAPTCHA-based Classifier's vulnerability, strategy, and outcomes by forming
a simultaneous two-player game. We apply the Fast Gradient Symbol Method (FGSM)
and One Pixel Attack on CAPTCHA Data to imitate real-life scenarios of possible
cyber-attack. Subsequently, to interpret this scenario from a Game theoretical
perspective, we represent the interaction in the Stackelberg Game in Kuhn tree
to study players' possible behaviors and actions by applying our Classifier's
actual predicted values. Thus, we interpret potential attacks in deep learning
applications while representing viable defense strategies in the game theory
prospect.
