Evolutionary Stable Strategies of Defend and Attack for Dependent and Multi-State Systems with Reliability Approach

Planning of useful and sustainable strategies is one of the most important goals of organizations to defend critical
systems. In this research, a modeling is considered for investment optimization of defense and attack in
complex with interdependent subsystems, in which failure of a subsystem will possibly affect the optimal performance
of other subsystems. In this study, a static model is proposed that according to the probabilities of a
successful attack, subsystems dependency ratio, different modes of operation of the system, reliability structure
and game theory approach in determining balancing point, presents a nonlinear planning model to determine the
amount of investment in defending and attacking of all subsystems. Then, according to the results obtained from
the proposed static model, the dynamics of the system and the concepts of evolutionary game theory, a new and
dynamic method is introduced to determine the stable strategies for defense and attack. According to the proposed
model, the evolutionarily stable strategy will be examined over time, from the perspective of a defender, attacker,
and the whole system. Finally, the proposed model is applied to a numerical example and its results are analyzed