Cyber and Physical Information Fusion for Infrastructure Protection: A Game-Theoretic Approach

We consider a class of infrastructures composed of discrete components that can be disrupted by either cyber or physical attacks, and are protected by cyber and physical reinforcements. We formulate a game between the provider and attacker, wherein their utility functions are in the form of sum of two terms, an infrastructure survival probability term and a cost term. We present a novel formulation that accounts for the cyber-physical interactions in two ways: (i) the conditional survival probabilities of cyber and physical sub-infrastructures are specified by multiples of marginal probabilities at the structure-level, and (ii) the survival probabilities of components are determined by cyber and physical component attacks as well as component reinforcements. We derive Nash Equilibrium conditions in terms of cost terms and component survival probabilities, and obtain provider strategies by combining the cyber and physical parameters. We propose sensitivity functions that highlight the dependence of infrastructure survival probability on cost parameters and component probabilities, under statistical independence conditions. This analysis shows a rather seemingly counter-intuitive qualitative behavior at NE that high costs and lower rewards lead to high infrastructure survival probability. We apply this approach to simplified models of cloud computing infrastructures and energy grids, both with a large number of components.