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Defence of homogeneous parallel multi-state systems subject to two sequential attacks

Single and double attacks are compared against a system consisting of identical parallel elements providing performance redundancy in a multi-state system. By destroying elements an attacker tries to maximize the expected damage caused by the reduction of the cumulative system performance. The attacker has a constrained resource which is distributed optimally between two attacks. The optimal number of attacked elements in each attack is determined. The attacker observes which elements are destroyed in the first attack and does not attack them in the second attack. First the optimal attack strategy against a system with a fixed number of elements is analysed. Thereafter a minmax two-period game between the attacker and the defender is considered. The defender distributes its constrained resource between deploying redundant elements and protecting them against the attack in the first period to minimize the expected damage. The attacker chooses its strategies in the second period to maximize the expected damage. A model and a methodology for finding the optimal defence and attack strategies are suggested. Illustrative examples of the optimal attack and defence are presented.