Two Sequential Attacks of a Parallel System when Defense and Attack Resources are Expendable

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), and the defender tries to minimize it. The attacker and the defender distribute their constrained resources optimally across two attacks. The attacker attacks all elements in the first attack, and all surviving elements in the second attack. The defender protects all elements before the first attack, and protects all surviving elements before the second attack. Both agents decide how to distribute their resources between the two attacks before the first attack. Both agents’ resources are expendable and last only one attack. Both agents observe which elements are destroyed and not destroyed in the first attack, and apply their remaining resources into attacking and protecting the remaining elements in the second attack. First the optimal attack and defense 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 the two attacks as well as between deploying redundant elements and protecting them against the attacks.