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# 经济代写|博弈论代考Game theory代写|ECON3503 Games in Strategic Form

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## 经济代写|博弈论代考Game theory代写|Games in Strategic Form

A game in strategic form is the fundamental model of non-cooperative game theory. The game has $N$ players, $N \geq 1$, and each player $i=1, \ldots, N$ has a nonempty set $S_i$ of strategies. If each player $i$ chooses a strategy $s_i$ from $S_i$, the resulting $N$-tuple $s=\left(s_1, \ldots, s_n\right)$ is called a strategy profile. The game is specified by assigning to each strategy profile $s$ a real-valued payoff $u_i(s)$ to each player $i$.

The payoffs represent each player’s preference. For two strategy profiles $s$ and $\hat{s}$, player $i$ strictly prefers $s$ to $\hat{s}$ if $u_i(s)>u_i(\hat{s})$, and is indifferent between $s$ and $\hat{s}$ if $u_i(s)=u_i(\hat{s})$. If $u_i(s) \geq u_i(\hat{s})$ then player $i$ weakly prefers $s$ to $\hat{s}$. Player $i$ is only interested in maximizing his own payoff, and not interested in the payoffs to other players (other than in trying to anticipate their actions); any “social” concern a player has about a particular outcome has to be (and could be) built into his own payoff. All players know the available strategies and payoffs of the other players, and know that they know them, etc. (that is, the game is “common knowledge”).
The game is played as follows: The players choose their strategies simultaneously (without knowing what the other players choose), and receive their respective payoffs for the resulting strategy profile. They cannot enter into any binding agreements about what they should play (which is why the game is called “noncooperative”). Furthermore, the game is assumed to be played only once, and therefore also called a one-shot game. Playing the same game (or a varying game) many times leads to the much more advanced theory of repeated games.

## 经济代写|博弈论代考Game theory代写|Best Responses and Equilibrium

Consider the game in Figure 3.2(a). This is the Prisoner’s Dilemma game, with further graphical information added to help the analysis of the game. Namely, certain payoffs are surrounded by boxes that indicate that they are best-response payoffs.

A best response is a strategy of a player that is optimal for that player assuming it is known what all other players do. In a two-player game, there is only one other player. Hence, for the row player, a best response is found for each column. In the Prisoner’s Dilemma game, the best response of the row player against column $C$ is row $D$ because his payoff when playing $D$ is 3 rather than 2 when playing $C$ (so in the cell for row $D$ and column $C$, the payoff 3 to player $I$ is put in a box), and the best response against column $D$ is also row $D$ (with payoff 1 , in a box, which is larger than payoff 0 for row $C$ ). Similarly, the best response of the column player against row $C$ is column $D$, and against row $D$ is column $D$, as shown by the boxes around the payoffs for the column player. Because the game is symmetric, the best-response payoffs are also symmetric.

The game in Figure 3.2(b) has payoffs that are nearly identical to those of the Prisoner’s Dilemma game, except for the payoff to player II for the top right cell, which is changed from 3 to 1 . Because the game is not symmetric, we name the strategies of the players differently, here $T$ and $B$ for the row player (for “top” and “bottom”) and $l$ and $r$ for the column player (“left” and “right”). To distinguish them more easily, we often write the strategies of player I in upper case and those of player II in lower case.

Figure 3.2(b) is called the Quality game. It may describe the situation of player I as a restaurant owner, who can provide food of good quality (strategy $T$ ) or bad quality (B), and a potential customer, player II, who may decide to eat there $(l)$ or not $(r)$. The customer prefers $l$ to $r$ only if the quality is good. However, whatever player II does, player I is better off by choosing $B$. These preferences are shown by the best-response boxes. The best response of player II to row $T$ is different from her best response to row $B$. The best response of player I to either column is always row $B$.

# 博弈论代写

## 经济代写|博弈论代考博弈论代写|最佳对策与均衡

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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。