Defense and Attack of Two-Component Multi-State Systems

A two component system can be fully operational, in two states of intermediate degradation, or fail. Each component is protected by a defender which maximizes its reliability weighted against the defense costs, and attacked by an attacker which maximizes its unreliability weighted against the attack costs. The system reduces to the series system when the values of the two intermediate states equal zero, and reduces to the parallel system when the values of the two intermediate states equal the value of the fully operational state. The attacker prefers the series system, the defender prefers the parallel system. The defender benefits from increasing the values of the two intermediate states. The article illustrates how the agents’ efforts and utilities depend on the values of the intermediate states, assuming these are equal, that one value is zero and the other varies, or that one value equals the value of the fully operational state while the other value varies.