Network Security Configurations: A Nonzero-Sum Stochastic Game Approach

In this paper, we study a network security configuration problem. More specifically, we consider distributed intrusion detection systems in a network subject to possible simultaneous attacks launched by a number of attackers. We formulate an N + M-person nonzero-sum stochastic game to capture the interactions among detection systems in the network as well as their interactions against exogenous intruders. We show the existence of stationary Nash equilibrium of the game and a value iteration method to attain an ∈-Nash equilibrium. Mimicking the concept of Shannon's capacity in information theory, we propose the notion of security capacity as the largest achievable payoff to an agent at an equilibrium to yield performance limits on the network security. Furthermore, we discuss a mathematical programming approach to characterize the equilibrium as well as the feasibility of a given security target.