Addressing Uncertainty in Stackelberg Games for Security: Models and Algorithms

Recently, there has been significant research interest in using game-theoretic approaches to allocate limited security resources to protect physical infrastructure including ports, airports, transit systems, and other critical national infrastructure as well as natural resources such as forests, tigers, fish, and so on. Indeed, the leader-follower Stackelberg game model is at the heart of many deployed applications. In these applications, the game model provides a randomized strategy for the leader (security forces), under the assumption that the adversary will conduct surveillance before launching an attack. Inevitably, the security forces are faced with the problem of uncertainty. For example, a security officer may be forced to execute a different patrol strategy from the planned one due to unexpected events. Also, there may be significant uncertainty regarding the amount of surveillance conducted by an adversary. While Bayesian Stackelberg games for modeling discrete uncertainty have been successfully used in deployed applications, they are NP-hard problems and existing methods perform poorly in scaling up the number of types: inadequate for complex real world problems. Furthermore, Bayesian Stackelberg games have not been applied to model execution and observation uncertainty and finally, they require the availability of full distributional information of the uncertainty.