Preventive strike vs. false targets and protection in defense strategy

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Abstract

A defender allocates its resource between defending an object passively and striking preventively against an attacker seeking to destroy the object. With no preventive strike the defender distributes its entire resource between deploying false targets, which the attacker cannot distinguish from the genuine object, and protecting the object. If the defender strikes preventively, the attacker's vulnerability depends on its protection and on the defender's resource allocated to the strike. If the attacker survives, the object's vulnerability depends on the attacker's revenge attack resource allocated to the attacked object. The optimal defense resource distribution between striking preventively, deploying the false targets and protecting the object is analyzed. Two cases of the attacker strategy are considered: when the attacker attacks all of the targets and when it chooses a number of targets to attack. An optimization model is presented for making a decision about the efficiency of the preventive strike based on the estimated attack probability, dependent on a variety of model parameters.

Introduction

Defending against external impacts and especially against intentional external impacts has attracted considerable research effort in recent years. One can distinguish between active and passive defense. Some measures aimed at mitigating the effect of external attacks, such as protective shields, are by their nature passive. Other measures can generate active defense, which means exerting offensive effort when certain conditions are met.

Earlier research has considered passive defense in the sense of defending against incoming attacks. Azaiez and Bier [1] consider the optimal resource allocation for security in reliability systems. They determine closed-form results for moderately general systems, assuming that the cost of an attack against any given component increases linearly in the amount of defensive investment in that component. Bier et al. [3] and Bier and Abhichandani [2] assume that the defender minimizes the success probability and expected damage of an attack.

Bier et al. [3] analyze the protection of series and parallel systems with components of different values. They specify optimal defenses against intentional threats to system reliability, focusing on the tradeoff between investment cost and security. The optimal defense allocation depends on the structure of the system, the cost-effectiveness of infrastructure protection investments and the adversary's goals and constraints. Levitin [9] considers the optimal element separation and protection in a complex multi-state series-parallel system and suggests an algorithm for determining the expected damage caused by a strategic attacker.

Patterson and Apostolakis [13] introduce importance measures for ranking the system elements in complex systems exposed to terrorist actions. Michaud and Apostolakis [12] analyze such measures of damage caused by the terror as impact on people, impact on environment, impact on public image, etc.

Bier et al. [4] assume that a defender allocates defense to a collection of locations while an attacker chooses a location to attack. They show that the defender allocates resources in a centralized, rather than decentralized, manner, that the optimal allocation of resources can be non-monotonic in the value of the attacker's outside option. Furthermore, the defender prefers its defense to be public rather than secret. Also, the defender sometimes leaves a location undefended and sometimes prefers a higher vulnerability at a particular location even if a lower risk could be achieved at zero cost. Dighe et al. [5] consider secrecy in defensive allocations as a strategy for achieving more cost-effective attacker deterrence. Zhuang and Bier [16] consider defender resource allocation for countering terrorism and natural disasters.

The preventive strike can be an effective measure of active defense aimed at destroying the potential attacker and, thus, preventing the defended object from destruction. However, the preventive strike can inflict a revenge strike, which causes expenditure of the defender's resources that could be used for passive defense. Thus, the optimal balance between the passive and active defense can considerably improve the survivability of the defended object.

Kroening [8] states that a preventive war is “initiated in the belief that military conflict, while not imminent, is inevitable, and that to delay would involve greater risk.” In contrast, preemption is defined as “an attack initiated on the basis of incontrovertible evidence that an enemy attack is imminent.” According to these two definitions, the focus in this paper is on preventive strike, and not on preemption.

As one example of preventive strike, Hausken [6] considers the optimal time to degrade a terrorist resource, which constitutes a threat which grows over time. The preventive strike may occur in the first period to prevent the threat from becoming larger in the second period, or in the second period if the first period threat is not overwhelming.

In earlier research Levitin and Hausken [10] and Levitin et al., [11] have considered how a defender balances between protecting an object passively and striking preventively against an attacker, equipped with one or multiple attack facilities, seeking to destroy the object. In this paper we let the defender determine a balance between striking preventively and deploying false targets to distract the attacker. The attacker cannot distinguish the genuine object from the false targets. First we assume that the attacker attacks all targets. Thereafter we assume that the attacker may attack a subset of the targets. In any attack against a group of targets the attacker distributes its effort evenly among the targets. This corresponds to the case when the attacker cannot direct the attack exactly against certain targets, but against a group of targets (for example, area coverage weapon attack against a group of separated targets).

The paper analyzes the defender's objective of minimizing the probability of destruction of an object it controls. The object may be an asset, a collection of assets, an infrastructure, a country, etc. The defender's two strategies are to defend passively or strike preventively, and, if the latter, which resource fraction to allocate to the preventive strike.

It is sometimes suggested that attack is the best defense, but not always. This paper seeks to determine when it is optimal to stay on the defensive and await the blow, and when it is optimal to go on the offensive and strike preventively. Our focus is on the quite challenging defense optimization where the defender has a fixed resource, which can be used passively or actively. The attacker has two resources, one resource that is used for attack, and one that is used to protect against a preventive strike by the defender.

As an example, consider an airborne bomber that has a mission to destroy some camouflaged object. The bomber can detect the targets with a given probability. The defender deploys false targets to dissipate the bomb strike and protects the object to reduce the probability of its destruction in the case of the strike. If the targets are detected the bomber distributes its load among a subset of targets it chooses. The defender can strike preventively using short range anti-aircraft missiles. As the missile launchers are located near the defended targets, the preventive strike reveals the locations of targets and, therefore, if the bomber, protected by an anti-missile system survives the strike, it attacks for certain. The defender has to make a choice between the passive defense (hoping that either it is not detected or that the object protection can survive the strike weakened by dissipation among several targets) and active defense (hoping that the attacker is destroyed). When the defender builds its defense it should decide how its limited budget is distributed between deploying the false targets, protecting the object and deploying anti-aircraft systems.

Section 2 presents the model when the attacker attacks all targets. Section 3 assumes that the attacker attacks a subset of the targets. Section 4 illustrates the solution. Section 5 considers the conservative defense strategy under uncertain contest intensities. Section 6 concludes.

Section snippets

Nomenclature

    PS

    preventive strike

    FT

    false target

    r

    total defender's resource

    R

    total attacker's offensive resource

    t

    effort with which the defended object is protected (measured as a fraction of r)

    H

    number of FTs deployed by the defender

    H

    optimal value of H in the case of PS

    H

    optimal value of H in the case of no PS

    Q

    number of targets attacked at random by the attacker

    Q

    optimal value of Q

    D

    attacker's protection resource

    c

    the cost of single false target

    T

    attacker's effort (resource) per attacked target

    x

    fraction of the

Attacker chooses a subset of targets to attack

If the attacker survives the preventive strike, it observes H+1 possible targets and cannot distinguish the object and the FTs. However the attacker can decide to attack a randomly chosen subset of targets concentrating its resource in the attack against fewer FTs and hoping that the defended object is among the attacked targets. If the attacker attacks Q targets, Q≤H+1, where Q is a free choice variable for the attacker, the per-target attack effort is T=R/Q and the probability that the

Illustrating the solution of the game

Fig. 4 presents zmin, H, H, Q(H,x), x and W for z=0.7, as functions of the relative FT cost σ, for δ=ρ=2, m=1 and different μ. The destruction probability W increases in σ as the FTs become more expensive and the defender can afford deploying fewer FTs. The dependence of W from the contest intensity is non-linear: the defender benefits from greater μ when it has the resource superiority in protecting the object and benefits from lower μ when its protection is inferior. For more

Conservative defense strategy under uncertain contest intensities

In many practical situations the values of the contest intensities cannot be exactly determined. Therefore, it would be useful to suggest a practical way to determine the optimal defense strategy for certain intervals of the contest intensities m and μ.

The most conservative defense strategy is to assume that the actual values of m and μ (belonging to exogenously defined intervals) are the most favorable for the attacker. This approach is equivalent to assuming that the attacker can choose m and

Conclusion

The article analyzes how a defender determines a balance between defending an object passively (by deploying false targets and protecting the object) and striking preventively against an attacker seeking to destroy the object. With no preventive strike the defender allocates its entire resource to passive defense. If the defender strikes preventively, the attacker's vulnerability depends on its protection and on the defender's resource allocated to the strike. If the attacker survives, the

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