Applications of Game Theory and Search Theory to Homeland Security Open Access
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This dissertation explores the use of game theory and search theory in the context of terrorism risk and homeland security. Since 9-11 the body of game theoretic literature related to terrorism has grown. What Myerson (1992) termed a "modeling dialogue" is necessary to test and challenge game assumptions and predictions against the realities of the terrorist threat. This dissertation contributes to the homeland security "modeling dialogue" with new models and with an analysis of the current literature. In the games reviewed in Chapter Three, a centralized defender must allocate a security budget across separate targets or attack scenarios. Chapter Four is concerned with the issue of whether or not there is a justification to invest in defenses against specific attack scenarios given the attacker's ability to switch targets or whether investing all security resources in counterterrorism would be a more effective way to reduce terrorism risk. The chapter contributes to the literature by identifying and making explicit the key assumptions that lead to contradictory results in the current literature on the topic. The chapter also contributes by creating a new sequential game with incomplete defender information that illustrates the theoretical justification for an overarching security strategy of investing in counterterrorism and in defenses against catastrophic attacks. The game is also used to mathematically define the threat-shifting, real vulnerability reduction and deterrent effects of security. There are two new findings from this model. First, counterterrorism can shift the threat between targets by increasing the importance of randomness in attacker target selection. Second, sometimes an increase in defenses at high-value targets can increase expected losses from terrorism unless accompanied by a sufficient increase in counterterrorism. The contribution of Chapter 5 is an analysis of the current literature on secrecy in order to reconcile conflicting results and to identify some specific situations in which the defender prefers secrecy or disclosure of information to the attacker. The dissertation also contributes by considering the effects of defender and attacker risk aversion on the benefits of secrecy. The results of the analysis show that a risk-averse defender facing a risk-averse attacker can benefit from disclosing target vulnerabilities. It can be optimal for the defender to publicize investments in the security of infrastructure systems, high profile-high value targets and for classes of targets while maintaining secrecy for specific targets within an infrastructure system or within a class of targets. Chapter 6 contributes to the literature by applying search models to attacker behavior. In the first search model, attacker search behavior is specified exogenously. The first search model produces a new result--additional target security can sometimes increase the marginal risk reduction benefit of counterterrorism. In the second search model, the attacker's search behavior is endogenous. A key result that differs from the defender attacker games is that an increase in counterterrorism reduces average attack severity. A third search model drops the assumption in the defender attacker games that the attacker will launch a single attack. The model shows that by increasing the risk to the attacker from search, counterterrorism reduces the number of simultaneous attacks per event. The model is also used to generate probability distributions for attack multiplicity for different types of attacks. The dissertation shows the relevance of the model of attack multiplicity to break-even analysis. Chapter 7 creates a new game in which private targets decide whether or not to invest in security. Unlike many target games in the literature, the threat-shifting game explicitly incorporates the reaction of the attacker to security and the real vulnerability loss reduction effects of security into the pay-offs. Previous games have found that private security decisions assume the form of a prisoner's dilemma that inevitably leads to an overinvestment in security. In the new threat-shifting game overinvestment in security is not inevitable provided the security measure is sufficiently effective at reducing vulnerability. Targets make different decisions about risk mitigation measures depending on whether the external costs of an event affect parties outside of the game or other similar targets in the game and whether or not the event is triggered by a natural disaster or an intelligent adversary.