Graduation Year

2007

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Susan E. Martonosi

Reader 2

Francis Edward Su

Abstract

The attacks on the World Trade Center in New York, the subway and bus bombings in London, and the suicide bombings in Casablanca are only a few of the examples in which in recent years, terrorists have opted to attack multiple targets at once. Often, their strong determination to attack makes it impossible to completely deter terrorists from attacking altogether, and instead, counterterrorist units must consider how to defend targets effectively to minimize damages. We attempt to model a version of this scenario by presenting a two target sequential game where two players try to attack and defend the targets respectively. The probability of successfully destroying a target is a function of resource allocations from both players, who are also subject to budget constraints. We attempt to find the defender’s strategy that will minimize expected damages by first exploring the attacker’s optimal strategy. We show that the attacker’s decision to attack only one or both targets is dependent on the size of the attacker’s allowed budget relative to other game parameters, and use that information to evaluate the defender’s strategy. We also numerically determine the optimal defender security investment, as well its sensitivity to other game parameters. We conjecture that as the damage and expected reward at a target increases, the defender’s allocation towards that target tends to increase, while an increase in the punishment results in the opposite effect. Such conjectures allow for the creation of a flexible defense policy in the more applicable bigger picture.

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