A robust approach to infrastructure security games

- Competitive game models addressing parameter uncertainty are developed.
- The existence and uniqueness of the defender's Nash strategy are proven.
- The equilibrium strategy of the robust game with private information is shown to be of threshold type.
- A case study with real world data is presented.

Most infrastructure security games assume that the parameters of the game are either deterministic or follow a known distribution. Whereas in reality some parameters of the game may be uncertain with no known distribution or distributional information about them may be unreliable. In this paper we develop distribution-free models of the incomplete-information infrastructure security game with and without private information. We assume that the players are uncertain about the node values and detection probabilities and they use a robust optimization approach to contend with such uncertainty. Moreover, the aim of the attack, to inflict maximum damage or to infiltrate, may be private to the adversary. Depending on the objective of the adversary and the existence of private information, we present three models for this game. We then prove the existence and uniqueness of the Nash equilibrium for the first two models and characterize the shape of the Nash equilibrium for the third model. Our results show that the equilibrium strategy for the robust game with private information is of threshold type. Finally, we apply the proposed approach to real data in order to determine the best allocation of defense resources.