Parallel systems under two sequential attacks

The paper compares the efficiency of single and double attack against a system consisting of identical parallel elements (1-out-of-N system). An attacker tries to maximize the system vulnerability (probability of total destruction). 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 applies its remaining resource into attacking the remaining elements in the second attack. First the optimal attack strategy against a system with a fixed number of elements is analyzed. Thereafter a minmax two period game between the attacker and the defender is considered in which the defender distributes its constrained resource between deploying redundant elements and protecting them against the attack.