Multi-Defender security games on networks

Stackelberg security game models and associated computational tools have seen deployment in a number of high-consequence security settings, such as LAX canine patrols and Federal Air Marshal Service. This deployment across essentially independent agencies raises a natural question: what global impact does the resulting strategic interaction among the defenders, each using a similar model, have? We address this question in two ways. First, we demonstrate that the most common solution concept of Strong Stackelberg equilibrium (SSE) can result in significant underinvestment in security entirely because SSE presupposes a single defender. Second, we propose a framework based on a different solution concept which incorporates a model of interdependencies among targets, and show that in this framework defenders tend to over-defend, even under significant positive externalities of increased defense.