# An Epistemic Utility-Theoretic Model in Fortifying Oil-and-Gas Production Networks
## 4 Results and Discussion
Figure 5 is the best illustration of adopting five deception resources (B\({}^{F}\)= 5), where the defender tries to protect three nodes and two pipelines with five deception resources and zero real hardening resource. This plan allowed the defender to save lots of operational costs and minimize the model's objective function. When the attacker thinks that it sees five protected facilities, it will not risk attacking, and accordingly, he would target other facilities that appear to be unprotected. When the defender employed five real hardening resources and five deception resources, the aggressor may see that the defender has protected 10 facilities, not being able to distinguish between three deception sources (sinks) facilities, three hardened sources (sinks) facilities, two deception pipelines, and three hardened pipelines. As a result, the aggressor will focus on the less critical facilities that were left unprotected due to limited available resources. The reader can see that the objective function would drop faster than the exclusively hardened case in Figure 4.  
The model monitored different scenarios for fortification and deception to face the adversaries. The deception strategy was able to trick the attacker from targeting the most essential facilities with only five deception resources. What if the defender increases his deception resources? What if 10 deception resources are considered in the defender fortification plan? Does the objection function behave better than adopting five deception plans? Figure 6 illustrates the judicious use of deception strategy; the fact that a limited amount of deception is better than excessive use of deception. Figure 6 is to monitor a comparison between three different scenarios, when no deception is involved, when five resources are utilized, and when 10 resources used in the fortification strategies. From the illustration, the objective function behavior with five deception resources is better than utilizing 10 deception resources. Compared with the case of no deception, this figure shows a saving of $214,957.3 per day by applying just five deceptive resources. As observed from the same figure, it is  
Figure 5: Model results verification: defender–attacker strategies with deception. Figure 6: Objective function cost reduction with and without deception strategy. interesting to see that the cost reduction with an additional five deception resources (making a total of 10) is less than the cost saving of applying only five deception resources. Implementing the deception concept judiciously will help the leader to allocate his resources wisely. For example, the defender will spend only one deception resource for a node that serves both oil-and-gas. Without deception, the defender needs to spend two hardening resources for that production source as shown in Figure 7. Identifying the source and sinks in the oil-and-gas network can be considered as another high-level contribution of this paper. Figure 8 is an illustration of another case study that verifies the bi-level model works as intended when the defender used resources to protect the network from hardening and deception strategies or a combination of the two. By so doing, the attacker has prevented from targeting the critical facilities that will result in shortages in the demand sites, where the deception resources are \(B^{F}=10\), defending resources are \(B^{D}=10\), and attacker resources are \(B^{A}=10\). The defender was able to protect Source No. 3 and the connected pipeline, where the false information was used to posture the attacker from attacking it. These results based on the last iteration, where the defender tried to optimize his strategies to find the best solution for the network. From these results, we can see that the defender and attacker resources can play a major regulation in constructing fortifications and disruptions strategies. Allocating the limited defense resources were implemented in a good way to maximize security for the purpose of protecting the network as possible.