Conquering Adversary Behavioral Uncertainty in Security Games: An Efficient Modeling Robust Based Algorithm

Real-world deployed applications of Stackelberg Security Games (Shieh et al. 2012; Basilico, Gatti, and Amigoni 2009; Letchford and Vorobeychik 2011) have led to significant research emphasis on modeling the attacker’s bounded rationality (Yang et al. 2011; Nguyen et al. 2013). One key assumption in behavioral modeling is the availability of a significant amount of data to obtain an accurate prediction. However, in real-world security domains such as the wildlife protection, this assumption may be inapplicable due to the limited access to real-world data (Lemieux 2014), leading to uncertainty in the attacker’s behaviors — a key research challenge of security problems. Recent research has focused on addressing uncertainty in behavioral modeling, following two different approaches: 1) one approach assumes a known distribution of multiple attacker types, each follows a certain behavioral model, and attempts to solve the resulting Bayesian games (Yang et al. 2014); and 2) another considers the existence of multiple attacker types of which behavioral models are perfectly known, but without a known distribution over the types. It then only considers the worst attacker type for the defender (Brown, Haskell, and Tambe 2014). These two approaches have several limitations. First, both still require a sufficient amount of data to precisely estimate either the distribution over attacker types (the former approach) or the model parameters for each individual type (the latter approach). Second, solving the resulting Bayesian games in the former case is computationally expensive. Third, the latter approach tends to be overly conservative as it only focuses on the worst-case attacker type. This paper remedies these shortcomings of state-of-theart approaches when addressing behavioral uncertainty in SSG by providing three key contributions. First, we present a new game model with uncertainty in which we consider a single behavioral model to capture decision making of the whole attacker population (instead of multiple behavioral models); uncertainty intervals are integrated with the chosen model to capture behavioral uncertainty. The idea of uncertainty interval is commonly used in literature (Aghassi and Bertsimas 2006) and has been shown to effectively repre-

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