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# 经济代写|博弈论代考Game theory代写|ECON3050 Definition of finite extensive form games with perfect information

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## 经济代写|博弈论代考Game theory代写|Definition of finite extensive form games with perfect information

In general, an extensive form game (with perfect information) $G$ is a tuple $G=\left(N, A, H, O, o, P,\left{\leq_i\right.\right.$ }$\left._{i \in N}\right)$ where

$N$ is a finite set of players.

A is a finite set of actions.

$H$ is a finite set of allowed histories. This is a set of sequences of elements of $A$ such that if $h \in H$ then every prefix of $h$ is also in $H$.
$Z$ is the set of sequences in $H$ that are not subsequences of others in $H$. Note that we can specify $H$ by specifying $Z ; H$ is the set of subsequences of sequences in $Z$.

$O$ is a finite set of outcomes.

$o$ is a function from $Z$ to $O$.

$P$ is a function from $H \backslash Z$ to $N$.

For each player $i \in N, \preceq_i$ is a preference relation over $O$. (I.e., a complete, transitive and reflexive binary relation). So for outcomes $x, y \in O$ we write $x \prec_1 y$ if player 1 strictly prefers $y$ to $x$. This means that given the choice, player 1 would rather have $y$ than $x$. We write $x \leq_1 y$ if player 1 is either indifferent between $x$ and $y$ or strictly prefers $y$.
We denote by $A(h)$ the actions available to player $P(h)$ after history $h$ :
$$A(h)={a \in A: h a \in H} .$$
Strategies are defined as for chess. A strategy profile $s=\left{s_i\right}_{i \in N}$ constitutes a strategy for each player. We can, as for chess, define $h(s)$ and $o(s)$ as the history and outcome associated with a strategy profile.

## 经济代写|博弈论代考Game theory代写|The ultimatum game

In the ultimatum game player 1 makes an offer $a \in{0,1,2,3,4}$ to player 2. Player 2 either accepts or rejects. If player 2 accepts then she receives $a$ dollars and player 1 receives $4-a$ dollars. If 2 rejects then both get nothing. This is how this game can be written in extensive form:

$N={1,2}$.

$A={0,1,2,3,4, a, r}$.

$Z={0 a, 1 a, 2 a, 3 a, 4 a, 0 r, 1 r, 2 r, 3 r, 4 r}$.

$O={(0,0),(0,4),(1,3),(2,2),(3,1),(4,0)}$. Each pair corresponds to what players 1 receives and what player 2 receives.

For $b \in{0,1,2,3,4}, o(b a)=(4-b, b)$ and $o(b r)=(0,0)$.

$P(\varnothing)=1, P(0)=P(1)=P(2)=P(3)=P(4)=2$.

For $a_1, b_1, a_2, b_2 \in{0,1,2,3,4},\left(a_1, a_2\right) \preceq_1\left(b_1, b_2\right)$ iff $a_1 \leq b_1$, and $\left(a_1, a_2\right) \preceq_2\left(b_1, b_2\right)$ iff $a_2 \leq b_2$.

A strategy for player 1 is just a choice among ${0,1,2,3,4}$. A strategy for player 2 is a map from ${0,1,2,3,4}$ to ${a, r}$ : player 2’s strategy describes whether or not she accepts or rejects any given offer.

# 博弈论代写

## 经济代写|博栾论代考Game theory代写|Definition of finite extensive form games with perfect information

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## MATLAB代写

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