Is it wise to leave some false targets unprotected?

The paper considers a system consisting of genuine elements and false targets that cannot be distinguished by the attacker's observation. The false targets can be destroyed with much less effort than the genuine elements. To enhance the attack efficiency the attacker uses a double attack strategy in which it tries first to eliminate with optimal effort as many false targets as possible in the first attack and then distributes its entire remaining resource among all surviving targets in the second attack. It is assumed that the defender can protect some of the false targets whereas the attacker attacks all targets it can observe. In both attacks the attacking resource is distributed evenly among the attacked targets. The model for evaluating the system vulnerability in the double attack is suggested for parallel and series systems. This model considers the cases of perfect and imperfect detection of the targets destroyed in the first attack. The defense strategy is analyzed based on a two period minmax game. The methodology of optimal attack and defense strategies analysis is demonstrated. In is shown that under certain conditions (high contest intensity, scarce defense resource, low FT cost, high probability of wrong identification of destroyed targets by the attacker) the defender benefits from protecting a subset of the false targets. An algorithm for determining the optimal number of false targets that should be protected is suggested.