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 under-investment 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.