This paper makes two contributions to the literature on terrorism: 1) It presents a model that explains the cyclical characteristics of terrorist attacks, and 2) It improves on the existing theoretical cyclical models since it takes explicitly into account terrorists' motivations and decision-making. The model assumes that the government acts as leader and terrorists as followers. Terrorists maximize terrorist acts over time constrained by their budget constraint, which yields a time path for terrorist activities. Then the government maximizes national security by taking the time path of terrorist activities and investments in enforcement as constraints. The model shows that permanent cyclical paths for enforcement, terrorist activities, terrorist capital and national security may arise as an optimal solution.
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