Parallel systems under two sequential attacks with imperfect detection of the first attack outcome

The paper compares the efficiency of single and double attack against a system consisting of identical parallel elements. An attacker maximizes the system vulnerability (probability of total destruction). In order to destroy the system, the attacker distributes its constrained resource optimally across two attacks and chooses the number of elements to be attacked in the first attack. The attacker observes which elements are destroyed and not destroyed in the first attack and allocates its remaining resource into attacking the remaining elements in the second attack. The paper considers two types of identification errors: wrong identification of a destroyed element as not destroyed, and wrong identification of a not destroyed element as destroyed. First, the influence of the identification error probabilities on 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, in which the defender in the first period distributes its constrained resource between deploying redundant elements and protecting them against the attack in the second period. It is shown how the identification error probabilities affect the defence strategy.