| Distributing limited homeland-security funds in protecting against terrorism is a difficult task. This thesis examines results of a game-theoretic model applied to the problem of identifying the optimal defensive resource allocation among potential terrorist targets. In particular, I examine how the optimal budget allocation depends on the cost effectiveness of security investments, the defender's valuations of various targets, and the extent of the defender's uncertainty about the attacker's target valuations. I first examine both monotonic and non-monotonic attacker objective functions, considering single- attribute measures of target attractiveness; damage estimates include expected property damage, expected fatalities, and two measures of critical infrastructure (airports and bridges) in the monotonic case and expected fatalities in the non-monotonic case. I examine a constrained and unconstrained defender budget in both cases. Next, I examine multi-attribute measures of target attractiveness (including those representing both attack difficulty and damage resulting from an attack) and explore how the defender's uncertainty about the attacker's preferences affects the defensive resource allocation in the constrained case. Results confirm that the cost effectiveness of defensive investment has a significant impact on optimal budget allocations. Moreover, multi-attribute measures of target attractiveness seem to yield more realistic levels of hedging, at least when some targets are not dominated by others on all attributes, since the defender may have significant uncertainty about which targets are most attractive to the attacker if different targets are attractive on different measures. Multi-attribute measures of target attractiveness (even with defender uncertainty about the attacker's attribute weights, not just about the overall target attractiveness) are not always sufficient to achieve significant hedging when some targets are dominated by others on most or all attributes; however, it may not be reasonable to expect high levels of hedging in these cases. Nonetheless, if more realistic levels of hedging are desired, additional models may be needed, such as models that allow for attributes that are important to the attacker but not observed by the defender, or models that combine uncertainty about the attacker's attribute weights with uncertainty about how the targets rate on the various attributes. |
