Defense strategies for asymmetric networked systems under composite utilities

We consider an infrastructure of networked systems with discrete components that can be reinforced at certain costs to guard against attacks. The communications network plays a critical, asymmetric role of providing the vital connectivity between the systems. We characterize the correlations within this infrastructure at two levels using (a) aggregate failure correlation function that specifies the infrastructure failure probability given the failure of an individual system or network, and (b) first-order differential conditions on system survival probabilities that characterize component-level correlations. We formulate an infrastructure survival game between an attacker and a provider, who attacks and reinforces individual components, respectively. They use the composite utility functions composed of a survival probability term and a cost term, and the previously studied sum-form and product-form utility functions are their special cases. At Nash Equilibrium, we derive expressions for individual system survival probabilities and the expected total number of operational components. We apply and discuss these estimates for a simplified model of distributed cloud computing infrastructure.