Posted on Categories:Game theory , 博弈论, 经济代写

# 经济代写|博弈论代考Game theory代写|CONDITIONAL BELIEFS ABOUT TYPES

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 经济代写|博弈论代考Game theory代写|CONDITIONAL BELIEFS ABOUT TYPES

The gift game in Figure 28.1 illustrates the idea of a conditional belief. Recall that in this game, player 2 does not observe nature’s decision. Therefore, at the beginning of the game, player 2 knows only that player 1 is the friend type with probability $p$ and the enemy type with probability $1-p$. This belief $p$ is called player 2’s initial belief about player 1’s type. Keep in mind that this is a belief about player 1’s type, not a belief about player 1’s strategy (which is the sort of belief with which we were dealing in Parts I through III of this book).

Although player 2 does not observe nature’s decision, player 2 does observe whether player 1 decided to give a gift. Furthermore, player 2 might learn something about player 1’s type by observing player 1’s action. As a result, player 2 will have an updated belief about player 1’s type. For example, suppose that you are player 2 in the gift game and suppose that player 1 behaves according to strategy $\mathrm{N}^{\mathrm{F}} \mathrm{G}^{\mathrm{E}}$; thus, you expect only to receive a gift from the enemy type. What should you conclude, then, if player 1 actually gives you a gift? Given player 1’s strategy, you should conclude that player 1 is an enemy. In reference to Figure 28.1 , when your information set is reached, you believe that you are playing at the lower of the two nodes in the information set.

In general, player 2 has an updated belief about player 1’s type, conditional on arriving at player 2’s information set (that is, conditional on receiving a gift). Note that player 2’s updated belief about player l’s type can be put in terms of a probability distribution over the nodes in player 2’s information set. In Figure 28.1, this probability distribution is described by the numbers $q$ and $1-q$ that appear beside the nodes. Literally, $q$ is the probability that player 2 believes he is the top node when his information set is reached. Thus, $q$ is the probability that player 2 believes player 1 is the friend type, conditional on receiving a gift.

## 经济代写|博弈论代考Game theory代写|SEQUENTIAL RATIONALITY

Taking account of conditional beliefs allows us to evaluate rational behavior at all information sets, even those that may not be reached in equilibrium play. Consider, again, the gift game pictured in Figure 28.1. Regardless of player l’s strategy, player 2 will have some updated belief $q$ at his information set. This number has meaning even if player 2 believes that player 1 adopts the strategy $\mathrm{N}^{\mathrm{F}} \mathrm{N}^{\mathrm{E}}$ (where neither type gives a gift). In this case, $q$ represents player 2 ‘s belief about the type of player 1 when the “surprise” of a gift occurs. Given the belief $q$, we can determine player 2’s optimal action at his information set. You can readily confirm that action $\mathrm{A}$ is best for player 2, whatever is $q$. Thus, sequential rationality requires that player 2 select $A$.
For another example, consider the gift game pictured in Figure 28.2. This is the same game discussed in Chapter 24. Note that regardless of the probability $q$, player 2 receives a payoff of 0 if he selects $\mathrm{R}$ at his information set.
In contrast, if player 2 chooses $\mathrm{A}$, then he gets a payoff of 1 with probability $q$ (the probability that his decision is taken from the top node in his information set) and he gets a payoff of -1 with probability $1-q$. Player 2 ‘s expected payoff of selecting $A$ is therefore
$$q+(-1)(1-q)=2 q-1$$
Player 2 will select $\mathrm{A}$ if $q>1 / 2$, he will select $\mathrm{R}$ if $q<1 / 2$, and he will be indifferent between $\mathrm{A}$ and $\mathrm{R}$ if $q=1 / 2$.

# 博弈论代写

## 经济代写|博弈论代考Game theory代写|SEQUENTIAL RATIONALITY

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。