## 6 Conclusions  
A zero-sum complete information game-theory methodology for the protection of CI was developed. The novelty of the model focuses on integration between the vulnerability of the CIs using topological network analysis, various threat scenarios, and comprehensive consequences considering direct and indirect loss. The cost effectiveness of the optimal solution considers ROI along the lifetime of the CI. Topological network analysis provides an effective tool for identifying the cascading effects and resilience of the CIs particularly in electric power stations. The limitation of topological network analysis in considering physical parameters and capacity of the components is complemented in the methodology by the vulnerability analysis. The results of the case study strongly suggest that, when only terrorist attacks are considered, protective strategies aimed at improving the robustness of CI have a much higher effectiveness and efficiency than those aimed at improving CI redundancy. Nevertheless, in CIs with lower direct loss and high indirect loss and importance, full redundancy should also be considered. Moreover, components with more connections to other components tend to be designed in a compact, space-efficient manner that may unintentionally result in their higher vulnerability to potential attacks, and demand higher priority in protection strategy. In other words, it can be inferred that a relatively loose arrangement of the critical components of the infrastructure could help to decrease its overall vulnerability to physical attacks. Particularly, in this case, an overcompact arrangement of the cardinal components may be responsible for the fact that reductions in the severity of a given attack scenario did _not_ translate into reductions in the severity of damage to essential components.  
As most research in CI protections focuses on the macro scale, such as the interaction of multiple infrastructures or even multiple systems, this paper has provided a potential approach to protection strategy analysis within a relative micro scale, considering the complexity of the interdependencies between the components of the critical infrastructure. The methodology proposed makes it possible to optimize the investment to critical infrastructure protections at lower levels, which can help to reduce expenditures on local infrastructure protection or on a single critical infrastructure for small projects. This paper also provides a complementary method to estimating terrorism risk. As research has been conducted on the changing occurrence of terrorist attacks over time [46], this research provides a  
Figure 5: Comparison of ROI between Protection Methodologies.  
possible approach to estimating the occurrence of terrorist attacks in space, specifically within the infrastructure, with the help of network modeling based on the connectivity within the infrastructure.  
In future research, it would be useful to include a wider variety of protection methods as well as possible response operations (e.g., buried in an underground cavern [47]) in order to present a more accurate estimation of potential damage and optimal protection strategies. The sensitivity of the methodology to various potential attack strategies can also be further developed through the examination of additional cases with diverse arrangements of functioning components.  
Conceptualization, H.-H.W., I.M.S., and M.J.S.; methodology, X.Y.; formal analysis, X.Y.; data curation, I.M.S.; writing--original draft preparation, X.Y.; writing--review and editing, H.-H.W.; visualization, X.Y.; supervision, I.M.S. and M.J.S. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.