Passivity-Based Distributed Strategies for Stochastic Stackelberg Security Games

Abstract

Stackelberg Security Games (SSGs) model scenarios where a defender implements a randomized security policy, while an attacker observes the policy and selects an optimal attack strategy. Applications of SSG include critical infrastructure protection and dynamic defense of computer networks. Current work focuses on centralized algorithms for computing stochastic, mixed-strategy equilibria and translating those equilibria into security policies, which correspond to deciding which subset of targets (e.g., infrastructure components or network nodes) are defended at each time step. In this paper, we develop distributed strategies for multiple, resource-constrained agents to achieve the same equilibrium utility as these centralized policies. Under our approach, each agent moves from defending its current target to defending a new target with a precomputed rate, provided that the current target is not defended by any other agent. We analyze this strategy via a passivity-based approach and formulate sufficient conditions for the probability distribution of the set of defended targets to converge to a Stackelberg equilibrium. We then derive bounds on the deviation between the utility of the system prior to convergence and the optimal Stackelberg equilibrium utility, and show that this deviation is determined by the convergence rate of the distributed dynamics. We formulate the problem of selecting a minimum-mobility security policy to achieve a desired convergence rate, as well as the problem of maximizing the convergence rate subject to mobility constraints, and prove that both formulations are convex. Our approach is illustrated and compared to an existing integer programming-based centralized technique through a numerical study.

This work was supported by ONR grant N00014-14-1-0029, NSF grant CNS-1446866 and a grant from the King Abdulaziz City for Science and Technology (KACST).