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defense investments: applying defender-attacker (-defender) optimization to terror risk assessment and mitigation
 
The U.S. Department of Homeland Security (DHS) is investing billions of dollars to protect us from terrorist attacks and their expected damage (i.e., risk). We present prescriptive optimization models to guide these investments. Our primary goal is to recommend investments from a set of available defensive options; each of these options can reduce our vulnerability to terrorist attack, or enable future mitigation actions for particular types of attack. Our models prescribe investments that minimize the maximum risk (i.e., expected damage) to which we are exposed. Our "Defend-Attack-Mitigate risk-minimization model" assumes that terrorist attackers will observe, and react to, any strategic defensive investment on the scale required to protect our entire country. We also develop a more general tri-level "Defender-Attacker-Defender risk-minimization model" in which (a) the defender invests strategically in interdiction and/or mitigation options (for example, by inoculating health-care workers, or stockpiling a mix of emergency vaccines) (b) the attacker observes those investments and attacks as effectively as possible, and (c) the defender then optimally deploys the mitigation options that his investments have enabled. We show with simple numerical examples some of the important insights offered by such analysis. As a byproduct of our analysis we discover optimal attacker behavior from our chosen defensive investment, and therefore we can focus intelligence collection on telltales of the most-likely and most-lethal attacks.