System survivability to continuous attacks: A game theoretic setting for constant attack rate processes

Asma Ben Yaghlane and Mohamed Naceur Azaiez

Journal of the Operational Research Society, 2019, vol. 70, issue 8, 1308-1320

Abstract: In this paper, we introduce the concept of system survivability, in the context of intelligent threats of continuous attacks. We define a constant attack rate (CAR) process as an attack on a targeted system that follows an exponential distribution. We consider the superposition of several CAR processes. We develop several related results. From the attacker side, we determine the optimal attack strategy that minimises the system survivability. We also determine the optimal strengthening strategy that maximises the system survivability under limited defensive resources. Next, we model the problem in a game-theoretic setting. We distinguish the cases of frequentist and Bayesian frameworks. We consider different levels of information availability to each antagonist and model games accordingly. In particular, we show that Nash equilibrium holds in the various versions of the problem. Moreover, we provide some numerical illustrations to clarify the process. Our contribution is a building block towards investigating other types of continuous attacks.

Date: 2019
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DOI: 10.1080/01605682.2018.1489350

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