Biblio

Many complex dynamical systems consist of a large number of interacting subsystems that operate harmoniously and make decisions that are designed for the benefit of the entire enterprise. If, in an attempt to disrupt the operation of the entire system, one subsystem gets attacked and is made to operate in a manner that is adversarial with the others, then the entire system suffers, resulting in an adversarial decision-making environment among its subsystems. Such an environment may affect not only the decision-making process of the attacked subsystem but also possibly the other remaining subsystems as well. The disruption caused by the attacked subsystem may cause the remaining subsystems to either coalesce as a unified team making team-based decisions, or disintegrate and act as independent decision-making entities. The decision-making process in these types of complex systems of systems is best analyzed within the general framework of cooperative and non-cooperative game theory. In this paper, we will develop an analysis that provides a theoretical basis for modeling the decision-making process in such complex systems. We show how cooperation among the subsystems can produce Noninferior Nash Strategies (NNS) that are fair and acceptable to all subsystems within the team while at the same time provide the subsystems in the team with the security of the Nash equilibrium against the opposing attacked subsystem. We contrast these strategies with the all Nash Strategies (NS) that would result if the operation of the entire system disintegrated and became adversarial among all subsystems as a result of the attack. An example of a system consisting of three subsystems with one opposing subsystem as a result of an attack is included to illustrate the results.

The communication infrastructure is a key element for management and control of the power system in the smart grid. The communication infrastructure, which can include equipment using off-the-shelf vulnerable operating systems, has the potential to increase the attack surface of the power system. The interdependency between the communication and the power system renders the management of the overall security risk a challenging task. In this paper, we address this issue by presenting a mathematical model for identifying and hardening the most critical communication equipment used in the power system. Using non-cooperative game theory, we model interactions between an attacker and a defender. We derive the minimum defense resources required and the optimal strategy of the defender that minimizes the risk on the power system. Finally, we evaluate the correctness and the efficiency of our model via a case study.