Security Games with Interval Uncertainty

Authors

Christopher Kiekintveld, The University of Texas at El PasoFollow
Towhidul Islam, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

2-2013

Comments

Technical Report: UTEP-CS-12-45a

To appear in Proceedings of The Twelfth International Conference on Autonomous Agents and Multiagent Systems AAMAS'2013, Saint Paul, Minnesota, May 6-10, 2013.

Abstract

Security games provide a framework for allocating limited security resources in adversarial domains, and are currently used in applications including security at the LAX airport, scheduling for the Federal Air Marshals, and patrolling strategies for the U.S. Coast Guard. One of the major challenges in security games is finding solutions that are robust to uncertainty about the game model. Bayesian game models have been developed to model uncertainty, but algorithms for these games do not scale well enough for many applications, and the problem is NP-hard.

We take an alternative approach based on using intervals to model uncertainty in security games. We present a fast polynomial time algorithm for security games with interval uncertainty. This provides the first viable approach for computing robust solutions to very large security games. In addition, we introduce a methodology for approximating the solutions to infinite Bayesian games with distributional uncertainty using intervals to approximate the distributions. We show empirically that using intervals is an effective approach for approximating solutions to these Bayesian games; our algorithm is both faster and results in higher quality solutions than the best previous methods.