Governments' and terrorists' defense and attack in a T-period game

Abstract

We analyze how a government allocates its resources between attacking to downgrade a terrorist’s resources and defending against a terrorist attack. Analogously, the terrorist allocates its resources between attacking a government’s asset and defending its own resources. A two-stage game is considered where the government moves first and the terrorist moves second. We show that (a) when the terrorist’s resources are low, the government attacks the terrorist’s resources sufficiently to deter the terrorist from attacking and does not defend; (b) when the terrorist’s resources are high, both the government and terrorist defend and attack. We analyze T periods of the two-stage game between two myopic players. First we assume no linkages between periods. We show that after an attack the government may enjoy incoming resources, which deter the terrorist for some periods. Between periods the terrorist’s resources may change because of arithmetically and geometrically changing incoming funds. We allow the government’s and the terrorist’s resources to be determined randomly in each time period. We also allow the government’s resources in one period to depend on the terrorist’s attacks in earlier time periods for three dynamics, where the terrorist’s resources are drawn from a normal distribution or change arithmetically or geometrically.