标签： ECOS3012

经济代写|博弈论代写Game Theory代考|ECON3503

Posted on 2023年3月24日2023年3月24日 by statistics-lab

如果你也在怎样代写博弈论Game Theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

博弈论是对理性主体之间战略互动的数学模型的研究。它在社会科学的所有领域，以及逻辑学、系统科学和计算机科学中都有应用。最初，它针对的是两人的零和博弈，其中每个参与者的收益或损失都与其他参与者的收益或损失完全平衡。在21世纪，博弈论适用于广泛的行为关系；它现在是人类、动物以及计算机的逻辑决策科学的一个总称。

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。

我们提供的博弈论Game Theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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|Further Discussions

Game theory attempts to bring mathematical precision to decision-making so that best strategies can be played, even in the arms race between the learner and the adversary. In game theory, we assume the players are rational-they seek to maximize their payoffs or minimize their losses. This assumption is not necessarily valid in real life, especially in cybersecurity domains. What appears irrational to one player may be rational to the opponent player. For example, when we model a game between airport security and terrorists, it may not be a good idea to view the terrorists based on our own experiences. When the opponent is not rational or simply plays poorly, it is important to realize that continuing to play the equilibrium strategy will lead to a losing situation or the loss of opportunity to exploit the opponent’s weaknesses.

Behavioral economists have long questioned the strict assumptions about rationality in existing theories in game theory (Aumann 1997). The actual decision-making by individuals is often irrational even in simple decision problems. Individuals typically fail to select the best response from a set of choice. As a matter of fact, optimization is so difficult that individuals are often unable to come up with their best responses to their opponents’ moves, unlike what the rational decision theory has always assumed. In response, theories that relax the rationality constraints have been proposed among which include: Quantal Response Equilibrium (QRE) (McKelvey and Palfrey 1995), a solution concept that promotes an equilibrium notion with bounded rationality that acknowledges the possibility that players do not always play a best response; Prospect Theory (Kahneman and Tversky 1979; Tversky and Kahneman 1992), a solution that introduces payoffs with respect to a reference point at which there is larger slope for losses than for gains and agents tend to overestimate small probabilities and underestimate large probabilities.

The same debate is applicable to mixed strategy games. In the airport security game, how the airport deploys security patrols depends on the response from the terrorists. If the rationality of the terrorists is predictable, it would be best for the airport to deploy its security patrols randomly by playing a mixed strategy. However, when there is a good reason to believe that the terrorists are not going to play the equilibrium strategy, airport security may be better off by playing pure strategies. Generally speaking, unless the odds are strongly in our favor, playing equilibrium strategies would be our best choice. Nevertheless, we should always keep in mind that our calculation of rationality may lead to different behavior, new rules may need to be defined in the game to take this into consideration.

经济代写|博弈论代写Game Theory代考|Adversarial Machine Learning

While there is a growing interest in applying machine learning to different data domains and deploying machine learning algorithms in real systems, it has become imperative to understand vulnerabilities of machine learning in the presence of adversaries. To that end, adversarial machine learning (Kurakin et al. 2016a; Vorobeychik and Kantarcioglu 2018; Shi et al. 2018b) has emerged as a critical field to enable safe adoption of machine learning subject to adversarial effects. One example that has attracted recent attention involves machine learning applications offered to public or paid subscribers via APIs; e.g. Google Cloud Vision (2020) provides cloud-based machine learning tools to build machine learning models. This online service paradigm creates security concerns of adversarial inputs to different machine learning algorithms ranging from computer vision to NLP (Shi et al. 2018c,d). As another application domain, automatic speech recognition and voice controllable systems were studied in terms of the vulnerabilities of their underlying machine learning algorithms (Vaidya et al. 2016; Zhang et al. 2017). As an effort to identify vulnerabilities in autonomous driving, attacks on self-driving vehicles were demonstrated in Kurakin et al. (2016), where the adversary manipulated traffic signs to confuse the learning model.

The manipulation in adversarial machine learning may happen during the training or inference (test) time, or both. During the training time, the goal of the adversary is to provide wrong inputs (features and/or labels) to the training data such that the machine learning algorithm is not properly trained. During the test time, the goal of the adversary is to provide wrong inputs (features) to the machine algorithm such that it returns wrong outputs. As illustrated in Figure 14.1, attacks built upon adversarial machine learning can be categorized as follows.

Attack during the test time.
a. Inference (exploratory) attack: The adversary aims to infer the machine learning architecture of the target system to build a shadow or surrogate model that has the same functionality as the original machine learning architecture (Barreno et al. 2006; Tramer et al. 2016; Wu et al. 2016; Papernot et al. 2017; Shi et al. 2017; Shi et al. 2018b). This corresponds to a white-box or black-box attack depending on whether the machine learning model such as the deep neural network structure is available to the adversary, or not. For a black-box attack, the adversary queries the target classifier with a number of samples and records the labels. Then, it uses this labeled data as its own training data to train a functionally equivalent (i.e. statistically similar) deep learning classifier, namely a surrogate model. Once the machine learning functionality is learned, the adversary can use the inference results obtained from the surrogate model for subsequent attacks such as confidence reduction or targeted misclassification.
b. Membership inference attack: The adversary aims to determine if a given data sample is a member of the training data, i.e. if a given data sample has been used to train the machine learning algorithm of interest (Nasr et al. 2018; Song et al. 2018; Jia et al. 2019; Leino and Fredrikson 2020). Membership inference attack is based on the analysis of overfitting to check whether a machine learning algorithm is trained for a particular data type, e.g. a particular type of images. By knowing which type of data the machine learning algorithm is trained to classify, the adversary can then design a subsequent attack more successfully.

博弈论代考

经济代写|博弈论代写Game Theory代考|Further Discussions

博弈论试图将数学精确性带入决策制定，以便即使在学习者和对手之间的军备竞赛中也能发挥最佳策略。在博弈论中，我们假设参与者是理性的——他们寻求最大化收益或最小化损失。这种假设在现实生活中不一定有效，尤其是在网络安全领域。对一个玩家来说不合理的事情可能对对手玩家来说是合理的。例如，当我们模拟机场安全和恐怖分子之间的博弈时，根据我们自己的经验来看待恐怖分子可能不是一个好主意。当对手不理性或只是打得不好时，重要的是要意识到继续采用均衡策略将导致失败的局面或失去利用对手弱点的机会。

长期以来，行为经济学家一直质疑博弈论中现有理论对理性的严格假设（Aumann 1997）。即使在简单的决策问题中，个人的实际决策也往往是非理性的。个人通常无法从一组选择中选择最佳反应。事实上，优化是如此困难，以至于个人往往无法对对手的举动做出最佳反应，这与理性决策理论一直假设的不同。作为回应，人们提出了放松理性约束的理论，其中包括：量子响应平衡 (QRE)（McKelvey 和 Palfrey 1995），这是一种解决方案概念，它促进具有有限理性的均衡概念，承认玩家并不总是玩游戏的可能性最好的回应；

同样的争论也适用于混合策略游戏。在机场安保博弈中，机场如何部署安保巡逻，取决于恐怖分子的反应。如果恐怖分子的理性是可以预见的，机场安保巡逻最好是随机部署，玩混合策略。然而，当有充分的理由相信恐怖分子不会采用均衡策略时，机场安全可能会通过采用纯策略而变得更好。一般而言，除非赔率对我们有利，否则采用均衡策略将是我们的最佳选择。然而，我们应该始终牢记，我们的理性计算可能会导致不同的行为，可能需要在游戏中定义新的规则来考虑到这一点。

经济代写|博弈论代写Game Theory代考|Adversarial Machine Learning

尽管人们对将机器学习应用于不同的数据域并在真实系统中部署机器学习算法的兴趣越来越大，但了解机器学习在存在对手的情况下的弱点已变得势在必行。为此，对抗性机器学习（Kurakin 等人 2016a；Vorobeychik 和 Kantarcioglu 2018 年；Shi 等人 2018b）已成为一个关键领域，可以安全采用受对抗影响的机器学习。最近引起关注的一个例子涉及通过 API 向公众或付费用户提供的机器学习应用程序；例如 Google Cloud Vision (2020) 提供基于云的机器学习工具来构建机器学习模型。这种在线服务范式对从计算机视觉到 NLP 的不同机器学习算法的对抗性输入产生了安全问题（Shi 等人，2018c，d）。作为另一个应用领域，自动语音识别和语音可控系统根据其底层机器学习算法的漏洞进行了研究（Vaidya 等人 2016 年；Zhang 等人 2017 年）。为了识别自动驾驶中的漏洞，Kurakin 等人演示了对自动驾驶车辆的攻击。(2016)，对手操纵交通标志来混淆学习模型。2016; 张等。2017）。为了识别自动驾驶中的漏洞，Kurakin 等人演示了对自动驾驶车辆的攻击。(2016)，对手操纵交通标志来混淆学习模型。2016; 张等。2017）。为了识别自动驾驶中的漏洞，Kurakin 等人演示了对自动驾驶车辆的攻击。(2016)，对手操纵交通标志来混淆学习模型。

对抗性机器学习中的操作可能发生在训练或推理（测试）时间，或两者兼而有之。在训练期间，对手的目标是向训练数据提供错误的输入（特征和/或标签），从而导致机器学习算法无法正确训练。在测试期间，对手的目标是向机器算法提供错误的输入（特征），使其返回错误的输出。如图 14.1 所示，基于对抗性机器学习的攻击可分为以下几类。

在测试时间内攻击。
A。推理（探索性）攻击：对手旨在推断目标系统的机器学习架构，以构建与原始机器学习架构具有相同功能的影子或替代模型（Barreno 等人，2006 年；Tramer 等人，2016 年； Wu 等人 2016 年；Papernot 等人 2017 年；Shi 等人 2017 年；Shi 等人 2018b)。这对应于白盒或黑盒攻击，具体取决于对手是否可以使用深度神经网络结构等机器学习模型。对于黑盒攻击，对手使用大量样本查询目标分类器并记录标签。然后，它使用这个标记数据作为自己的训练数据来训练一个功能等效（即统计相似）的深度学习分类器，即代理模型。
b. 成员推理攻击：对手旨在确定给定数据样本是否是训练数据的成员，即给定数据样本是否已用于训练感兴趣的机器学习算法（Nasr 等人，2018 年；Song 等人，2018 年）。 2018 年；Jia 等人 2019 年；莱诺和弗雷德里克森 2020 年）。Membership inference attack 是基于过度拟合的分析，以检查机器学习算法是否针对特定数据类型（例如特定类型的图像）进行了训练。通过了解训练机器学习算法分类的数据类型，对手可以更成功地设计后续攻击。

经济代写|博弈论代写Game Theory代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。

有限元方法代写

有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

随机分析代写

随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。

回归分析代写

多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。

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，工具箱允许您学习和应用专业技术。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。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|博弈论代写Game Theory代考|ECON90022

Posted on 2023年3月24日2023年3月24日 by statistics-lab

如果你也在怎样代写博弈论Game Theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的博弈论Game Theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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|A Single Leader Multi-followers Stackelberg Game

In a single leader multiple followers (SLMF) game (Basar and Olsder 1999), the leader makes its optimal decision prior to the decisions of multiple followers. The Stackelberg game played by the leader is:
$$
\begin{array}{ll}
\min _{s^{\ell}, s^} & F\left(s^{\ell}, s^\right) \
\text { s.t. } & G\left(s^{\ell}, s^\right) \leq 0 \ & H\left(s^{\ell}, s^\right)=0
\end{array}
$$
where $F$ is the leader’s objective function, constrained by $G$ and $H ; s^{\prime}$ is the leader’s decision and $s^$ is in the set of the optimal solutions of the lower level problem: $$ s^ \in\left{\begin{array}{ll}
\underset{s_i}{\operatorname{argmin}} & f_i\left(s^t, s_i\right) \
\text { s.t. } & g_i\left(s^{\ell}, s_i\right) \leq 0 \
& h_i\left(s^{\ell}, s_i\right)=0
\end{array}\right} \quad \forall i=1, \ldots, m
$$
where $m$ is the number of followers, $f_i$ is the $i^{\text {th }}$ follower’s objective function constrained by $g_l$ and $h_i$

For the sake of simplicity, we assume the followers are not competing among themselves. This is usually a valid assumption in practice since adversaries rarely affect each other through their actions. In a Bayesian Stackelberg game, the followers may have many different types and the leader does not know exactly the types of adversaries it may face when solving its optimization problem. However, the distribution of the types of adversaries is known or can be inferred from past experience. The followers’ strategies and payoffs are determined by the followers’ types. The followers play their optimal responses to maximize the payoffs given the leader’s strategy. The Stackelberg equilibrium includes an optimal mixed strategy of the learner and corresponding optimal strategies of the followers.

Problem Definition Given the payoff matrices $R^{\ell}$ and $R^f$ of the leader and the $m$ followers of $n$ different types, find the leader’s optimal mixed strategy given that all followers know the leader’s strategy when optimizing their rewards. The leader’s pure strategies consist of a set of generalized linear learning models $\langle\phi(x), w\rangle$ and the followers’ pure strategies include a set of vectors performing data transformation $x \rightarrow x+\delta x$.

Given the payoff matrices $R^{\ell}$ and $R^f$ discussed in Section 13.5.3.3 (as shown in Table 13.6), let $r^f$ denote the follower’s maximum payoff, $\mathcal{L}$ and $\mathcal{F}$ denote the indices of the pure strategies in the leader’s policy $s^{\ell}$ and the follower’s policy $s^f$.

经济代写|博弈论代写Game Theory代考|Real Datasets

For the two real datasets we again use spam base (UCI Machine Learning Repository 2019) and web spam (LIBSVM Data 2019). The learning tasks are binary classification problems, differentiating spam or webspam from legitimate e-mail or websites.

Spambase Dataset Recall that in the spam base dataset, the task is to differentiate spam from legitimate e-mail. There are 4601 e-mail messages in the dataset including approximately 1800 spam messages. The dataset has 57 attributes and one class label. Training and test datasets are separate. The results are averaged over 10 random runs. The detailed results are shown in Table 13.8. The $f_{\mathrm{a}}=0$ column is left out for the same reason as explained earlier on the artificial datasets.

This dataset serves as an excellent example to demonstrate the power of the mixed strategy. In the cases where $p=0.1$, that is, when we assume legitimate e-mail is modified $10 \%$ of the time (while spam is always modified), the two equilibrium predictors Equi $^{* 1}$ and Equi ${ }^{* 2}$ exhibit very stable performance in terms of predictive accuracy. Their error rates fluctuate slightly at 0.37 regardless of how aggressively the test data has been modified. On the other hand, $S \mathrm{SM}^{* 1}$ and $S_{V M}{ }^{* 2}$ significantly outperform the equilibrium predictors Equi ${ }^{* 1}$ and Equi $^{* 2}$ and the invariant SVM when $f_{\mathrm{a}} \leq 0.5$. However, the performance of SVM ${ }^{* 1}$ and SVM ${ }^{* 2}$ dropped quickly as the attack gets more intense $\left(f_{\mathrm{a}}>0.5\right)$, much poorer than the equilibrium predictors. The mixed strategy, although not the best, demonstrates superb performance by agreeing with the winning models the majority of the time. The standard SVM has similar performance to the equilibrium predictors, behaving poorly as the attack gets intense. When $p=0.5$, that is, when legitimate e-mail is modified half of the time while all spam is modified, equilibrium predictors still demonstrate very stable performance while the performance of the equilibrium predictors Equi $^{* 1}$ and Equi ${ }^{* 2}$ deteriorates sharply right after the attack factor increases to 0.3 . The mixed strategy, again not the best predictor, demonstrates the most consistent performance among all the predictors given any attack intensity levels.

We also tested the case where the attack factor $f_{\mathrm{a}} \in(0,1)$ is completely random under uniform distribution for each attacked sample on this dataset. The probability of negative data being attacked increases gradually from 0.1 to 0.9 . The results are illustrated in Figure 13.11. Again, we observe similar behavior of all the predictors: stable equilibrium predictors, $\mathrm{SVM}^{* 1}, \mathrm{SVM}^{* 2}$, and SVM progressively deteriorating as $p$ increases. The mixed strategy, although weakened as more negative data is allowed to be modified, consistently lies in between the equilibrium predictors and the $S V M$ predictors.

博弈论代考

经济代写|博弈论代写Game Theory代考|A Single Leader Multi-followers Stackelberg Game

在单一领导者多追随者 (SLMF) 博亦中（Basar 和 Olsder 1999），领导者在多个追随者做出决定之前做出其最优决策。领导者玩的 Stackelberg 游戏是:
在哪里 $F$ 是领导者的目标函数，受制于 $G$ 和 $H ; s^{\prime}$ 是领导者的决定^在较低级别问题的最优解集合中:
在哪里 $m$ 是追随者的数量， $f_i$ 是个 $i^{\text {th }}$ 追随者的目标函数受制于 $g_l$ 和 $h_i$
为了简单起见，我们假设追随者之间没有竞争。这在实践中通常是一个有效的假设，因为对手很少通过他们的行动相互影响。在贝叶斯 Stackelberg 博恋中，追随者可能有许多不同的类型，领导者在解决其优化问题时并不知道它可能面临的对手的确切类型。然而，对手类型的分布是已知的，或者可以从过去的经验中推断出来。追随者的策略和收益由追随者的类型决定。追随者根据领导者的策略发挥他们的最佳反应以最大化收益。Stackelberg 均衡包括学习者的最优混合策略和跟随者的相应最优策略。
问题定义给定支付矩阵 $R^{\ell}$ 和 $R^f$ 领导者和 $m$ 追随者 $n$ 不同的类型，找到领导者的最优混合策略，因为所有追随者在优化他们的奖励时都知道领导者的策略。领导者的纯策略由一组广义线性学习模型组成 $\langle\phi(x), w\rangle$ 跟随者的纯策略包括一组执行数据转换的向量 $x \rightarrow x+\delta x$.
给定支付矩阵 $R^{\ell}$ 和 $R^f$ 在第 13.5.3.3 节中讨论过 (如表 13.6 所示)，让 $r^f$ 表示跟随者的最大收益， $\mathcal{L}$ 和 $\mathcal{F}$ 表示领导者政策中纯策略的指标 $s^{\ell}$ 和追随者的政策 $s^f$.

经济代写|博弈论代写Game Theory代考|Real Datasets

对于这两个真实数据集，我们再次使用垃圾邮件库 (UCI Machine Learning Repository 2019) 和网络垃圾邮件 (LIBSVM Data 2019)。学习任务是二元分类问题，将垃圾邮件或网络垃圾邮件与合法电子邮件或网站区分开来。

Spambase 数据集回想一下，在垃圾邮件基础数据集中，任务是区分垃圾邮件和合法电子邮件。数据集中有 4601 封电子邮件，包括大约 1800 封垃圾邮件。该数据集有 57 个属性和一个类标签。训练和测试数据集是分开的。结果取 10 次随机运行的平均值。详细结果如表13.8所示。这 $f_{\mathrm{a}}=0$ 出于与前面在人工数据集上解释的相同原因，列被遗漏了。
该数据集是展示混合策略强大功能的绝佳示例。在这种情况下 $p=0.1$ ，也就是说，当我们假设合法的电子邮件被修改时 $10 \%$ 的时间 (而垃圾邮件总是被修改)，两个均衡预测器 Equi1 和装备 ${ }^{ 2}$ 在预测准确性方面表现出非常稳定的性能。无论测试数据修改得多么激进，它们的错误率都在 0.37 处轻微波动。另一方面， $S \mathrm{SM}^{* 1}$ 和 $S_{V M}{ }^{* 2}$ 显着优于均衡预测变量 Equi1 和装备 ${ }^{ 2}$ 和不变的 SVM 当 $f_{\mathrm{a}} \leq 0.5$. 但是，SVM 的性能1 和支持向量机 ${ }^{ 2}$ 随着攻击变得更加激烈而迅速下降 $\left(f_{\mathrm{a}}>0.5\right)$ ，比均衡预测变量差得多。混合策略虽然不是最好的，但在大多数情况下都与获胜模型一致，因此表现出色。标准 SVM 具有与平衡预测器相似的性能，随着攻击变得激烈，表现不佳。什么时候 $p=0.5$ ，也就是说，当合法电子邮件的一半时间被修改而所有垃圾邮件都被修改时，平衡预测器仍然表现出非常稳定的性能，而平衡预测器 Equi 的性能 ${ }^{* 1}$ 和装备 $^{* 2}$ 在攻击因子增加到 0.3 后立即急剧恶化。混合策略 (同样不是最佳预测器) 在给定任何攻击强度级别的所有预测器中展示了最一致的性能。
我们还测试了攻击因素的情况 $f_{\mathrm{a}} \in(0,1)$ 对于该数据集上的每个受攻击样本，在均匀分布下是完全随机的。负面数据被攻击的概率从 0.1 逐渐增加到 0.9 。结果如图 13.11 所示。同样，我们观察到所有预测变量的相似行为: 稳定均衡预测变量， $\mathrm{SVM}^{* 1}, \mathrm{SVM}^{* 2}$ ，并且 SVM 逐渐恶化为 $p$ 增加。混合策略虽然随着更多负面数据被允许修改而减弱，但始终位于均衡预测变量和 $S V M$ 预测因子。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|博弈论代写Game Theory代考|ECON2070

Posted on 2023年3月18日2023年3月18日 by statistics-lab

如果你也在怎样代写博弈论Game Theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的博弈论Game Theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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|Equilibrium Strategy Determination

In this game, the defender is considered the controller as it can select the actions which move the game from a state to another. The defender will also control when to apply the MTD, i.e. it will determine the duration between the time steps of the stochastic game. Assuming that the attacker has enough power, it can complete the brute-force attack in time $t_i$ for $i=1,2, \ldots, N$ for each one of the encryption techniques. Then, the defender should choose the time step $t$ to take the next action as follows:
$$
t<\min \left(t_i\right), \quad i=1,2, \ldots, N .
$$
By doing this, the defender can make sure that it takes a timely action before the attacker succeeds in revealing one of the keys.
The accumulated utility of player $i$ at state $s$ will be
$$
\Phi_i(\boldsymbol{f}, \boldsymbol{g}, s)=\sum_{t=1}^{\infty} \beta^{t-1} \cdot U_i\left(f\left(s_t\right), g\left(s_t\right), s_t\right),
$$
where $\boldsymbol{f}$ and $\boldsymbol{g}$ are the strategies adopted by the defender and attacker, respectively. The strategy specifies a vector of actions to be chosen at each of the states, e.g. $\boldsymbol{f}=\left[f\left(s_1\right), \ldots, f\left(s_K\right)\right]$ for all the $K$ states. Actions $f\left(s_t\right)$ and $g\left(s_t\right)$ are the actions chosen at $s_t$, which is the state of the game at time $t$, according to strategies $\boldsymbol{f}, \boldsymbol{g}$. State $s_t \in \mathcal{\delta}$ is determined by the defender’s action at time $t-1$. The game is assumed to start at a specific state $s=s_1$. Note that the utility in (10.4) is always bounded at infinity due to the fact that $0<\beta<1$.

When designing the bimatrix, the defender needs to calculate the accumulated utility when choosing each pure strategy against all of the attacker’s pure strategies. The defender, as a controller, can know the next state resulting from its actions, and, thus, it sums the utilities in all states using the discount factor $\boldsymbol{\beta}$. Let $\boldsymbol{X}$ be the defender’s accumulated utility matrix for all defender’s pure strategies’ permutations and all attacker’s pure strategies’ permutations. We let $\boldsymbol{F}{\boldsymbol{\bullet} \bullet}=\left[\boldsymbol{f}_1, \boldsymbol{f}_2, \ldots, \boldsymbol{f}{K^k}\right]$ be a matrix of all defender’s pure strategies’ permutation where each row represents actions in this strategy and similarly $\boldsymbol{G}{i \bullet}=\left[\boldsymbol{g}_1, \boldsymbol{g}_2, \ldots, \boldsymbol{g}{N^k}\right]$ the matrix of all attacker’s pure strategies’ permutation.

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

For our simulations, we choose a system that uses two encryption techniques with two different keys per technique. Thus, the number of system states is four and the defender has four actions in each state. For the bimatrix, the attacker has $2^4=16$ different strategy permutations and the defender has $4^4=256$ different strategy permutations. The power values are set to 1 and 3 to pertain to the ratio between the power consumption in the two different encryption techniques. These values are the same for both players. We set $R_1$ and $R_2$ to be 10 and 5 depending on the opponent’s actions. We choose these values to be higher than the power values in order for the utilities to be positive. The transition reward is set to 5 and 10 for switching to another state defined by another key or another technique, respectively.

First, we run simulations when there is no transition cost, $q=0$. The equilibrium strategies for both the attacker and defender are shown in Table 10.2. Note that actions $a_1, a_2$ represent the selection of two keys for the same encryption technique and actions $a_3, a_4$ represent two keys for another technique. Table 10.1 shows the probabilities over all actions for each player. These probabilities show how players should select actions in every state. For the defender, if it starts in state $s_3$, then it should move to state $s_1$ with the highest probability and move to state $s_2$ with a very similar probability. This is because the defender will change the technique and so gets a higher transition reward. We can see that the probability of moving to the same state is always very low and can reach 0 as in state $s_1$. The probability of moving to a state that has a similar encryption key is always less than that of moving to a state with different technique as the transition reward will be lower. For the attacker, the probability of attacking the same technique that is used in the current state is always higher than attacking any other technique.

In Figure 10.3, we show the effect of the discount factor on the defender’s utility at equilibrium in every state. First, we can see that all utility values at all states increase as the discount factor increases. This is due to the fact that increasing the discount factor will make the defender care more about future rewards thus choosing the actions that will increase these future rewards. Figure 10.3 also shows that the defender’s values at states 1 and 2 are higher than at states 3 and 4 . This because states 1 and 2 adopt the first encryption technique which uses less power than the encryption technique used in states 3 and 4 . The difference mainly arises in the first state before switching to other states and applying the discount factor. Clearly, changing the discount factor has a big effect on changing the equilibrium strategy, and, thus, the game will move between states with different probabilities resulting in a different accumulated reward.

博弈论代考

经济代写|博弈论代写Game Theory代考|Equilibrium Strategy Determination

在此游戏中，防御者被视为控制器，因为它可以选择将游戏从一种状态移动到另一种状态的动作。防御者还将控制何时应用 MTD，即它将确定随机游戏的时间步长之间的持续时间。假设攻击者拥有足够的力量，可以及时完成暴力破解 $t_i$ 为了 $i=1,2, \ldots, N$ 对于每一种加密技术。然后，防御者应该选择时间步长 $t$ 采取下一步行动如下:
$$
t<\min \left(t_i\right), \quad i=1,2, \ldots, N
$$
通过这样做，防御者可以确保在攻击者成功泄露其中一个密钥之前采取及时的行动。玩家的侽积效用 $i$ 在状态 $s$ 将
$$
\Phi_i(\boldsymbol{f}, \boldsymbol{g}, s)=\sum_{t=1}^{\infty} \beta^{t-1} \cdot U_i\left(f\left(s_t\right), g\left(s_t\right), s_t\right)
$$
在哪里 $\boldsymbol{f}$ 和 $\boldsymbol{g}$ 分别是防御者和攻击者所采用的策略。该策略指定了在每个状态下要选择的动作向量，例如 $\boldsymbol{f}=\left[f\left(s_1\right), \ldots, f\left(s_K\right)\right]$ 对于所有的 $K$ 状态。动作 $f\left(s_t\right)$ 和 $g\left(s_t\right)$ 是在 $s_t$ ，这是当时的游戏状态 $t$, 根据策略 $\boldsymbol{f}, \boldsymbol{g}$. 状态 $s_t \in \delta$ 由防御者当时的动作决定 $t-1$. 假定游戏从特定状态开始 $s=s_1$. 请注意，由于以下事实，(10.4) 中的效用总是有界于无穷大 $0<\beta<1$.
在设计双矩阵时，防御者需要计算选择每个纯策略时对攻击者所有纯策略的侽积效用。作为控制器的防御者可以知道其行为导致的下一个状态，因此它使用折扣因子对所有状态下的效用求和 $\beta$. 让 $\boldsymbol{X}$ 是防御者所有防御者纯策略排列和所有攻击者纯策略排列的侽积效用矩阵。我们让 $\boldsymbol{F} \bullet \bullet=\left[\boldsymbol{f}_1, \boldsymbol{f}_2, \ldots, \boldsymbol{f} K^k\right]$ 是所有防御者纯策略排列的矩阵，其中每一行代表该策略中的动作，类似地 $\boldsymbol{G} i \bullet=\left[\boldsymbol{g}_1, \boldsymbol{g}_2, \ldots, \boldsymbol{g} N^k\right]$ 所有攻击者纯策略排列的矩阵。

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

对于我们的模拟，我们选择一个系统，该系统使用两种加密技术，每种技术有两个不同的密钥。因此，系统状态的数量为四个，防御者在每个状态下有四个动作。对于双矩阵，攻击者有 $2^4=16$ 不同的策略排列，防御者有 $4^4=256$ 不同的策略排列。功率值设置为 1 和 3 ，以适应两种不同加密技术的功耗比率。这些值对于两个玩家都是相同的。我们设置 $R_1$ 和 $R_2 10$ 和 5 取决于对手的行动。我们选择这些值高于功率值以使效用为正。转换奖励分别设置为 5 和 10 ，用于切换到由另一个键或另一种技术定义的另一个状态。
首先，我们在没有转换成本的情况下运行模拟， $q=0$. 表 10.2 显示了攻击者和防御者的均衡策略。注意动作 $a_1, a_2$ 表示为相同的加密技术和操作选择两个密钥 $a_3, a_4$ 代表另一种技术的两个键。表 10.1 显示了每个参与者所有行动的概率。这些概率显示了玩家在每个状态下应该如何选择动作。对于防御者，如果它开始于状态 $s_3$ ，那么它应该移动到状态 $s_1$ 以最高的概率移动到状态 $s_2$ 概率非常相似。这是因为防守者会改变技术并因此获得更高的过渡奖励。我们可以看到移动到相同状态的概率总是很低，可以达到 $0 s_1$. 移动到具有相似加密密钥的状态的概率总是小于移动到具有不同技术的状态的概率，因为转换奖励会更低。对于攻击者来说，攻击当前状态下使用的相同技术的概率总是高于攻击任何其他技术的概率。
在图 10.3 中，我们显示了贴现因子对防御者在每个状态下的均衡效用的影响。首先，我们可以看到所有状态下的所有效用值都随着贴现因子的增加而增加。这是因为增加折扣因子会使防御者更关心末来的回报，从而选择会增加这些末来回报的行动。图 10.3 还显示防御者在状态 1 和 2 的值高于状态 3 和 4。这是因为状态 1 和 2 采用第一种加密技术，该技术比状态 3 和 4 中使用的加密技术使用更少的功率。差异主要出现在切换到其他状态并应用折扣因子之前的第一个状态。显然，改变贴现因子对改变均衡策略有很大影响。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|博弈论代写Game Theory代考|ECON3503

Posted on 2023年3月18日2023年3月18日 by statistics-lab

如果你也在怎样代写博弈论Game Theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的博弈论Game Theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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|Numerical Example

Consider a game that has two states. In an MTD scenario, the defender will have two actions representing selecting between each of these two states. Similarly, the attacker is assumed to have two actions of attacking profiles (both can be applied at either state).

A defender’s strategy can then be given as $\boldsymbol{f}=[a b]$, where $a$ is the action of moving to state $s_1$ and $b$ is the action of moving to state $s_2$.
The defender’s and attacker’s strategies’ permutation will be given as:
$$
\boldsymbol{F}=\left[\begin{array}{ll}
1 & 1 \
1 & 2 \
2 & 1 \
2 & 2
\end{array}\right] \boldsymbol{G}=\left[\begin{array}{ll}
1 & 1 \
1 & 2 \
2 & 1 \
2 & 2
\end{array}\right]
$$
where $\boldsymbol{F}$ and $\boldsymbol{G}$ represent the defender’s and the attacker’s permutations, respectively.
Since each player has four different permutations, each of the formulated matrices (bimatrix) will be of size $4 \cdot 4$ representing all the possible combinations of the players’ permutations. The elements of these matrices will be the accumulated utilities for each player resulting from starting at combination and considering all the future transitions.

Now suppose that the mixed Nash equilibrium for the bimatrix game, calculated from any numerical algorithm such as Lemke and Howson (1964), is given by:
$$
\boldsymbol{x}^=\left[\begin{array}{l} 0.2 \ 0.1 \ 0.3 \ 0.4 \end{array}\right] \boldsymbol{y}^=\left[\begin{array}{l}
0.0 \
0.1 \
0.4 \
0.5
\end{array}\right]
$$

where each row in $\boldsymbol{x}^$ and $\boldsymbol{y}^$ represents the players’ probabilities of selecting a strategy in $\boldsymbol{F}$ and $\boldsymbol{G}$, respectively.

Finally, the stochastic game equilibrium strategies can be calculated by summing the probabilities of choosing each action over the corresponding states. For example, the defender can choose action 1 at state 1 twice in $\boldsymbol{F}$ with probabilities 0.2 and 0.1 (from $\boldsymbol{x}^$ ). When summed, the defender knows that when the game is at state 1 , it will choose action 1 with a probability 0.3 . Following the same approach, we can compute the full equilibrium matrices as follows: $$ \boldsymbol{E}^=\left[\begin{array}{ll}
0.3 & 0.5 \
0.7 & 0.5
\end{array}\right] \boldsymbol{H}^=\left[\begin{array}{ll} 0.1 & 0.4 \ 0.9 & 0.6 \end{array}\right] $$ where $\boldsymbol{E}^$ and $\boldsymbol{H}^*$ are the defender’s and the attacker’s equilibrium solutions, respectively, and that the rows of the matrices represent players’ actions and the columns represent the game states.

经济代写|博弈论代写Game Theory代考|A Case Study for Applying Single-Controller

Consider a wireless sensor network that consists of a BS and a number of wireless nodes. The network is deployed for sensing and collecting data about some phenomena in a given geographic area. Sensors will collect data and use multi-hop transmissions to forward this data to a central receiver or BS. The multiple access follows a slotted Aloha protocol. Time is divided into slots and the time slot size equals the time required to process and send one packet. Sensor nodes are synchronized with respect to time slots. We assume that nodes are continuously working and so every time slot there will be data that must be sent to the BS.

All packets sent over the network are assumed to be decrypted using a given encryption technique and a previously shared secret key. All the nodes in the system are pre-programmed with a number of encryption techniques along with a number of encryption keys per technique, as what is typically done in sensor networks (Casola et al. 2013). The BS chooses a specific encryption technique and key by sending a specific control signal over the network including the combination it wants to use. We note that the encryption technique and key sizes should be carefully selected in order not to consume a significant amount of energy when encrypting or decrypting packets. Increasing the key size will increase the amount of consumed energy particularly during the decryption (Lee et al. 2010). Since the BS is mostly receiving data, it spends more time decrypting packets rather than encrypting them and, thus, it will be highly affected by key size selection.

In our model, an eavesdropper is located in the communication field of the BS and it can listen to packets sent or received by the BS. As packets are encrypted, the attacker will seek to decrypt the packets it receives in order to get information. The attacker knows the encryption techniques used in the network and so it can try every possible key on the received packets until getting useful information. This technique is known as brute-force attack.

The idea of using multiple encryption techniques was introduced in Casola et al. (2013). However, in this work, each node individually selects one of these technique to encrypt transmitted packets. The receiving node can know the used technique by a specific field in the packet header. Large encryption keys were used which require a significant amount of power to be decrypted. Nonetheless, these large keys are highly unlikely to be revealed using a brute-force attack in a reasonable time. Here, we propose to use small encryption keys to save energy and, in conjunction with that, we enable the BS to change the encryption method in a way that reduces the chance that the encryption key is revealed by the attacker. This is the main idea behind MTD. In this model, the encryption key represents the attack surface, and by changing the encryption method, the BS will make it harder for the eavesdropper to reveal the key and get the information from the system. Naturally, the goals of the eavesdropper and the BS are not aligned. On the one hand, the BS wants to protect the data sent over the network by changing encryption method. On the other hand, the attacker wants to reveal the used key in order to get information. To understand the interactions between the defender and the attacker, one can use game theory to study their behavior in this MTD scenario. The problem is modeled as a game in which the attacker and the defender are the players. As the encryption method should be changed over time and depending on the attacker’s actions, we must use a dynamic game.

博弈论代考

经济代写|博弈论代写Game Theory代考|Numerical Example

考虑一个有两个状态的游戏。在 MTD 场景中，防御者将有两个动作代表在这两个状态中的每一个之间进行选择。类似地，假设攻击者有两个攻击配置文件的操作（都可以在任一状态下应用）。
防御者的策略可以表示为 $\boldsymbol{f}=[a b]$ ，在哪里 $a$ 是移动到状态的动作 $s_1$ 和 $b$ 是移动到状态的动作 $s_2$. 防御者和攻击者的策略排列如下:
在哪里 $\boldsymbol{F}$ 和 $\boldsymbol{G}$ 分别代表防御者和攻击者的排列。
由于每个玩家都有四种不同的排列，因此每个公式化的矩阵 (双矩阵) 的大小都是 $4 \cdot 4$ 代表玩家排列的所有可能组合。这些矩阵的元素将是每个玩家从组合开始并考虑所有末来转换的侽积效用。
现在假设双矩阵博栾的混合纳什均衡，由 Lemke 和 Howson (1964) 等任何数值算法计算得出，由下式给出:
$$
\boldsymbol{x}^{=}\left[\begin{array}{llll}
0.2 & 0.1 & 0.3 & 0.4
\end{array}\right] \boldsymbol{y}=\left[\begin{array}{llll}
0.0 & 0.1 & 0.4 & 0.5
\end{array}\right]
$$
最后，可以通过对相应状态下选择每个动作的概率求和来计算随机博孪均衡策略。例如，防御者可以在状态 1 中选择动作 1 两次 $\boldsymbol{F}$ 概率为 0.2 和 0.1 (来自 lboldsymbol $x}^{\wedge}$ ). 求和时，防御者知道当游戏处于状态 1 时，它会以 0.3 的概率选择动作 1 。按照相同的方法，我们可以按如下方式计算完整的平衡矩阵:
在哪里 Iboldsymbol{E $}^{\wedge}$ 和 $\boldsymbol{H}^*$ 分别是防御者和攻击者的均衡解，矩阵的行代表玩家的行为，列代表游戏状态。

经济代写|博弈论代写Game Theory代考|A Case Study for Applying Single-Controller

考虑一个由 BS 和许多无线节点组成的无线传感器网络。该网络用于感测和收集有关给定地理区域中某些现象的数据。传感器将收集数据并使用多跳传输将此数据转发到中央接收器或 BS。多路访问遵循时隙 Aloha 协议。时间分为时隙，时隙大小等于处理和发送一个数据包所需的时间。传感器节点在时隙方面同步。我们假设节点连续工作，因此每个时隙都会有必须发送到 BS 的数据。

假设通过网络发送的所有数据包都使用给定的加密技术和先前共享的密钥进行解密。系统中的所有节点都使用多种加密技术以及每种技术的多种加密密钥进行预编程，这与传感器网络中的典型做法相同（Casola 等人，2013 年）。BS 通过在网络上发送特定的控制信号（包括它要使用的组合）来选择特定的加密技术和密钥。我们注意到，应仔细选择加密技术和密钥大小，以免在加密或解密数据包时消耗大量能量。增加密钥大小会增加消耗的能量，尤其是在解密期间（Lee 等人，2010 年）。由于 BS 主要接收数据，

在我们的模型中，窃听器位于 BS 的通信领域，它可以监听 BS 发送或接收的数据包。由于数据包被加密，攻击者将试图解密它收到的数据包以获取信息。攻击者知道网络中使用的加密技术，因此它可以在收到的数据包上尝试每个可能的密钥，直到获得有用的信息。这种技术被称为蛮力攻击。

Casola 等人介绍了使用多种加密技术的想法。(2013)。然而，在这项工作中，每个节点单独选择其中一种技术来加密传输的数据包。接收节点可以通过包头中的特定字段知道所使用的技术。使用了需要大量能量才能解密的大型加密密钥。尽管如此，这些大密钥极不可能在合理的时间内使用暴力攻击来泄露。在这里，我们建议使用小的加密密钥来节省能源，与此同时，我们使 BS 能够以一种降低加密密钥被攻击者泄露的机会的方式改变加密方法。这是 MTD 背后的主要思想。在这个模型中，加密密钥代表攻击面，通过改变加密方式，BS 将使窃听者更难泄露密钥并从系统中获取信息。自然地，窃听者和 BS 的目标并不一致。一方面，BS 想通过改变加密方法来保护通过网络发送的数据。另一方面，攻击者想要泄露使用的密钥以获取信息。要了解防御者和攻击者之间的交互，可以使用博弈论来研究他们在此 MTD 场景中的行为。该问题被建模为一个游戏，其中攻击者和防御者是玩家。由于加密方法应该随着时间的推移而改变，并且取决于攻击者的行为，我们必须使用动态游戏。窃听者和 BS 的目标不一致。一方面，BS 想通过改变加密方法来保护通过网络发送的数据。另一方面，攻击者想要泄露使用的密钥以获取信息。要了解防御者和攻击者之间的交互，可以使用博弈论来研究他们在此 MTD 场景中的行为。该问题被建模为一个游戏，其中攻击者和防御者是玩家。由于加密方法应该随着时间的推移而改变，并且取决于攻击者的行为，我们必须使用动态游戏。窃听者和 BS 的目标不一致。一方面，BS 想通过改变加密方法来保护通过网络发送的数据。另一方面，攻击者想要泄露使用的密钥以获取信息。要了解防御者和攻击者之间的交互，可以使用博弈论来研究他们在此 MTD 场景中的行为。该问题被建模为一个游戏，其中攻击者和防御者是玩家。由于加密方法应该随着时间的推移而改变，并且取决于攻击者的行为，我们必须使用动态游戏。要了解防御者和攻击者之间的交互，可以使用博弈论来研究他们在此 MTD 场景中的行为。该问题被建模为一个游戏，其中攻击者和防御者是玩家。由于加密方法应该随着时间的推移而改变，并且取决于攻击者的行为，我们必须使用动态游戏。要了解防御者和攻击者之间的交互，可以使用博弈论来研究他们在此 MTD 场景中的行为。该问题被建模为一个游戏，其中攻击者和防御者是玩家。由于加密方法应该随着时间的推移而改变，并且取决于攻击者的行为，我们必须使用动态游戏。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|博弈论代写Game Theory代考|ECON3503

Posted on 2023年3月15日2023年3月15日 by statistics-lab

如果你也在怎样代写博弈论Game Theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的博弈论Game Theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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|Hypergames on Graphs

A hypergame models the situation where different players perceive their interaction with other players differently and consequently play different games in their own minds depending on their perception. We consider the case where the difference in perception arises because of incomplete and potentially incorrect information. For instance, suppose a subset of nodes in the network are honeypots, the attacker may mistake these to be true hosts. We formulate a hypergame to model the interaction between the defender and the attacker given asymmetric information.
First, let’s review the definition of hypergames.
Definition 6.2 (Hypergame; Bennett 1980; Vane 2000) Given two players, a game perceived by player 1 is denoted by $\mathcal{G}_1$, and a game perceived by player 2 is denoted by $\mathcal{G}_2$. A level-1 hypergame is defined as a tuple:
$$
\mathcal{H} \mathcal{G}^1=\left\langle\mathcal{G}_1, \mathcal{G}_2\right\rangle
$$
In a level-1 hypergame, none of the player’s is aware of other player’s perception.
When one player becomes aware of the other player’s (mis)perception, the interaction is captured by a level- 2 two-player hypergame, defined as a tuple:
$$
\mathcal{H} \mathcal{G}^2=\left\langle\mathcal{H} \mathcal{G}^1, \mathcal{G}_2\right\rangle
$$
where P1 perceives the interaction as a level-1 hypergame (as P1 is aware of P2’s game $\mathcal{G}_2$ in addition to his own) and $\mathrm{P} 2$ perceives the interaction as the game $\mathcal{G}_2$.

We refer to the games $\mathcal{G}_1$ (resp., $\mathcal{G}_2$ ) as P1’s (resp., P2’s) perceptual game in level-1 hypergame, and $\mathcal{H} \mathcal{G}^1$ as P1’s perceptual game in level-2 hypergame. As P2 is not aware that she might be misperceiving the game, her perceptual game in level-2 hypergame is still $\mathcal{G}_2$.

In general, if P1 computes his strategy by solving an $(m-1)$ th level hypergame and P2 computes her strategy using an $n$th level hypergame with $n<m$, then the resulting hypergame is said to be a level- $m$ hypergame given as:
$$
\mathcal{H} \mathcal{G}^m=\left\langle\mathcal{H} \mathcal{G}_1^{m-1}, \mathcal{H} \mathcal{G}_2^n\right\rangle
$$

经济代写|博弈论代写Game Theory代考|Synthesis of Reactive Defense Strategies with Cyber Deception

When the attacker has a one-sided misperception of labeling function, as defined in Definition 6.3, the defender might strategically utilize this misperception to deceive the attacker into choosing a strategy that is advantageous to the defender. To understand when the defender might have such a deceptive strategy and how to compute it, we study the solution concept of hypergame.

Solution Approach A hypergame $\mathcal{H} \mathcal{G}^2=\left\langle\mathcal{H} \mathcal{G}^1, \mathcal{G}_2\right\rangle$ is defined using two games, namely $\mathcal{G}_1$ and $\mathcal{G}_2$. Under one-sided misperception of labeling function, defender is aware of both games. Therefore, to synthesize a deceptive strategy, the defender must take into account the strategy that the attacker will use, based on her misperception. That is, the defender must solve two games: game $\mathcal{G}_2$ to identify the set of states in the game transition system $G_2 \otimes \mathcal{A}$ that the attacker perceives as winning for her under labeling function $L_2$ and game $\mathcal{G}_1$ to identify the set of states in the game transition system $G_1 \otimes \mathcal{A}$ that are winning for the defender under (ground-truth) labeling function $L=L_1$. After solving the two games, the defender can integrate the solutions to obtain a set of states, at which the attacker makes mistakes due to the difference between $L_2$ and $L$. Let us introduce a notation to denote these sets of winning states.

$\mathcal{G}_1$ : P1’s winning region is Win $\operatorname{Win}_1 \subseteq S \times Q$ and P2’s winning region is Win $_2 \subseteq S \times Q$.
$\mathcal{G}_2: \mathrm{P} 1$ ‘s winning region is $\mathrm{Win}_1^{\mathrm{P2}} \subseteq S \times Q$ and P2’s winning region is $\mathrm{Win}_2^{\mathrm{P2}} \subseteq S \times Q$.
Figure 6.7 provides a conceptual representation partitions of the state space of a game transition system. Due to misperception, the set of states are partitioned into the following regions:
Win $\mathrm{W}_1$ : is a set of states from which P1 can ensure satisfaction of security objectives, even if P2 has complete and correct information. Thus, P1 can take the winning strategy $\pi_1$.
$\mathrm{Win}_1^{\mathrm{P} 2} \cap \mathrm{Win}_2$ is a set of states where P2 is truly winning but perceives the states to be losing for her due to misperception. Thus, P2 may either give up the attack mission or play randomly.
$\mathrm{Win}_2^{\mathrm{P2}} \cap \mathrm{Win}_2$ is a set of states in which P2 is truly winning and perceives those states to be winning. In this scenario, she will carry out the winning strategy $\pi_2^{\mathrm{P2}}$. However, this strategy can be different from the true winning strategy $\pi_2$ that P2 should have played if she had complete and correct information. This difference creates unique opportunities for P1 to enforce security of the system.

博弈论代考

经济代写|博弈论代写Game Theory代考|Hypergames on Graphs

超级博亦模拟了不同玩家对他们与其他玩家的互动有不同看法的情况，因此根据他们的看法在他们自己的头脑中玩不同的游戏。我们考虑由于不完整和可能不正确的信息而导致感知差异的情况。例如，假设网络中的一部分节点是蜜罐，攻击者可能会将它们误认为是真正的主机。我们制定了一个超博娈来模拟给定信息不对称的防御者和攻击者之间的交互。
首先，让我们回顾一下超博栾的定义。
定义 6.2 (Hypergame；Bennett 1980；Vane 2000) 给定两个玩家，玩家 1 感知的游戏表示为 $\mathcal{G}_1$ ，玩家 2 感知到的游戏表示为 $\mathcal{G}_2$.一级超博变被定义为一个元组:
$$
\mathcal{H \mathcal { G } ^ { 1 }}=\left\langle\mathcal{G}_1, \mathcal{G}_2\right\rangle
$$
在 1 级超博亦中，没有玩家知道其他玩家的感知。
当一个玩家意识到另一个玩家的（错误）感知时，交互被 2 级双人超博恋捕获，定义为元组:
$$
\mathcal{H} \mathcal{G}^2=\left\langle\mathcal{H} \mathcal{G}^1, \mathcal{G}_2\right\rangle
$$
其中 $\mathrm{P} 1$ 将交互视为 1 级超博恋 (因为 $\mathrm{P} 1$ 知道 $\mathrm{P} 2$ 的游戏 $\mathcal{G}_2$ 除了他自己的) 和 $\mathrm{P} 2$ 将交互视为游戏 $\mathcal{G}_2$.
我们指的是游戏 $\mathcal{G}_1$ (分别， $\mathcal{G}_2$ ) 作为 P1 (resp., P2) 在 level-1 hypergame 中的感知游戏，并且 $\mathcal{H} \mathcal{G}^1$ 作为 2 级超博娈中 $P 1$ 的感知博恋。由于 $P 2$ 不知道她可能误解了游戏，她在 level-2 hypergame 中的感知游戏仍然是 $\mathcal{G}_2$.
一般来说，如果 P1 通过解决一个问题来计算他的策略 $(m-1)$ th level hypergame 和 P2 计算她的策略使用 $n$ th级超博恋 $n<m$ ，那么由此产生的超博恋被称为水平- $m$ 超博栾给出：
$$
\mathcal{H} \mathcal{G}^m=\left\langle\mathcal{H} \mathcal{G}_1^{m-1}, \mathcal{H} \mathcal{G}_2^n\right\rangle
$$

经济代写|博弈论代写Game Theory代考|Synthesis of Reactive Defense Strategies with Cyber Deception

当攻击者对标签函数有片面的误解时，如定义 6.3 所定义，防御者可能会战略性地利用这种误解来欺骗攻击者选择对防御者有利的策略。为了了解防御者何时可能采用这种欺骗性策略以及如何计算它，我们研究了超博弈的解决方案概念。
解决方法超博栾 $\mathcal{H} \mathcal{G}^2=\left\langle\mathcal{H} \mathcal{G}^1, \mathcal{G}_2\right\rangle$ 使用两个游戏定义，即 $\mathcal{G}_1$ 和 $\mathcal{G}_2$. 在对标签功能的片面误解下，防守者意识到了这两种游戏。因此，要综合欺骗性策略，防御者必须考虑攻击者将根据自己的误解使用的策略。也就是说，防守者必须解决两场比寋: 比赛 $\mathcal{G}_2$ 识别游戏转换系统中的状态集 $G_2 \otimes \mathcal{A}$ 攻击者认为在标签功能下为她赢得胜利 $L_2$ 和游戏 $\mathcal{G}_1$ 识别游戏转换系统中的状态集 $G_1 \otimes \mathcal{A}$ 在 (真实情况) 标签功能下为防御者赢得胜利 $L=L_1$. 解决完这两个游戏后，防御者可以将解决方案整合以获得一组状态，攻击者由于之间的差异而犯错误 $L_2$ 和 $L$. 让我们引入一个符号来表示这些获胜状态集。

$\mathcal{G}_1: \mathrm{P} 1$ 的获胜区域是WinWin $\operatorname{Win}_1 \subseteq S \times Q \mathrm{P} 2$ 的获胜区域是 $\operatorname{Win}_2 \subseteq S \times Q$.
$\mathcal{G}_2: \mathrm{P} 1$ 的获胜区域是 $\mathrm{Win}_1^{\mathrm{P} 2} \subseteq S \times Q \mathrm{P} 2$ 的获胜区域是 $\mathrm{Win}_2^{\mathrm{P} 2} \subseteq S \times Q$. 图 6.7 提供了游戏转换系统状态空间的概念表示分区。由于误解，状态集被划分为以下区域:
赢 $W_1$ : 是一组状态，即使 $P 2$ 拥有完整和正确的信息，P1 也可以确保满足安全目标。因此，P1 可以釆取必胜策略 $\pi_1$.
$\operatorname{Win}_1^{\mathrm{P2}} \cap \mathrm{Win}$ 是一组状态，其中 $P 2$ 真正获胜，但由于误解而认为这些状态对她来说是失败的。因此，P2 要么放弃攻击任务，要么随机游玩。
$\mathrm{Win}_2^{\mathrm{P} 2} \cap \mathrm{Win}_2$ 是 $\mathrm{P} 2$ 真正获胜并认为这些状态获胜的一组状态。在这种情况下，她将执行制胜战略 $\pi_2^{\mathrm{P} 2}$. 但是，此策略可能与真正的获胜策略不同 $\pi_2$ 如果她有完整和正确的信息， $P 2$ 应该玩。这种差异为 P1 创造了独特的机会来加强系统的安全性。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|博弈论代写Game Theory代考|ECON90022

Posted on 2023年3月15日2023年3月15日 by statistics-lab

如果你也在怎样代写博弈论Game Theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的博弈论Game Theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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|A Theory of Hypergames on Graphs

A game arena is a transition system with labels assigned to the states. It captures different configurations of the network and the actions that the attacker and the defender may use to change the current configuration. A configuration of system is a set of state variables that jointly define the current state of the system. For instance, a state variable may be a collection of the current host compromised by the attacker, IP addresses of different hosts over the network, an enumeration of services running over each host, or a list of users currently accessing the hosts with their privileges (root, user, and none). Suppose that there are $n$ state variables and we denote the $i$ th state variable as $X_i$, then the domain of a state space can be given by $S=X_1 \times X_2 \times \cdots \times X_n$. Given this notion of state, we formally define a game arena as follows:

Definition 6.1 (Arena) A turn-based, deterministic game arena between two players P1 (defender, pronoun “he”) and P2 (attacker, pronoun “she”) is a tuple
$$
G=\langle S, A, T, \mathcal{A} \mathcal{P}, L\rangle,
$$
whose components are defined as follows:

$S=S_1 \cup S_2$ is a finite set of states partitioned into two sets $S_1$ and $S_2$. At a state in $S_1$, P1 chooses an action and at a state in $S_2, \mathrm{P} 2$ selects an action.
$A=A_1 \cup A_2$ is the set of actions. $A_1$ (resp., $A_2$ ) is the set of actions for P1 (resp., P2);
$T:\left(S_1 \times A_1\right) \cup\left(S_2 \times A_2\right) \rightarrow S$ is a deterministic transition function that maps a state-action pair to the next state.
$\mathcal{A P}$ is the set of atomic propositions.
$L: S \rightarrow 2^{\mathcal{A P}}$ is the labeling function that maps each state $s \in S$ to a set $L(s) \subseteq \mathcal{A} \mathcal{P}$ of atomic propositions that evaluate to true at that state.

经济代写|博弈论代写Game Theory代考|Specifying the Security Properties in LTL

We consider qualitative formal specifications for defender and attacker objectives. Different from quantitative utility functions in terms of costs, qualitative logic formulas capture hard security constraints that the network defense system must satisfy.

The defender has two types of goals, namely (i) operational objectives, such as the services should eventually be available to the legitimate users, and (ii) defense objectives, such as the attacker should never be able to compromise servers with sensitive information. However, the intention of attacker is often unknown. Thus, we consider the worst-case scenario where the attacker’s objective is to violate the security goal of the defender.
We choose to express the security goal of the defender using LTL (Manna and Pnueli 1992). LTL allows us to express the security properties of system with respect to time. We shall now present the formal syntax and semantics of LTL and then discuss several examples.

Let $\mathcal{A P}$ be a set of atomic propositions. Linear Temporal Logic (LTL) has the following syntax,
$$
\varphi:=\mathrm{T}|\perp| p|\varphi| \neg \varphi\left|\varphi_1 \wedge \varphi_2\right| \bigcirc \varphi \mid \varphi_1 \mathrm{U} \varphi_2
$$
where

$T, \perp$ represent universally true and false, respectively.
$p \in \mathcal{A} \mathcal{P}$ is an atomic proposition.
$O$ is a temporal operator called the “next” operator (see semantics below).
$\mathrm{U}$ is a temporal operator called the “until” operator (see semantics below).
Let $\Sigma:=2^{\mathcal{A} P}$ be the finite alphabet. Given a word $w \in \Sigma^\omega$, let $w[i]$ be the $i$ th element in the word and $w[i \ldots]$ be the subsequence of $w$ starting from the ith element. For example, $w=a b c, w[0]=a$, and $w[1 \ldots]=b c$. Formally, we have the following definition of the semantics:
$w \vDash p$ if $p \in w[0]$;
$w \vDash \neg p$ if $p \notin w[0]$
$w \vDash \varphi_1 \wedge \varphi_2$ if $w \vDash \varphi_1$ and $w \vDash \varphi_2$.
$w \vDash \bigcirc \varphi$ if $w[1 \ldots] \vDash \varphi$.
$w \vDash \varphi \cup \psi$ if $\exists i \geq 0, w[i \ldots] \vDash \psi$ and $\forall 0 \leq j<i, w[j \ldots] \vDash \varphi$.

博弈论代考

经济代写|博弈论代写Game Theory代考|A Theory of Hypergames on Graphs

游戏竞技场是一个转换系统，标签分配给状态。它捕获网络的不同配置以及攻击者和防御者可能用来更改当前配置的操作。系统配置是一组共同定义系统当前状态的状态变量。例如，状态变量可能是当前被攻击者攻陷的主机的集合、网络上不同主机的 IP 地址、在每个主机上运行的服务的枚举，或者当前使用其权限访问主机的用户列表（root、用户和无）。假设有 $n$ 状态变量，我们表示 $i$ 第状态变量为 $X_i$ ，那么状态空间的域可以由下式给出 $S=X_1 \times X_2 \times \cdots \times X_n$. 鉴于这种状态概念，我们正式定义一个游戏竞技场如下:
定义 6.1 (竞技场) 两个玩家 P1 (防御者，代词“他”) 和 P2（攻击者，代词“她”) 之间的回合制确定性游戏竞技场是一个元组
$$
G=\langle S, A, T, \mathcal{A} \mathcal{P}, L\rangle
$$
其组件定义如下:

$S=S_1 \cup S_2$ 是分成两组的有限状态集 $S_1$ 和 $S_2$. 在一个状态 $S_1$ ，P1 选择一个动作并且处于一个状态 $S_2, \mathrm{P} 2$ 选择一个动作。
$A=A_1 \cup A_2$ 是动作集。 $A_1$ (分别， $A_2$ ) 是 P1 (resp., P2) 的动作集；
$T:\left(S_1 \times A_1\right) \cup\left(S_2 \times A_2\right) \rightarrow S$ 是将状态-动作对映射到下一个状态的确定性转换函数。
$\mathcal{A} \mathcal{P}$ 是原子命题的集合。
$L: S \rightarrow 2^{\mathcal{A P}}$ 是映射每个状态的标签函数 $s \in S$ 一组 $L(s) \subseteq \mathcal{A} \mathcal{P}$ 在该状态下评估为真的原子命题。

经济代写|博弈论代写Game Theory代考|Specifying the Security Properties in LTL

我们考虑防御者和攻击者目标的定性正式规范。与成本方面的定量效用函数不同，定性逻辑公式捕获网络防御系统必须满足的硬安全约束。
防御者有两种类型的目标，即 (i) 操作目标，例如服务最终应该对合法用户可用，以及 (ii) 防御目标，例如攻击者永远无法破坏具有敏感信息的服务器。然而，攻击者的意图往往是末知的。因此，我们考虑最坏的情况，即攻击者的目标是破坏防御者的安全目标。
我们选择使用 LTL (Manna and Pnueli 1992) 来表达防御者的安全目标。LTL 允许我们表达系统相对于时间的安全属性。我们现在将介绍 LTL 的形式语法和语义，然后讨论几个例子。
让 $\mathcal{A} \mathcal{P}$ 是一组原子命题。线性时间逻辑 (LTL) 具有以下语法，
$$
\varphi:=\mathrm{T}|\perp| p|\varphi| \neg \varphi\left|\varphi_1 \wedge \varphi_2\right| \bigcirc \varphi \mid \varphi_1 \mathrm{U} \varphi_2
$$
在哪里

$T, \perp$ 分别代表普遍正确和普遍错误。
$p \in \mathcal{A} \mathcal{P}$ 是一个原子命题。
$O$ 是一个称为“下一个”运算符的时间运算符（参见下面的语义）。
U是一个称为”until”运算符的时间运算符 (参见下面的语义)。
让 $\Sigma:=2^{\mathcal{A P}}$ 是有限的字母表。给了一个字 $w \in \Sigma^\omega$ ，让 $w[i]$ 成为 $i$ 单词中的第 th 个元素和 $w[i \ldots]$ 是的后续 $w$ 从第 $\mathrm{i}$ 个元素开始。例如， $w=a b c, w[0]=a$ ，和 $w[1 \ldots]=b c$. 形式上，我们有以下语义定义:
$w \models p$ 如果 $p \in w[0]$;
$w \models \neg p$ 如果 $p \notin w[0]$
$w \models \varphi_1 \wedge \varphi_2$ 如果 $w \models \varphi_1$ 和 $w \models \varphi_2$.
$w \models \bigcirc \varphi$ 如果 $w[1 \ldots] \models \varphi$.
$w \models \varphi \cup \psi$ 如果 $\exists i \geq 0, w[i \ldots] \models \psi$ 和 $\forall 0 \leq j<i, w[j \ldots] \models \varphi$.

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|博弈论代写Game Theory代考|ECON40010

Posted on 2023年3月9日2023年3月9日 by statistics-lab

如果你也在怎样代写博弈论Game Theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的博弈论Game Theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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|Solution Concepts

Since EFGs can be converted into NFGs, the solution concepts introduced in Section 2.3 .1 still apply. Also, there are other solution concepts specifically for EFGs. We briefly introduce some of them at a high level.

One solution concept is subgame perfect equilibrium (or subgame perfect Nash equilibrium, SPE in short). It is a refinement of NE. This means the set of SPE is a subset of NE. A strategy profile is an SPE equilibrium if, in every subgame of the original game, the strategies remain an NE. A subgame is defined as the partial tree consisting of a node and all its successors, with the requirement that the root node of the partial tree is the only node in its information set. This means if the players play a small game that is part of the original game, they still have no incentive to deviate from their current strategy. A subgame can be a subgame of another subgame rooted at its ancestor node. A finite EFG with perfect recall always has an SPE. To find an SPE in a finite game with perfect information, one can use backward induction as all the information sets are singletons. First, consider the smallest subgames rooted at a parent node of a terminal node. After solving these subgames by determining the action to maximize the acting player’s expected utility, one can solve a slightly larger subgame whose subgames have already been solved, assuming the player will play according to the smaller subgames’ solution. This process continues until the original game is solved. The resulting strategy is an SPE. For games of imperfect or incomplete information, backward induction cannot be applied as it will require reasoning about the information sets with more than one node. The SPE concept can also be defined through the one-shot deviation principle: a strategy profile is an SPE if and only if no player can gain any utility by deviating from their strategy for just one decision point and then reverting back to their strategy in any subgame.

In the example game in Figure 2.1, if we remove the dashed box, the game becomes one with perfect information, and it has two subgames in addition to the original game, with the root nodes being nodes 2 and 3 respectively. In this new game, Player 1 choosing $L$ and Player 2 choosing $r$ at both nodes 2 and 3 is an NE but not an SPE, because, in the subgame rooted at node 3, Player 2 choosing $\mathrm{r}$ is not the best action. In contrast, Player 1 choosing $\mathrm{R}$ and Player 2 choosing $\mathrm{r}$ at node 2 , 1 at node 3 is an SPE.

Another solution concept is sequential equilibrium (Kreps and Wilson 1982), which is a further refinement of SPE. A sequential equilibrium consists of not only the players’ strategies but also the players’ beliefs for each information set. The belief describes a probability distribution on the nodes in the information set since the acting player cannot distinguish them when they play the game. Unlike SPE which only considers the subgames rooted from a node that is the only element in its information set, the sequential equilibrium requires that the players are sequentially rational and takes the best action in terms of expected utility concerning the belief at every information set even if it is not a singleton.

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

Consider a two-player NFG with finite actions. The two players choose an action in their action set simultaneously without knowing the other player’s strategy ahead of time. In an NE of the game, each player’s strategy is a best response to the other player’s strategy. But what if one player’s strategy is always known to other players ahead of time? This kind of role asymmetry is depicted in a Stackelberg game.

In a Stackelberg game, one player is the leader and chooses her strategy first, and the other players are followers who observe the leader’s strategy and then choose their strategies. The leader has to commit to the strategy she chooses, i.e. she cannot announce a strategy to the followers and play a different strategy when the game is actually played. She can commit to either a pure strategy or a mixed strategy. If she commits to a mixed strategy, the followers can observe her mixed strategy but not the realization of sampled action from this mixed strategy. A Stackelberg game can be described in the same way as before, with a tuple $(\mathcal{N}, \mathcal{A}, u)$ for games in normal form and $(\mathcal{N}, \mathcal{A}, \mathcal{H}, \mathcal{Z}, \chi, \rho, \sigma, u)$ for games in extensive form, with the only difference that one of the players (usually Player 1 ) is assumed to be the leader.

At first sight, one may think that the followers have an advantage as they have more information than the leader when they choose their strategies. However, it is not the case. Consider the Football vs. Concert game again. If the row player is the leader and commits to choosing the action $\mathrm{F}$, a rational column player will choose action $\mathrm{F}$ to ensure a positive payoff. Thus, the row player guarantees herself a utility of 2, the highest utility she can get in this game, through committing to playing pure strategy $\mathrm{F}$. In the real world, it is common to see similar scenarios. When a couple is deciding what to do during the weekend, if one of them has a stronger opinion and insists on going to the activity he or she prefers, they will likely choose that activity in the end. In this example game, the leader ensures a utility that equals the best possible utility she can get in an NE. In some other games, the leader can get a utility higher than any NE in the game by committing to a good strategy. In the example game in Table 2.5 (Up, Right) is the only NE, with the row player’s utility being 4 . However, if the row player is the leader and commits to a uniform random strategy, the column player will choose Left as a best response, yielding an expected utility of 5 for the row player. This higher expected utility for the row players shows the power of commitment.

博弈论代考

经济代写|博弈论代写Game Theory代考|Solution Concepts

由于 EFG 可以转换为 NFG，因此第 2.3.1 节中介绍的解决方案概念仍然适用。此外，还有其他专门针对 EFG 的解决方案概念。我们简要介绍了其中的一些。

一种解决方案概念是子博弈完美均衡（或子博弈完美纳什均衡，简称 SPE）。它是NE的改进。这意味着 SPE 的集合是 NE 的子集。如果在原始博弈的每个子博弈中，策略仍然是 NE，则策略配置文件是 SPE 均衡。子博弈定义为由一个节点及其所有后继节点组成的部分树，要求部分树的根节点是其信息集中的唯一节点。这意味着如果玩家玩的是原游戏的一部分的小游戏，他们仍然没有动力偏离他们当前的策略。一个子博弈可以是另一个以其祖先节点为根的子博弈的子博弈。具有完美召回率的有限 EFG 始终具有 SPE。要在具有完美信息的有限游戏中找到 SPE，可以使用反向归纳法，因为所有信息集都是单例。首先，考虑以终端节点的父节点为根的最小子博弈。在通过确定使行动玩家的预期效用最大化的行动来解决这些子博弈之后，可以解决一个稍大的子博弈，其子博弈已经被解决，假设玩家将根据较小的子博弈的解决方案进行游戏。这个过程一直持续到原始游戏被解决为止。由此产生的策略是 SPE。对于信息不完善或不完整的博弈，不能应用反向归纳，因为它需要对具有多个节点的信息集进行推理。SPE的概念也可以通过单次偏差原则来定义：

在图 2.1 的示例游戏中，如果我们去掉虚线框，则游戏变成一个完全信息游戏，除了原游戏之外还有两个子游戏，根节点分别为节点 2 和 3。在这个新游戏中，玩家 1 选择大号和玩家 2 选择r在节点 2 和 3 上都是 NE 但不是 SPE，因为在以节点 3 为根的子博弈中，玩家 2 选择r不是最好的行动。相反，玩家 1 选择R和玩家 2 选择r在节点 2 处，节点 3 处的 1 是一个 SPE。

另一个解决方案概念是序贯平衡（Kreps 和 Wilson 1982），它是 SPE 的进一步改进。序贯均衡不仅包括参与者的策略，还包括参与者对每个信息集的信念。信念描述了信息集中节点的概率分布，因为代理玩家在玩游戏时无法区分它们。与 SPE 只考虑以节点为根的子博弈不同，该节点是其信息集中的唯一元素，序贯均衡要求参与者是序贯理性的，并且根据与每个信息集的信念有关的预期效用采取最佳行动，即使它不是单身人士。

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

考虑具有有限动作的两人 NFG。两个玩家同时在他们的行动集中选择一个行动，而事先不知道对方的策略。在一个 NE 游戏中，每个玩家的策略是对其他玩家策略的最佳反应。但是如果一个玩家的策略总是被其他玩家提前知道呢？Stackelberg 博弈描述了这种角色不对称。

在 Stackelberg 博弈中，一个玩家是领导者并首先选择她的策略，而其他玩家是观察领导者策略然后选择自己策略的追随者。领导者必须对她选择的策略做出承诺，即她不能向追随者宣布策略并在实际进行游戏时采取不同的策略。她可以致力于纯策略或混合策略。如果她承诺采用混合策略，则追随者可以观察到她的混合策略，但看不到从该混合策略中采样的动作的实现。Stackelberg 游戏可以用与之前相同的方式描述，用一个元组(否,A,在)对于正常形式的游戏和(否,A,H,和,H,r,p,在)对于广泛形式的游戏，唯一的区别是其中一名玩家（通常是玩家 1 ）被假定为领导者。

乍一看，人们可能会认为追随者具有优势，因为他们在选择策略时比领导者拥有更多的信息。然而，事实并非如此。再次考虑足球与音乐会比赛。如果行玩家是领导者并承诺选择行动F, 一个理性的列玩家会选择行动F以确保获得积极的回报。因此，划船玩家通过致力于玩纯策略来保证自己的效用为 2，这是她在该游戏中可以获得的最高效用F. 在现实世界中，类似的场景很常见。当一对夫妇在决定周末做什么时，如果其中一方有更强烈的意见并坚持参加他或她喜欢的活动，他们很可能最终会选择那个活动。在这个示例游戏中，领导者确保效用等于她在 NE 中可以获得的最佳效用。在其他一些游戏中，领导者可以通过承诺一个好的策略来获得比游戏中任何 NE 更高的效用。在表 2.5 的示例游戏中（上，右）是唯一的 NE，行玩家的效用为 4 。但是，如果行玩家是领导者并采用统一的随机策略，则列玩家将选择左作为最佳响应，从而为行玩家产生 5 的预期效用。划船运动员的这种更高的预期效用显示了承诺的力量。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|博弈论代写Game Theory代考|ECON6025

Posted on 2023年3月9日2023年3月9日 by statistics-lab

如果你也在怎样代写博弈论Game Theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的博弈论Game Theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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|Normal-Form Games

In this section, we introduce normal-form games (NFGs) and formally introduce the solution concepts we mentioned in Section 2.2. Most of the notations and definitions are adapted from Leyton-Brown and Shoham 2008. The normal form is the most basic form of games to represent players’ interactions and strategy space. An NFG captures all possible combinations of actions or strategies for the players and their corresponding payoffs in a matrix, or multiple matrices for more than two players. A player can choose either a pure strategy that deterministically selects a single strategy or play a mixed strategy that specifies a probability distribution over the pure strategies. The goal for all players is to maximize their expected utility. Formally, a finite, $N$-person NFG is described by a tuple $(\mathcal{N}, \mathcal{A}, u)$, where:

$\mathcal{N}={1, \ldots, N}$ is a finite set of $N$ players, indexed by $i$.
$A=A_1 \times \cdots \times A_N$ is a set of jnint actions of the players, where $\mathcal{A}_i$ is a finite set of actions available to player $i . a=\left(a_1, \ldots, a_N\right) \in \mathcal{A}$ is called an action profile with $a_i \in \mathcal{A}_i$.
$u=\left(u_1, \ldots, u_N\right)$ where $u_i: \mathcal{A} \mapsto \mathbb{R}$ is a utility (or payoff) function for player $i$. It maps an action profile $a$ to a real value. An important characteristic of a game is that player $i$ ‘s utility depends on not only his own action $a_i$ but also the actions taken by other players; thus, the utility function is defined over the space of $\mathcal{A}$ instead of $\mathcal{A}i$. A player can choose a mixed strategy. We use $S_i=\Delta^{\left|\mathcal{A}_l\right|}$ to denote the set of mixed strategies for player $i$, which is the probability simplex with dimension $\left|\mathcal{A}_i\right|$. Similarly, $S=S_1 \times \cdots \times S_N$ is the set of joint strategies and $s=\left(s_1, \ldots, s_N\right) \in S$ is called a strategy profile. The support of a mixed strategy is defined as the set of actions that are chosen with a nonzero probability. An action of player $i$ is a pure strategy and can be represented by a probability distribution with support size 1 (of value 1 in one dimension and 0 in all other dimensions). The utility function can be extended to mixed strategies by using expected utility. That is, if we use $s_l\left(a_i\right)$ to represent the probability of choosing action $a_i$ in strategy $s_i$, the expected utility for player $i$ given strategy profile $s$ is $u_i(s)=\sum{a \in \mathcal{A}} u_i(a) \prod_{l^{\prime}=1}^n s_{l^{\prime}}\left(a_{l^{\prime}}\right)$. A game is zero-sum if the utilities of all the players always sum up to zero, i.e. $\sum_l u_i(s)=0, \forall s$ and is nonzero-sum or general-sum otherwise.
Many classic games can be represented in normal form. Table 2.3 shows the game Prisoner’s Dilemma (PD). Each player can choose between two actions, Cooperate (C) and Defect (D). If they both choose $\mathrm{C}$, they both suffer a small loss of -1 . If they both choose $\mathrm{D}$, they both suffer a big loss of -2 . However, if one chooses $\mathrm{C}$ and the other chooses $\mathrm{D}$, the one who chooses $\mathrm{C}$ suffers a huge loss while the other one does not suffer any loss. If the row player chooses a mixed strategy of playing C with probability 0.4 and D 0.6 , while the column player chooses the uniform random strategy, then the row player’s expected utility is $-1.4=(-1) \cdot 0.4 \cdot 0.5+(-3) \cdot 0.4 \cdot 0.5+(-2) \cdot 0.6 \cdot 0.5$. Now we provide the formal definition of best response. We use $-i$ to denote all players but $i$.

经济代写|博弈论代写Game Theory代考|Extensive-Form Games

Extensive-form games (EFGs) represent the sequential interaction of players using a rooted game tree. Figure 2.1 shows a simple example game tree. Each node in the tree belongs to one of the players and corresponds to a decision point for that player. Outgoing edges from a node represent actions that the corresponding player can take. The game starts from the root node, with the player corresponding to the root node taking an action first. The chosen action brings the game to the child node, and the corresponding player at the child node takes an action. The game continues until it reaches a leaf node (also called a terminal node), i.e. each leaf node in the game tree is a possible end state of the game. Each leaf node is associated with a tuple of utilities or payoffs that the players will receive when the game ends in that state. In the example in Figure 2.1, there are three nodes. Node 1 belongs to Player 1 (P1), and nodes 2 and 3 belong to Player 2 (P2). Player 1 first chooses between action L and R, and then Player 2 chooses between action 1 and r. Player 1 ‘s highest utility is achieved when Player 1 chooses L, and Player 2 chooses 1 .

There is sometimes a special fictitious player called Chance (or Nature), who takes an action according to a predefined probability distribution. This player represents the stochasticity in many problems. For example, in the game of Poker, each player gets a few cards that are randomly dealt. This can be represented by having a Chance player taking an action of dealing cards. Unlike the other real players, the Chance player does not rationally choose an action to maximize his utility since he does not have a utility function. In the special case where Nature only takes an action at the very beginning of the game, i.e. the root of the game tree, the game is essentially a Bayesian game, as we will detail in Section 2.7.

In a perfect information game, every player can perfectly observe the action taken by players in the previous decision points. For example, when two players are playing the classic board game of Go or Tic-Tac-Toe, each player can observe the other players’ previous moves before she decides her move. However, it is not the case in many other problems. An EFG can also capture imperfect information, i.e. a game where players are sometimes uncertain about the actions taken by other players and thus do not know which node they are at exactly when they take actions. The set of nodes belonging to each player is partitioned into several information sets. The nodes in the same information set cannot be distinguished by the player that owns those nodes. In other words, the player knows that she is at one of the nodes that belong to the same information set, but does not know which one exactly. For example, in a game of Poker where each player has private cards, a player cannot distinguish between certain nodes that only differ in the other players’ private cards. Nodes in the same information set must have the same set of actions since otherwise, a player can distinguish them by checking the action set. It is possible that an information set only contains one node, i.e. a singleton. If all information sets are singletons, the game is a perfect information game. The strategy of a player specifies what action to take at each information set. In the example game in Figure 2.1, the dashed box indicates that nodes 2 and 3 are in the same information set, and Player 2 cannot distinguish between them. Thus, nodes 2 and 3 have the same action set. This information set effectively makes the example game a simultaneous game as Player 2 has no information about Player 1s previous actions when he makes a move.

博弈论代考

经济代写|博弈论代写Game Theory代考|Normal-Form Games

在本节中，我们介绍了规范形式的博変 (NFG) 并正式介绍了我们在 2.2 节中提到的解决方案概念。大多数符号和定义改编自 Leyton-Brown 和 Shoham 2008。范式是博恋中表示玩家交互和策略空间的最基本形式。NFG 捕获参与者的所有可能的行动或策略组合以及他们在矩阵中的相应收益，或者捕获两个以上参与者的多个矩阵。玩家可以选择确定性地选择单一策略的纯策略，也可以选择指定纯策略概率分布的混合策略。所有参与者的目标都是最大化他们的预期效用。形式上，一个有限的， $N$-person NFG 由元组描述 $(\mathcal{N}, \mathcal{A}, u)$ ，在哪里:

$\mathcal{N}=1, \ldots, N$ 是一个有限集 $N$ 球员，索引i.
$A=A_1 \times \cdots \times A_N$ 是玩家的一组 jnint 动作，其中 $\mathcal{A}_i$ 是玩家可用的一组有限动作 i. $a=\left(a_1, \ldots, a_N\right) \in \mathcal{A}$ 被称为动作配置文件 $a_i \in \mathcal{A}_i$.
$u=\left(u_1, \ldots, u_N\right)$ 在哪里 $u_i: \mathcal{A} \mapsto \mathbb{R}$ 是玩家的效用 (或收益) 函数 $i$. 它映射了一个动作配置文件 $a$ 到一个真正的价值。游戏的一个重要特征是玩家 $i$ 的效用不仅取决于他自己的行动 $a_i$ 还有其他玩家采取的行动；因此，效用函数定义在 $\mathcal{A}$ 代替 $\mathcal{A} i$. 玩家可以选择混合策略。我们用 $S_i=\Delta^{\left|\mathcal{A}l\right|}$ 表示玩家的混合策略集 $i$ ，这是具有维度的概率单纯形 $\left|\mathcal{A}_i\right|$. 相似地， $S=S_1 \times \cdots \times S_N$ 是一组联合策略，并且 $s=\left(s_1, \ldots, s_N\right) \in S$ 称为策略配置文件。混合策略的支持被定义为以非零概率选择的一组动作。玩家的一个动作 $i$ 是一种纯策略，可以用支持大小为 1 的概率分布表示（在一个维度上值为 1 ，在所有其他维度上值为 0 ) 。效用函数可以通过使用期望效用扩展到混合策略。也就是说，如果我们使用 $s_l\left(a_i\right)$ 表示选择动作的概率 $a_i$ 在战略上 $s_i$ ，玩家的预期效用 $i$ 给定的战略概兄 $s$ 是 $u_i(s)=\sum a \in \mathcal{A} u_i(a) \prod{l^{\prime}=1}^n s_{l^{\prime}}\left(a_{l^{\prime}}\right)$. 如果所有玩家的效用总和为零，则游戏是零和游戏，即 $\sum_l u_i(s)=0, \forall s$ 否则是非零和或一般和。
许多经典游戏都可以用正常形式表示。表 2.3 显示了囚徒困境 (PD) 游戏。每个玩家都可以在合作 (C) 和背叛 (D) 两种行动之间进行选择。如果他们都选择C，他们都遭受 -1 的小损失。如果他们都选择 $\mathrm{D}$ ，他们都遭受了 -2 的巨大损失。然而，如果选择C另一个选择D，选择的人C遭受巨大损失，而另一个则没有遭受任何损失。如果行玩家选择以概率 0.4 和 D 0.6 玩 C 的混合策略，而列玩家选择均匀随机策略，则行玩家的期望效用为
$-1.4=(-1) \cdot 0.4 \cdot 0.5+(-3) \cdot 0.4 \cdot 0.5+(-2) \cdot 0.6 \cdot 0.5$. 现在我们提供最佳响应的正式定义。我们用 $-i$ 表示所有玩家，但 $i$.

经济代写|博弈论代写Game Theory代考|Extensive-Form Games

广泛形式的博弈 (EFG) 表示玩家使用有根博弈树的顺序交互。图 2.1 显示了一个简单的博弈树示例。树中的每个节点都属于其中一名玩家，并对应于该玩家的一个决策点。来自节点的出边表示相应玩家可以采取的动作。游戏从根节点开始，根节点对应的玩家先行动。选择的动作将游戏带到子节点，子节点的相应玩家采取动作。游戏继续进行，直到到达一个叶节点（也称为终端节点），即游戏树中的每个叶节点都是游戏的一个可能结束状态。每个叶节点都与一个效用或收益元组相关联，当游戏在该状态下结束时，玩家将收到这些效用或收益。在图 2.1 的示例中，有三个节点。节点 1 属于玩家 1 (P1)，节点 2 和 3 属于玩家 2 (P2)。玩家 1 首先在动作 L 和 R 之间进行选择，然后玩家 2 在动作 1 和 r 之间进行选择。当玩家 1 选择 L 而玩家 2 选择 1 时，玩家 1 的效用最高。

有时有一个特殊的虚构玩家，称为机会（或自然），他根据预定义的概率分布采取行动。这个玩家代表了很多问题中的随机性。例如，在扑克游戏中，每个玩家都会得到几张随机发的牌。这可以通过让 Chance 玩家采取发牌动作来表示。与其他真实玩家不同，机会玩家不会理性地选择一个行动来最大化他的效用，因为他没有效用函数。在自然只在博弈开始时采取行动的特殊情况下，即博弈树的根，博弈本质上是贝叶斯博弈，我们将在 2.7 节中详细介绍。

在一个完美的信息博弈中，每个玩家都可以完美地观察到玩家在之前的决策点采取的行动。例如，当两个玩家正在玩围棋或井字棋等经典棋盘游戏时，每个玩家在决定自己的走法之前都可以观察其他玩家之前的走法。然而，在许多其他问题中并非如此。EFG 还可以捕获不完全信息，即玩家有时不确定其他玩家采取的行动的游戏，因此不知道他们在采取行动时确切处于哪个节点。属于每个玩家的节点集被分成几个信息集。同一信息集中的节点不能被拥有这些节点的玩家区分。换句话说，玩家知道她在属于同一个信息集的节点之一，但不知道具体是哪一个。例如，在每个玩家都有私人牌的扑克游戏中，玩家无法区分仅在其他玩家的私人牌上不同的某些节点。同一信息集中的节点必须具有相同的动作集，否则玩家可以通过检查动作集来区分它们。一个信息集有可能只包含一个节点，即单例。如果所有的信息集都是单例的，那么这个博弈就是一个完美的信息博弈。玩家的策略指定了在每个信息集上采取什么行动。在图2.1的示例游戏中，虚线框表示节点2和节点3在同一个信息集中，玩家2无法区分它们。因此，节点 2 和 3 具有相同的动作集。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|博弈论代写Game Theory代考|ECOS3012

Posted on 2022年12月29日2022年12月29日 by statistics-lab

如果你也在怎样代写博弈论Game Theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的博弈论Game Theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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|STRATEGIC GAMES

Prisoner’s Dilemma is a canonical example of a strategic game because, as we will see shortly, it typifies many scenarios that confront decision makers. Further, being a simple scenario, it can be used to illustrate many of the fundamental concepts of game theory, and it also clearly demonstrates a fundamental dilemma in our (human) decision-making processes.

We model this scenario as a strategic game in which the two suspects, each confined in a separate interrogation room, are the players. We will often refer to our two players in strategic games as Rose and Colin. (This convention helps later to emphasize the distinction between row and column players and was popularized by Phil Straffin in his book Game Theory and Strategy [110].) They each have two strategies available to them which we name Quiet and Confess. Table $3.1$ lists each of the strategy profiles in the form (Rose, Colin) and the resulting outcome.

We assume that each suspect is primarily concerned about their own sentence and wants to minimize it. Table $3.2$ provides payoffs (a common synonym for utilities) for each player. Here we use the utility function 6 minus the number of years in prison; this is consistent with the player preferences. Based on our assumptions, these payoffs are ordinal. For these payoffs to also be vNM, we would need to assume that the suspects are risk neutral in the number of years to be served in prison.

Tables $3.1$ and $3.2$ complete the construction of the model by identifying the strategies, outcomes, and payoffs. We will refer to this model of the Prisoner’s Dilemma scenario as the Prisoner’s Dilemma strategic game.

We are now ready to look for a solution that maximizes the payoffs to the players. By observing that $5>3$, we see that Confess is the best response strategy for Rose if she knows that Colin will choose Quiet. Further, we can observe that Confess is also a best response for Rose if she knows Colin will choose Confess. We formalize the definition of a best response strategy below.

经济代写|博弈论代写Game Theory代考|FINALJEOPARDY

As we observed in Section 3.1, the phrase “Prisoner’s Dilemma” has been used to describe many real-world scenarios; however, not all of these scenarios actually fit the mathematical definition. This can only be revealed by constructing and analyzing a model of the scenario.

We examine a situation in Jeopardy! which fans have identified as a Prisoner’s Dilemma. In the Final Jeopardy round, each contestant makes a wager as to whether they can answer a specific question correctly. When making the wager, contestants know the category of the question, but not the question itself, and the amount of money each of the other contestants has available. Each player’s wager can be between 0 and their current winnings. Depending on whether the contestant answers the question correctly, they win or lose the amount of money wagered. The contestant with the most money after this final round of play wins the game. The winner keeps all of their winnings, and the other two contestants lose essentially all of their money. If there is a tie at the end of the round, a simple, essentially random, tie-breaker rule is applied to identify the winner.

The so-called Prisoner’s Dilemma situation occurs when two contestants are tied for the lead, and the third contestant has less than half of the money of either of the first two contestants. For simplicity we will assume that it is contestants 1 and 2 who are tied with the most money.

In this situation, aficionados of Jeopardy! often refer to “Jeek’s Rule,” which asserts that while they could wager any amount up to their current winnings, contestants 1 and 2 should either wager nothing or everything. We discuss the reasonableness of this rule and then make it an assumption when we define our strategic game.

Let $E$ ‘ be the amount of money contestants 1 and ‘ 2 have each won at the time Final Jeopardy begins. Let $w_i$ denote the wager of contestant $i$ and suppose that contestant 1 ‘s wager satisfies $0<w_1<E$. There are four cases to consider:

Case 1: Both contestants answer the question correctly. In this case, if $w_1<w_2$, contestant 1 regrets not wagering $E$ in order to win. If $w_1 \geq w_2$, then contestant 1 regrets not wagering $E$ to maximize their winnings.

Case 2: Contestant 1 answers the question correctly and contestant 2 does not. Here contestant 1 regrets not wagering $E$ in order to maximize their winnings.

Case 3 : Contestant 1 answers the question incorrectly and contestant 2 answers correctly. Then contestant 1 is indifferent about their bet unless $w_2=0$, in which case they regret not wagering $w_1=0$.

Case 4: Both contestants answer the question incorrectly. Here, if $w_1 \geq w_2$, contestant 1 regrets not wagering $w_1=0$ in order to win. If $w_1<w_2$, then contestant 1 regrets not wagering $w_1=0$ to maximize their winnings.

博弈论代考

经济代写|博弈论代写Game Theory代考|STRATEGIC GAMES

囚徒困境是战略游戏的一个典型例子，因为正如我们很快就会看到的，它代表了决策者面临的许多场景。此外，作为一个简单的场景，它可以用来说明博弈论的许多基本概念，它也清楚地展示了我们（人类）决策过程中的一个基本困境。

我们将此场景建模为一个战略游戏，其中两名嫌疑人是玩家，每个人都被关在一个单独的审讯室里。我们经常将战略游戏中的两名球员称为罗斯和科林。（此约定后来有助于强调行和列玩家之间的区别，并由 Phil Straffin 在他的书博弈论和策略 [110] 中推广。）他们每个人都有两种可用的策略，我们将其命名为 Quiet 和 Confess。桌子3.1列出表格中的每个策略配置文件 (Rose, Colin) 和结果结果。

我们假设每个嫌疑人主要关心的是他们自己的刑期，并希望将其减至最少。桌子3.2为每个玩家提供收益（公用事业的常见同义词）。这里我们使用效用函数 6 减去入狱年数；这符合玩家的喜好。根据我们的假设，这些收益是有序的。为了让这些回报也成为 vNM，我们需要假设嫌疑人在监狱服刑的年数上是风险中性的。

表3.1和3.2通过确定策略、结果和收益来完成模型的构建。我们将这种囚徒困境场景模型称为囚徒困境战略博弈。

我们现在准备寻找一种解决方案，使玩家的收益最大化。通过观察5>3，我们看到如果 Rose 知道 Colin 会选择 Quiet，Confess 是她最好的应对策略。此外，我们可以观察到如果 Rose 知道 Colin 会选择 Confess，那么 Confess 也是她的最佳回应。我们在下面正式定义最佳响应策略。

经济代写|博弈论代写Game Theory代考|FINALJEOPARDY

正如我们在第 $3.1$ 节中观察到的， “图困境”一词已被用来描述许多现实世界的场景；然而，并非所有这些场景实际上都符合数学定义。这只能通过构建和分析场景模型来揭示。
我们检查处于危险中的情况！粉丝将其确定为囚徒困境。在 Final Jeopardy 回合中，每位参赛者都会就他们是否能正确回答特定问题下注。下注时，参塞者知道问题的类别，但不知道问题本身，也不知道其他参塞者每个人可用的金额。每个玩家的赌注可以介于 0 和他们当前的奖金之间。根据参赛者是否正确回答问题，他们赢或输下注的金额。最后一轮比赛结束后，钱最多的参寒者将赢得比䗙。获胜者保留了所有的奖金，而另外两名参寒者基本上输掉了所有的钱。如果在回合结束时出现平局，一个简单的，基本上是随机的，
当两名参塞者并列领先，而第三名参塞者的钱少于前两名参塞者中任何一方的一半时，就会出现所谓的囚徒困境情况。为简单起见，我们假设参塞者 1 和 2 的奖金最多。
在这种情况下，危险的爱好者！通常提到”Jeek 规则”，该规则断言，虽然他们可以下注任何金额，但不超过他们当前的奖金，但参寒者 1 和 2 要么什么都不下，要么全下。我们讨论这条规则的合理性，然后在定义我们的战略游戏时将其作为假设。
让 $E^{\prime}$ 是参赛者 1 和 2 在 Final Jeopardy 开始时各自赢得的金额。让 $w_i$ 表示参赛者的赌注 $i$ 并假设参赛者 1 的赌注满足 $0<w_1<E$. 有四种情况需要考虑:
案例 1: 两位参寨者都正确回答了问题。在这种情况下，如果 $w_1<w_2$ ，选手1后悔没有下注 $E$ 为了赢。如果 $w_1 \geq w_2$ ，那么选手 1 后悔没有下注 $E$ 以最大化他们的奖金。
案例 2: 参寒者 1 正确回答了问题，而参赛者 2 没有。这里选手 1 后悔没有下注 $E$ 为了最大化他们的奖金。，在这种情况下，他们后悔没有下注 $w_1=0$.
案例 4: 两位参寒者都答错了问题。在这里，如果 $w_1 \geq w_2$ ，选手 1 后悔没有下注 $w_1=0$ 为了赢。如果 $w_1<w_2$ ，那么选手 1 后悔没有下注 $w_1=0$ 以最大化他们的奖金。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|博弈论代写Game Theory代考|ECON6025

Posted on 2022年12月29日2022年12月29日 by statistics-lab

如果你也在怎样代写博弈论Game Theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的博弈论Game Theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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|CONSTRUCTING UTILITIES

We have already suggested how we might construct a utility function to model a player’s choices when there are a finite number of outcomes. Ordinal preferences can be revealed by asking the player to choose among all outcomes and assign those outcomes the highest utility, asking the player to choose among all outcomes not previously chosen and assign those outcomes the second highest utility, and so forth. vNM preferences can be obtained by asking the player to name the highest and lowest ranked outcomes $o_h$ and $o_l$, assign utilities of $u\left(o_h\right)=1$ and $u\left(o_l\right)=0$ to these outcomes, and then for each remaining outcome $o$ determine a probability $p$ for which the player would be willing to choose either the outcome $o$ or the lottery $(1-p) o_l+p o_h$ and assign $u(o)=p$.

In this section, we examine four specific scenarios to illustrate a variety of ways utility functions may be created.

To model Self-Interest and Other-Interest, we simplify our scenario to examine the monthly salaries of the job offers for each spouse. Suppose Scarlett and Regis receive $\$ x$ thousand and $\$ y$ thousand, respectively; we will denote this by $(x, y)$. Consider the following four possible outcomes: $(7,0),(6,6),(5,7)$, and $(1,6)$. If Scarlett is exclusively self-interested, she would rank order these outcomes in the given order. If Scarlett is primarily interested in Regis receiving money and only secondarily interested in receiving money for herself, Scarlett would rank order the outcomes $(5,7),(6,6),(1,6)$, and $(7,0)$. If Scarlett had a mixture of self-interest, other-interest, and a desire for equity, she might rank order the outcomes $(6,6),(5,7),(7,0)$, and $(1,6)$.

In fact, this last rank order would be obtained if Scarlett considered $\$ 1,000$ given to Regis to be worth the same to her as her receiving $\$ 500$, suggesting the utility function $u(x, y)=x+0.5 y$. Of course, this is only an ordinal utility function unless, at minimum, Scarlett is indifferent between the outcome $(7,0)$ with utility $u(7,0)=7$ and the lottery $L=0.6(6,6)+0.4(1,6)$ with utility
$$
u(L)=0.6 u(6,6)+0.4 u(1,6)=0.6(9)+0.4(4)=7 .
$$
This example demonstrates how we can incorporate both self-interest and altruistic interests into a player’s utility function. Therefore, maximizing a utility function does not necessarily imply selfishness, but rather achieving the most preferred outcome based on the player’s interests.

经济代写|博弈论代写Game Theory代考|DETERMINING RISK

In the duopoly scenario, and in most other economic models, the utility of an outcome is cquivalent to some dollar value associated with the outcome. While we can see how dollar values might capture the intensity of a player’s preferences, dollar values are not necessarily vNM utilities. For example, receiving $\$ 11.00$ instead of $\$ 10.00$ means significantly more than receiving $\$ 1001.00$ instead of $\$ 1000.00$ to most people. To explore this difference, we consider the relationship between the expected utility of a lottery, as given by the Expected Utility Hypothesis, and the utility of the expected value of the lottery.

Consider the following raffle: For $\$ 25$, you can purchase a $\frac{1}{400}$ chance for a $\$ 10,000$ college scholarship. We can represent this lottery with our usual notation
$$
\left.\frac{399}{400}(\text { losing } \$ 25)+\frac{1}{400} \text { (winning } \$ 9,975\right) \text {, }
$$ but since the outcomes are numerical, we can calculate the expected monetary value of the raffle as
$$
\frac{399}{400}(-\$ 25)+\frac{1}{400}(\$ 9,975)=\$ 0 .
$$
The expected monetary value of entering or not entering the raffle is the same, however, entering the raffle involves a small chance of a large gain offset by a large chance of a small loss, while not entering the raffle involves no chance of a gain or a loss. Entering the raffle involves risk while not entering the raffle does not.

Most parents of college students are willing to enter the raffle, but many college students themselves are not. For the college parents,
$$
\left.\left.u\left(\frac{399}{400} \text { (losing } \$ 25\right)+\frac{1}{400} \text { (winning } \$ 9,975\right)\right)>u(\$ 0),
$$
but for the students themselves,
$$
\left.u\left(\frac{399}{400}(\text { losing } \$ 25)+\frac{1}{400} \text { (winning } \$ 9,975\right)\right)<u(\$ 0) .
$$
For the parents, the utility of the lottery is greater than the utility of the expected value, making them risk loving in this scenario. On the other hand, the students are risk adverse since the utility of the lottery is less than the utility of the expected value. This principle holds in general, as we describe in the following definition.

博弈论代考

经济代写|博弈论代写Game Theory代考|CONSTRUCTING UTILITIES

我们已经提出了如何构建效用函数来模拟玩家在结果数量有限时的选择。序数偏好可以通过要求玩家在所有结果中进行选择并为这些结果分配最高效用，要求玩家在所有先前末选择的结果中进行选择并为这些结果分配第二高效用等来揭示。可以通过要求玩家说出排名最高和最低的结果来获得 vNM 偏好 $o_h$ 和 $o_l$ ，分配实用程序 $u\left(o_h\right)=1$ 和 $u\left(o_l\right)=0$ 这些结果，然后是每个剩余的结果 $o$ 确定一个概率 $p$ 玩家愿意选择的结果 $o$ 或彩票 $(1-p) o_l+p o_h$ 并分配 $u(o)=p$.
在本节中，我们将研究四个特定场景来说明可以创建效用函数的各种方式。
为了对自利和其他利益建模，我们简化了我们的场景，以检查每个配偶的工作机会的月薪。假设思嘉和瑞吉斯收到 $\$ x$ 千和 $\$ y$ 千，分别；我们将用 $(x, y)$. 考虑以下四种可能的结果: $(7,0),(6,6),(5,7)$ ，和 $(1,6)$. 如果斯嘉丽完全是自利的，她会按照给定的顺序对这些结果进行排序。如果 Scarlett 主要对 Regis 收钱感兴趣，仅次于为自己收钱，Scarlett 将对结果进行排序 $(5,7),(6,6),(1,6)$ ，和 $(7,0)$. 如果思嘉混合了自身利益、他人利益和对公平的渴望，她可能会对结果进行排序 $(6,6),(5,7),(7,0)$ ，和 $(1,6)$
事实上，如果斯嘉丽考虑，就会获得最后的排名顺序 $\$ 1,000$ 给予 Regis 的价值与她收到的价值相同 $\$ 500$ ，提示效用函数 $u(x, y)=x+0.5 y$. 当然，这只是一个有序的效用函数，除非至少 Scarlett 对结果无动于衷 $(7,0)$ 实用 $u(7,0)=7$ 和彩票 $L=0.6(6,6)+0.4(1,6)$ 实用
$$
u(L)=0.6 u(6,6)+0.4 u(1,6)=0.6(9)+0.4(4)=7 .
$$
这个例子展示了我们如何将自利和利他利益结合到玩家的效用函数中。因此，最大化效用函数并不一定意味着自私，而是基于参与者的利益实现最偏好的结果。

经济代写|博弈论代写Game Theory代考|DETERMINING RISK

在双头垄断的情况下，以及在大多数其他经济模型中，结果的效用等同于与结果相关的一些美元价值。虽然我们可以看到美元价值如何捕捉玩家偏好的强度，但美元价值不一定是 VNM 效用。例如，接收 $\$ 11.00$ 代替 $\$ 10.00$ 意味着远远超过接收 $\$ 1001.00$ 代替 $\$ 1000.00$ 对大多数人来说。为了探索这种差异，我们考虑了预期效用假设给出的彩票预期效用与彩票预期价值的效用之间的关系。
考虑以下抽奖活动：对于 $\$ 25$ ，你可以购买一个 $\frac{1}{400}$ 一个机会 $\$ 10,000$ 大学奖学金。我们可以用我们通常的符号来表示这张彩票
$$
\left.\left.\frac{399}{400} \text { ( losing } \$ 25\right)+\frac{1}{400} \text { (winning } \$ 9,975\right) \text {, }
$$
但由于结果是数字的，我们可以计算抽奖的预期货币价值
$$
\frac{399}{400}(-\$ 25)+\frac{1}{400}(\$ 9,975)=\$ 0 .
$$
参加或不参加抽奖的预期货币价值是相同的，但是，参加抽奖有小概率的大收益被大概率的小损失所抵消，而不参加抽奖则没有获得收益的机会或亏损。参加抽奖有风险，不参加抽奖则没有风险。
大多数大学生家长都愿意参加抽奖，但很多大学生自己却不愿意。对于大学生家长来说，
$$
u\left(\frac{399}{400}(\text { losing } \$ 25)+\frac{1}{400}(\text { winning } \$ 9,975)\right)>u(\$ 0)
$$
但对于学生自己来说，
$$
u\left(\frac{399}{400}(\text { losing } \$ 25)+\frac{1}{400}(\text { winning } \$ 9,975)\right)<u(\$ 0) .
$$
对于父母来说，彩票的效用大于期望值的效用，使他们在这种情况下冒险去爱。另一方面，学生是风险厌恶的，因为彩票的效用小于期望值的效用。正如我们在下面的定义中所描述的那样，这个原则通常是成立的。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写