Optimal Cyber-Defense Strategies for Advanced Persistent Threats: A Game Theoretical Analysis

We introduce a novel mathematical model that treats network security as a game between cyber attackers and network administrators. The model takes the form of a zero-sum repeated game where each sub-game corresponds to a possible state of the attacker. Our formulation views state as the set of compromised edges in a graph opposed to the more traditional node-based view. This provides a more expressive model since it allows the defender to anticipate the direction of attack. Both players move independently and in continuous time allowing for the possibility of one player moving several times before the other does. This model shows that defense-in-depth is not always a rational strategy for budget constrained network administrators. Furthermore, a defender can dissuade a rational attacker from attempting to attack a network if the defense budget is sufficiently high. This means that a network administrator does not need to make their system completely free of vulnerabilities, they only to ensure the penalties for being caught outweigh the potential rewards gained.