On the value of terrorists private information in a governments defensive resource allocation problem

The ability to understand and predict the sequence of events leading to a terrorist attack is one of the main issues in developing pre-emptive defense strategies for homeland security. This article, explores the value of terrorists private information on a governments defense allocation decision. In particular, two settings with different informational structures are considered. In the first setting, the government knows the terrorists target preference but does not know whether the terrorist is fully rational in his target selection decision. In the second setting, the government knows the degree of rationality of the terrorist but does not know the terrorists target preference. The governments equilibrium budget allocation strategy for each setting is fully characterized and it is shown that the government makes resource allocation decisions by comparing her valuation for each target with a set of thresholds. The Value Of Information (VOI) from the perspective of the government for each setting is derived. The obtained results show that VOI mainly depends on the governments budget and the degree of heterogeneity among the targets. In general, VOI goes to zero when the governments budget is high enough. However, the impact of heterogeneity among the targets on VOI further depends on whether the terrorists target preference matches those of the governments or not. Finally, various extensions on the baseline model are performed and it is shown that the structural properties of budget allocation equilibrium still hold true.