Infrastructure resilience using cyber-physical game-theoretic approach

We consider a class of infrastructures supported by cyber and physical components, which are subject to disruptions. We study reinforcement strategies for cyber and physical components to achieve resilience, specified by the probability of infrastructure survival, against disruptions using a game-theoretic formulation. The game utility function is a sum of the infrastructure survival probability term and a cost term. We account for cyber-physical interactions at two different levels: (i) the conditional survival probability of cyber sub-infrastructure is specified by a linear function of the marginal probability, and (ii) the survival probabilities of components are determined by the numbers of cyber and physical component attacks as well as reinforcements. At Nash Equilibrium, we identify 12 performance regions based on cyber-physical correlations and component costs, where each is determined by a lower survival probability of either cyber or physical sub-infrastructure. We also derive sensitivity functions that highlight the dependence of infrastructure survival probability on cost parameters and component probabilities as well as cyber-physical correlations, under statistical independence conditions. We apply this approach to models of the energy grid derived at different levels of abstraction.