False targets vs. redundancy in homogeneous parallel systems

System defense against natural threats and disasters that have a stochastic nature includes providing redundancy and protecting system elements. The defense against strategic intentional attacks can also include deploying false targets aimed at misleading the attacker. Distribution of the available resources among different defensive means is an important problem that arises in organizing the defense of complex civil infrastructures, industrial systems or military objects. The article considers defense resource allocation in a system exposed to external intentional attack. The expected damage caused by the attack is evaluated as system unsupplied demand. The defender distributes its limited resource between deploying redundant genuine elements and false elements, both of which are targets of attack. The attacker attacks a subset of the elements and distributes its limited resource evenly among the attacked elements. Two cases are considered: in the first one the number of attacked elements and the vulnerability of each genuine element are fixed and the defense resource distribution is determined as a solution of an optimization problem; in the second one the number of attacked elements is the attacker's free choice variable and the element's vulnerability depends on a contest determined by the defender's and attacker's resources allocated to each element. The defender's optimal resource distribution strategy is determined as a solution of a two-period minmax game. It is shown that the optimal number of genuine elements decreases monotonically with the growth of the element cost and vulnerability, whereas the optimal number of false elements demonstrates non-monotonic behavior. The contest intensity is an important factor influencing the optimal defense resource distribution. It cannot be ignored when the defense strategy is determined, and it thus also impacts the attack strategy.