Addressing Scalability and Robustness in Security Games with Multiple Boundedly Rational Adversaries

Abstract

Boundedly rational human adversaries pose a serious challenge to security because they deviate from the classical assumption of perfect rationality. An emerging trend in security game research addresses this challenge by using behavioral models such as quantal response (QR) and subjective utility quantal response (SUQR). These models improve the quality of the defender’s strategy by more accurately modeling the decisions made by real human adversaries. Work on incorporating human behavioral models into security games has typically followed two threads. The first thread, scalability, seeks to develop efficient algorithms to design patrols for large-scale domains that protect against a single adversary. However, this thread cannot handle the common situation of multiple adversary types with heterogeneous behavioral models. Having multiple adversary types introduces considerable uncertainty into the defender’s planning problem. The second thread, robustness, uses either Bayesian or maximin approaches to handle this uncertainty caused by multiple adversary types. However, the robust approach has so far not been able to scale up to complex, large-scale security games. Thus, each of these two threads alone fails to work in key real world security games. Our present work addresses this shortcoming and merges these two research threads to yield a scalable and robust algorithm, MIDAS (MaxImin Defense Against SUQR), for generating game-theoretic patrols to defend against multiple boundedly rational human adversaries. Given the size of the defender’s optimization problem, the key component of MIDAS is incremental cut and strategy generation using a master/slave optimization approach. Innovations in MIDAS include (i) a maximin mixed-integer linear programming formulation in the master and (ii) a compact transition graph formulation in the slave. Additionally, we provide a theoretical analysis of our new model and report its performance in simulations. In collaboration with the United States Coast Guard (USCG), we consider the problem of defending fishery stocks from illegal fishing in the Gulf of Mexico and use MIDAS to handle heterogeneity in adversary types (i.e., illegal fishermen) in order to construct robust patrol strategies for USCG assets.