A Stackelberg security game with random strategies based on the extraproximal theoretic approach

Abstract

In this paper we present a novel approach for representing a real-world attacker defender Stackelberg security game- theoretic model based on the extraproximal method. We focus on a class of ergodic controlled finite Markov chain games. The extraproximal problem formulation isc onsidered as a nonlinear programming problem withr espect to stationary distributions. The Lagrange principle and Tikhonov's regularization method are employed to ensure the convergence of the costfunctions.We transform the problem into a system of equations in aproximal format, and a two-step (prediction and basic) iterated procedure is applied to solve the formulated problem.In particular, the extraproximal method is employed for computing mixed strategies, providing a strong optimization formulation to compute the Stackelberg/Nas hequilibrium. Mixed strategies are especially found when the resources available for both the defender and the attacker are limited. In this sense,each equation in this system is an optimization problem for which the minimum is found using aquadratic programming approach.The model supports a defenderand N attackers. In order to address the dynamic execution uncertainty in security patrolling, we provide a game theoretic based method fo rscheduling randomized patrols. Simulation results provide avalidations of our approach.