Protection vs. false targets in series systems

The paper analyses the optimal distribution of the defense resources between protecting the genuine system elements and deploying false elements (targets) in a series system, which is destroyed when any genuine element is destroyed. False and genuine elements cannot be distinguished by the attacker. We analyze a two-period game where the defender builds the defense in the first period, whereas the attacker attacks in the second period. Three cases are considered: the attacker attacks only one element, the attacker attacks all system elements, the attacker chooses the number of elements to attack that maximizes the overall system vulnerability. The probability of element destruction in the case of attack is defined as a contest function depending on the ratio of the defender's and attacker's effort and on a contest intensity parameter. The dependence of the minmax defense strategy (number of false elements) and the most harmful attack strategy (number of attacked elements) on the amount of resources available to the counterparts, on the number of genuine system elements and on the contest intensity is analyzed. Illustrative examples are presented.