Refinement of Strong Stackelberg Equilibria in Security Games

Abstract

Given the real-world deployments of attacker-defender Stackelberg security games, robustness to deviations from expected attacker behaviors has now emerged as a critically important issue. This paper provides four key contributions in this context. First, it identifies a fundamentally problematic aspect of current algorithms for security games. It shows that there are many situations where these algorithms face multiple equilibria, and they arbitrarily select one that may hand the defender a significant disadvantage, particularly if the attacker deviates from its equilibrium strategies due to unknown constraints. Second, for important subclasses of security games, it identifies situations where we will face such multiple equilibria. Third, to address these problematic situations, it presents two equilibrium refinement algorithms that can optimize the defender's utility if the attacker deviates from equilibrium strategies. Finally, it experimentally illustrates that the refinement approach achieved significant robustness in consideration of attackers' deviation due to unknown constraints.

Using Polymatrix Extensive Stackelberg Games in Security – Aware Resource Allocation and Task Scheduling in Computational Clouds

“…It means that he chooses his optimal strategy, which is also optimal from the leader's perspective. WSE assumes that the follower chooses the worst strategy from the leader's perspective [18]. Let x = (x 1 , x 2 , .…”

“…Calculating leader strategy means finding optimal computing capacities. It is possible if there exists the solution of problem (18) over the convex set [0, 1] n−1 . Follower strategy is calculated by solving problem (17) and (18).…”

“…It is possible if there exists the solution of problem (18) over the convex set [0, 1] n−1 . Follower strategy is calculated by solving problem (17) and (18). Finding optimal schedule is very time consuming process, therefore the suboptimal schedules are used.…”

Stackelberg Security Games: Models, Applications and Computational Aspects

“…It means that he chooses his optimal strategy, which is also optimal from the leader's perspective. WSE assumes that the follower chooses the worst strategy from the leader's perspective [7]. Formally, both scenarios can be defined in the following way:…”

An Overview of Recent Application Trends at the AAMAS Conference: Security, Sustainability, and Safety

“…For example, while the Stackelberg formulation assumes that the adversary conducts careful surveillance and thus has perfect knowledge of the defender's mixed strategy, in reality, the adversary's surveillance may be limited or error prone, requiring security game algo- rithms to be robust to such an occurrence (Yin et al 2011). Similarly, these algorithms must handle the significant uncertainty of the defender's model of the adversary's payoffs (Kiekintveld, Marecki, and Tambe 2011) and uncertainty over the capability of the attacker as well (An et al 2011b). While there are many such uncertainties, we will briefly highlight work that focuses on the adversary's bounded rationality, which introduces uncertainty in the adversary's decision procedure.…”