Protection vs. separation in parallel non-homogeneous systems

Abstract

The article considers strategic defense and attack of a system consisting of N functionally identical parallel elements of n types distinguished by element’s performance. The elements can be separated in order to reduce the damage caused by an outside attack. The defender distributes its resource between separation and protecting the elements from attacks. The attacker attacks optimally. The vulnerability of each element is determined by a contest between the defender and the attacker expressed as a contest success function. Ten propositions are developed with and without resource constraints to show when separation is efficient. With two different types of elements, the defender can never justify separation by maintaining its contest success against the attacker for one type of elements. To possibly justify separation, the contest success must be decreased against one type and increased against the other type. For the case of two types of elements a condition is developed for the highest separation cost the defender is willing to incur if it chooses not to protect any of the elements of type 1. Without resource constraints, separation is not efficient if the unit costs of protection are equal for all elements, and the unit costs of attack are the same for all elements. However, separation is efficient if lower unit costs of defense can be obtained through the separation process for sufficiently many of the elements, especially those elements with high performance, or if the number of elements of the same type is large.