A Robust Solution Concept for Human Bounded Rationality in Security Games

Game-theoretic approaches have been proposed for addressing the complex problem of assigning limited security resources to protect a critical set of targets. However, many of the standard assumptions fail to address human adversaries who security forces will likely face. To address this challenge, previous research has attempted to integrate models of human decision-making into the game-theoretic algorithms for security settings. The current leading approach, based on experimental evaluation, is derived from a well-founded solution concept known as quantal response and is known as BRQR. One critical difficulty with opponent modeling in general is that, in security domains, information about potential adversaries is often sparse or noisy and furthermore, the games themselves are highly complex and large in scale. Thus, we chose to examine a completely new approach to addressing human adversaries that avoids the complex task of modeling human decision-making. We leverage and modify robust optimization techniques to create a new type of optimization where the defender’s loss for a potential deviation by the attacker is bounded by the distance of that deviation from the expected-value-maximizing strategy. To demonstrate the advantages of our approach, we introduce a systematic way to generate meaningful reward structures and compare our approach with BRQR in the most comprehensive investigation to date involving 104 security settings where previous work has tested only up to 10 security settings. Our experimental analysis reveals our approach performing as well as or outperforming BRQR in over 90% of the security settings tested and we demonstrate significant runtime benefits. These results are in favor of utilizing an approach based on robust optimization in these complex domains to avoid the difficulties of opponent modeling.