Protection of simple series and parallel systems with components of different values

We apply game theory, optimization, and reliability analysis to identify optimal defenses against intentional threats to system reliability. The goals are to identify optimal strategies for allocating resources among possible defensive investments, and to develop qualitative guidelines that reflect those strategies. The novel feature of the approach is the use of reliability analysis together with game theory and optimization to study optimal management of intentional threats to system reliability. Thus, this work extends and adapts the existing body of game-theoretic work on security to systems with series or parallel structures. The results yield insights into the nature of optimal defensive investments that yield the best tradeoff between investment cost and security. In particular, the results illustrate how the optimal allocation of defensive investments depends on the structure of the system, the cost-effectiveness of infrastructure protection investments, and the adversary's goals and constraints.