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Active and Passive Defense against Multiple Attack Facilities

The paper considers a situation when a terrorist with N attack facilities allocates its resource between attacking an object and protecting the facilities that will be used in the attack. A government allocates its resource between protecting the object passively and striking actively and preventively against all or a subset of the attack facilities. The government strikes preventively if the object destruction probability is lower than when choosing passive defense. The paper formulates a zero-sum situation in which the terrorist chooses how to distribute its resource between the attack and protection efforts where the government chooses how to distribute its resource between the (PS) preventive strike and protection efforts and decides how many facilities to strike. It is shown that independently of the number of facilities the government strikes, the sum of the fraction of the terrorist's resource allocated to attack and the fraction of the government's resource allocated to the PS always equals one. The condition of the PS effectiveness is formulated. Examples are provided to illustrate the methodology of the model analysis.