CHAPTER 3 An Analytical Framework for Cyber-Physical Networks and |E P | = a P b P P 1 P -1 67 , respectively, to ensure the continued operation of infrastructure. (ii) If the disrupter knows C and P , then choice given by max{u 2 (V C ), u 2 (E P )}, for |V C | = C and |E P | = P , will result in the loss of infra- structure operation. In general, by considering different ranges for the underlying parameters, one can identify different behaviors at the Nash equilibrium [86], ranging from a complete disruption of CPN to a fully operational state. This basic formulation can be extended in dif- ferent directions. (a) General CPN models and scenarios: The sim- plistic graph model may be expanded to more accurately reflect the cyber and phys- ical components as well as the complexity of real-life scenarios such as simultaneous cyber time, such as strategies of an active dis- rupter. Under certain circumstances, CPN infrastructure may have to be continually updated in view of escalated attacks or increased frequency of natural disruptions. Such problems may be more aptly formu- lated as dynamic games, for example, Stack- elberg games. (e) Dynamic profile generation: The failure modes of computational nodes and commu- nications systems may have to be learned dynamically. In particular, cyber attack attempts on computational nodes can be used to build profiles and detect potential trends, which can be incorporated into game- theoretic formulations. (f) Active information defense: Further exten- sions game describe here may include cases where the provider intentionally publicizes misleading information, such as locations of