### 经济代写|博弈论代写Game Theory代考|ECON2112

statistics-lab™ 为您的留学生涯保驾护航 在代写博弈论Game Theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写博弈论Game Theory代写方面经验极为丰富，各种代写博弈论Game Theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 经济代写|博弈论代写Game Theory代考|Simulation Results

We want to show that using proactive deception a defender can reveal the attacker type earlier than otherwise. We define an early identification as to when the defender can use proactive deception to determine the attacker type in an earlier round compared to when the defender just observes. Vulnerabilities in the nodes are (indirectly) represented by exploits on the edge between two nodes. We randomly generated 20 networks, somewhat similar to Figure 3.2, with 18 nodes with values and costs chosen randomly from the range $[0,10]$ including one public node. We considered exploits $\phi_{0}, \phi_{1}, \phi_{2}, \phi_{3}, \phi_{4}, \phi_{5}$ with cost chosen randomly from the range $[0,10]$. Next, we assign exploits to the edges in such a way that it allows the attackers to have unique attack plans to their goals except for the starting node. Depending on the edge density (number of edges from a node) and shared vulnerability parameters we randomly connect edges with exploits between nodes where the two nodes are in different attack plans of different attackers. We used six HPs and the vulnerabilities are picked from randomly chosen nodes existing in the network so that the HPs can act as decoys. The games are limited to five rounds. In each round $r$, the defender $d$ deploys $0 \leq k \leq 2$ decoys. In the attack plan library, we considered three attacker types, $a, b, c$ with different goals.

In the first experiment, we show that depending on different density of edges and shared vulnerabilities between nodes, how early a defender can identify the attacker type he is facing varies. Each of the three attackers, $a, b, c$ has some unique and some shared exploits in their possession. Attacker $a$ has exploits $\phi_{0}, \phi_{1}, \phi_{2}$. Attacker $b$ has $\phi_{2}, \phi_{3}, \phi_{1}$. Attacker $c$ has exploits $\phi_{4}, \phi_{5}, \phi_{2}$. We picked the attacker $b$ as the acting attacker.

Figure $3.6$ shows the results. In the first row in Figure 3.6a-c, defender just observes the attacker actions. As the density and shared vulnerabilities increases, it takes more rounds for the defender to identify the attacker type $b$. In the second row in Figure $3.6 \mathrm{e}$ and $\mathrm{f}$, the defender deploys HPs. If we compare the figures of the same edge density and shared vulnerabilities from the two rows, it is easy to notice that the use of deception facilitates early identification except Figure 3.6d where it was the same. However, an increase in edge density and shared vulnerabilities between nodes harms performance.

The second experiment is the same as the first except that we kept the edge density and shared vulnerabilities between nodes fixed to $40 \%$ and we varied the shared exploits between the attackers. We chose the attacker $c$ as the acting attacker. We can observe in Figure 3.7a-c that as we increase the sharing of exploits between the attackers it takes longer for the defender to identify the attacker type $c$. When all the attackers have the same exploits the defender was unable to identify the attacker type even at round 4 without using any deception. However, in the second row in Figure $3.7 \mathrm{~d}-\mathrm{f}$ as the defender strategically uses deception, identification of attacker $c$ happens earlier. The performance of the early identification decreases as the shared exploits between the attacker’s increases. Another observation is noticeable in Figure $3.7 \mathrm{~d}$ : the defender was not able to identify the attacker type, however, the attacker did not find any policy to continue its attack. This shows that the use of strategical deception can also act as a deterrent for the attackers.

## 经济代写|博弈论代写Game Theory代考|Scalability

In our current game model, the defender makes a move after considering the attacker’s last known position, and every possible way $k$ HPs can be allocated between two real nodes in the network. Let’s define $\sigma(i, j)$ as a slot where a HP can be allocated between node $i$ and node $j$. The current algorithm makes sure that node $i$ is always one hop distance away from the attacker’s last known position and node $j$ does not include the goal nodes to exclude trivial cases.

Using this approach the number of slots of $\sigma(i, j)$ where $k$ HPs can be allocated increases very quickly with both network size (branching factors) and $k$ that makes the algorithm not very scalable. For our initial experiments, we used a network of size 18. Now we will present a simple heuristics that makes sure that the algorithm can handle larger instances of networks compared to our initial approach.

## 经济代写|博弈论代写Game Theory代考|Heuristics

In the real world, sensors, intrusion detection systems, and forensic analysis are used to collect data and to analyze the alerts and to understand the Techniques, Tactics and Procedures (TTP) used by an attacker. Utilizing the same tools and analytics it is also possible to form a belief on the approximate time interval of the attacks of an attacker and his preferences towards different features of the network, for example, OS, application, ports, hardware, etc. Rather than just focusing on TTP used by an attacker the defender can try to understand the attacker’s behavior that drives the attacks and the attacker’s propagation throughout the network. If the defender knows the last position of the attacker in the network, the time interval and preferences and attacker behavior can be used to get an estimate on his future attacks in the network to form a radius from the last known position of the attacker to consider the slots for HP allocation. Using these estimations on the attacker’s future positions in the network, many of the unnecessary slots also can be filtered out.

In our game model, we do not capture this complex behavior of attacker preferences, behaviors, and intervals of attacks. We simplify it by assuming that the defender knows the attacker’s last position in each round and the defender also knows that the attacker only moves one hop per round. Using these assumptions the defender can consider slots $\sigma(i, j)$ where the distance between node $i$ and node $j$ is always two hops and node $i$ is always one hop away from the last known position of the attacker. It is also unnecessary to consider $\operatorname{slots} \sigma(i, j)$ where node $i$ and node $j$ are only one hop away since it will only introduce costs to the paths and we assume that the attacker chooses a path that minimizes his costs. More unnecessary slots can be eliminated from considerations utilizing domain knowledge; for example, the defender knows that the attacker only moves forward (which is not realistic) however, this is one of our assumptions of the game model. As a result, it is not necessary to consider slots that are behind the attacker’s last known position.

## 有限元方法代写

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