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.     

Is it wise to protect false targets?

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. We show that even when an attacker cannot distinguish between the genuine elements and the false targets, in many cases it can enhance the attack efficiency using a double attack strategy in which it tries first to eliminate with minimal 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. The model for evaluating the system vulnerability in the double attack is suggested for a single genuine element, and multiple genuine elements configured in parallel or in series. This model assumes that in both attacks the attacking resource is distributed evenly among the attacked targets. The defender can optimize its limited resource distribution between deploying more false targets and protecting them better. The attacker can optimize its limited resource distribution between two attacks. The defense strategy is analyzed based on a two period minmax game. A numerical procedure is suggested that allows the defender to find the optimal resource distribution between deploying and protecting the false targets. The methodology of optimal attack and defense strategies analysis is demonstrated. It is shown that protecting the false targets may reduce the efficiency of the double attack strategy and make this strategy ineffective in situations with low contest intensity and few false targets.     

Intelligence and impact contests in systems with redundancy, false targets, and partial protection

The paper considers a system consisting of identical elements that can be intentionally attacked. The cumulative performance of the system elements should meet a demand. To prevent loss of demand the defender provides system redundancy (deploying genuine system elements (GEs) with cumulative performance exceeding the demand); deploys false elements (FEs), and protects the GEs. If the attacker cannot distinguish GEs and FEs, he chooses the number of elements to attack and attacks at random these elements distributing his resource evenly among the attacked elements. In order to get the information about the system the attacker allocates a part of his resource into the intelligence activity. Analogously, the defender allocates a part of his resource into the counter-intelligence activity. The attacker's strategy presumes distribution of his resource among the intelligence and attack effort and choice of the number of attacked elements. If the attacker wins the intelligence contest, he can identify both FEs and unprotected GEs ignoring the former ones and destroying the latter ones with negligible effort. The defender's strategy presumes distribution of his resource among the counter-intelligence and the three defensive actions. The paper considers a three-period non-cooperative minmax game between the defender and the attacker and presents an algorithm for determining the agents’ optimal strategies.     

Meeting a demand vs. enhancing protections in homogeneous parallel systems

The article considers defense resource allocation in a system exposed to planned and forced losses. The defender distributes its limited resource between deploying identical system elements and their protection from attacks. Planned losses arise if there are not enough elements to meet the demand. Forced losses arise if an external attack reduces the performance below the demand. The attacker distributes its effort evenly among all the elements or among elements from a chosen subset. The vulnerability of each element is determined by an attacker–defender contest success function. The expected damage caused by the attack is proportional to the system performance reduction below a planned level of demand satisfaction.     

Protection vs. redundancy in homogeneous parallel systems

The article considers defense resource allocation in a system exposed to external intentional attack. The defender distributes its resource between deploying redundant elements and their protection from attacks. The attacker distributes its effort evenly among all of the elements or among elements from a chosen subset. The vulnerability of each element is determined by an attacker–defender contest success function. The expected damage caused by the attack is evaluated as system unsupplied demand. The article considers both the cases without and with performance redundancy.     

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.