Fighting terrorism: How to position rapid response teams?

In light of recent terrorist attacks, we introduce and study a Stackelberg game between a government and a terrorist. In this game, the government positions a number of heavily-armed rapid response teams on a line segment (e.g., a long boulevard or shopping avenue) and then the terrorist attacks a location with the highest potential impact of an attack. This potential impact, which we call damage, is the product of the time it takes the closest rapid response team to react and the damage caused per time unit, which is modeled via a damage rate function. We prove that there exists a subgame perfect Nash equilibrium that balances the possible damage on all intervals of the line segment that result from positioning the rapid response teams. We discuss the implications for various types of damage rate functions including one mimicking a busy boulevard with various hotspot locations.