经济代写|博弈论代写Game Theory代考|ECON3050

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|Stackelberg Security Games

A special class of Stackelberg games is the Stackelberg security game (SSG). The SSG model has wide applications in security-related domains. It has led to several application tools successfully deployed in the field, including ARMOR for setting up checkpoints and scheduling canine patrols at the Los Angeles International Airport, PROTECT for protecting ports of New York and Boston (Tambe 2011), and PAWS for protecting wildlife from poaching (Fang et al. 2016).

An SSG (Kiekintveld et al. 2009; Paruchuri et al. 2008) is a two-player game between a defender and an attacker. The defender must protect a set of $T$ targets from the attacker. The defender tries to prevent attacks using $M$ defender resources. In the simplest case, each defender resource (which corresponds to a patroller, a checkpoint, a canine team, or a ranger in security-related domains) can be allocated to protect one target and $M<T$. Thus, a pure strategy for the defender is an assignment of the $M$ resources to $M$ targets and a pure strategy for the adversary is a target $k \in{1 \ldots T}$ to be attacked. In a slightly more complex setting, each defender resource can be assigned to a patrol schedule, which covers a subset of targets, and it is impossible to cover all the targets with limited resources. Denote the jth defender pure strategy as $B_{j}$, an assignment of all the security resources. $B_{j}$ is represented as a column vector $B_{j}=\left\langle B_{j k}\right\rangle^{T}$, where $B_{j k} \in{0,1}$ indicates whether target $k$ is covered by $B_{j}$. For example, in a game with four targets and two resources, each of which can cover one target, $B_{j}=\langle 1,1,0,0\rangle$ represents the pure strategy of assigning one resource to target 1 and another to target 2. Each target $k \in{1 \ldots T}$ is assigned a set of payoffs $\left{P_{k}^{a}, R_{k}^{a}, P_{k}^{d}, R_{k}^{d}\right}:$ If an attacker attacks target $k$ and it is protected by a defender resource, the attacker gets utility $P_{k}^{a}$ and the defender gets utility $R_{k}^{d}$. If target $k$ is not protected, the attacker gets utility $R_{k}^{a}$ and the defender gets utility $P_{k}^{d}$. In order to be a valid security game, it must hold that $R_{k}^{a}>P_{k}^{d}$ and $R_{k}^{d}>P_{k}^{d}$, i.e. when the attacked target is covered, the defender gets a utility higher than that when it is not covered, and the opposite holds for the attacker. The defender is the leader and commits to a strategy first. The attacker can observe the defender’s strategy before selecting their strategy. This assumption reflects what happens in the real world in many cases. For example, in the airport security domain, the airport security team sends canine teams to protect the terminals every day. A dedicated attacker may be able to conduct surveillance to learn the defender’s strategy.

经济代写|博弈论代写Game Theory代考|Applications in Cybersecurity

Several works have used the Stackelberg game model to formulate problems in cybersecurity. Schlenker et al. (2018) and Thakoor et al. (2019) model the cyber deception problem as a Stackelberg game between the defender and the attacker. Similar to SSGs, the defender is protecting a set of targets from the attacker. In contrast to SSGs where the defender allocates resources to stop any potential attack on a subset of targets, in this work, the defender can choose to set up honeypots or provide a camouflage of existing machines in a network. By such deception techniques, the defender can make the honeypots appear to be important, or value targets appear unimportant. Thus, she can induce the attacker to attack a unimportant to the defender. Cranford et al. (2018) focuses on human behavior in cyber deception games. Schlenker et al. (2017) proposes a Stackelberg game model for the problem of allocating limited human limited human resources to investigate cybersecurity alerts. Stackelberg game models have also been used to model defense in cyber-physical systems (Wang et al. 2018; Yuan et al. 2016; Zhu and Martinez 2011). Li and Vorobeychik (2014, 2015) considers the detection and filtering of spam and phishing emails and formulate the problem as a Stackelberg game where an intelligent attacker will try to adapt to the defense strategy.

经济代写|博弈论代写Game Theory代考|Repeated Games

A repeated game is an EFG consisting of repetitions of a stage game. The stage game can be an NFG. For example, the repeated PD game is a game where the players repeatedly play the stage game of a PD game for multiple rounds. Also, we often see people playing the RPS game for three or five consecutive rounds in practice. A finitely repeated game has a finite number of rounds, and a player’s final payoff is the sum of their payoffs in each round. Infinitely repeated games last forever; there can be a discount factor $\delta \in(0,1)$ for future rounds when computing the final payoff.

The repetition of the stage game enables a much larger strategy space for the players comparing with the strategy space of the stage game. A player’s action in a round can be based on the players’ actions in the previous rounds. For example, in the repeated PD game, a player can use a Tit-for-Tat strategy, meaning that the player always chooses the same action as the one taken by the other player in the previous round of the game except for the first round where the player chooses Cooperate. In other words, if her opponent chose Cooperate in the last round, she will reward the other player’s kindness by choosing Cooperate in this round. Otherwise, she will penalize the other player by choosing Defect. A player can also choose a grim trigger strategy: she chooses Cooperate in the first round and continues to choose Cooperate if the other player never chooses Defect, but penalizes the other player by always choosing Defect for the rest of the game right after the other player chooses Defect for the first time.

In fact, both players playing the grim trigger strategy is an NE in an infinitely repeated PD game, as a player who deviates from it will get a utility of 0 in the round he deviates but at most $-2$ for each round in the rest of the game as the other player will always choose Defect. Both players choosing Tit-for-Tat is also an NE with a large enough $\delta$. If the player deviates by choosing Defect for $k-1$ consecutive rounds starting from round $t$ and then chooses Cooperate again, he can get at most a total utility of $0+\delta \times(-2)+\delta^{2} \times(-2)+\cdots+\delta^{k-1} \times(-2)+\delta^{k} \times(-3)$ for round $t$ to $t+k$. In comparison, not deviating leads to a total utility of $(-1)+\delta \cdot(-1)+\cdots+\delta^{k} \cdot(-1)$ during this period.

经济代写|博弈论代写Game Theory代考|Stackelberg Security Games

SSG (Kiekintveld et al. 2009; Paruchuri et al. 2008) 是防守方和进攻方之间的两人游戏。防守方必须保护一组吨攻击者的目标。防御者试图阻止攻击使用米后卫资源。在最简单的情况下，每个防御者资源（对应于巡逻员、检查站、警犬队或安全相关域中的游侠）可以被分配来保护一个目标和米<吨. 因此，防御者的纯策略是米资源米目标和对对手的纯粹策略是目标ķ∈1…吨被攻击。在稍微复杂的设置中，每个防御者资源都可以分配到一个巡逻计划，该计划涵盖目标的子集，并且不可能在资源有限的情况下覆盖所有目标。将第 j 个防御者纯策略表示为乙j，所有安全资源的分配。乙j表示为列向量乙j=⟨乙jķ⟩吨， 在哪里乙jķ∈0,1表示目标是否ķ被覆盖乙j. 例如，在一个有四个目标和两个资源的游戏中，每个资源可以覆盖一个目标，乙j=⟨1,1,0,0⟩表示将一种资源分配给目标 1 并将另一种资源分配给目标 2 的纯策略。每个目标ķ∈1…吨分配了一组收益\left{P_{k}^{a}, R_{k}^{a}, P_{k}^{d}, R_{k}^{d}\right}：\left{P_{k}^{a}, R_{k}^{a}, P_{k}^{d}, R_{k}^{d}\right}：如果攻击者攻击目标ķ它受到防御者资源的保护，攻击者获得效用磷ķ一个防御者得到效用Rķd. 如果目标ķ不受保护，攻击者获得实用程序Rķ一个防御者得到效用磷ķd. 为了成为一个有效的安全游戏，它必须持有Rķ一个>磷ķd和Rķd>磷ķd，即当被攻击的目标被覆盖时，防御者获得的效用高于没有被覆盖时的效用，而攻击者则相反。防御者是领导者，首先致力于战略。攻击者可以在选择他们的策略之前观察防御者的策略。这一假设反映了现实世界中许多情况下发生的情况。例如，在机场安检领域，机场安检队每天都会派出警犬队来保护航站楼。专门的攻击者可能能够进行监视以了解防御者的策略。

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MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。