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

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  • Asma Ben Yaghlane
  • Mohamed Naceur Azaiez

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.

Suggested Citation

  • Asma Ben Yaghlane & Mohamed Naceur Azaiez, 2019. "System survivability to continuous attacks: A game theoretic setting for constant attack rate processes," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(8), pages 1308-1320, August.
    • Handle: RePEc:taf:tjorxx:v:70:y:2019:i:8:p:1308-1320
    DOI: 10.1080/01605682.2018.1489350
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    References listed on IDEAS

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    1. M. Naceur Azaiez, 2009. "A Bayesian Model for a Game of Information in Optimal Attack/Defense Strategies," International Series in Operations Research & Management Science, in: Vicki M. M. Bier & M. Naceur Azaiez (ed.), Game Theoretic Risk Analysis of Security Threats, chapter 5, pages 99-123, Springer.
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