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# 经济代写|微观经济学代考Microeconomics代写|ECON310 A Monopoly with No Barriers to Entry

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## 经济代写|微观经济学代考Microeconomics代写|A Monopoly with No Barriers to Entry

We will now describe a game on so-called extensive form, where the question is whether a monopolist can uphold her monopoly if there are no barriers to entry. In a game on extensive form there is, in contrast to games on normal form, an order to the choices. One could say that we have added a time dimension.
There are two firms, The Incumbent (J) and the Entrant (E). J has, at the beginning, a monopoly in the market and $\mathrm{E}$ has to choose whether to enter the market or not. If she decides to enter it, $\mathrm{J}$ can choose to start a price war, i.e. lower the price to punish $\mathrm{E}$, or to accept the competitor. The problem with a price war is that it also hurts $\mathrm{J}$ herself.

• The players; The Incumbent (J) and the Entrant (E).
• Actions; For E: choose “enter” or “not enter”; for J: choose “price war” or “accept.”
• Information; E knows what the game structure looks like, but not how $\mathrm{J}$ will decide later on. $\mathrm{J}$, on the contrary, knows how E has chosen when it is her time to choose. $\mathrm{J}$ consequently has more information than $\mathrm{E}$.
• Strategies. For E there are two strategies:
1. Choose “enter.”
2. Choose “not enter.”
For J, there are also two strategies:
3. Choose “price war.”
4. Choose “accept.”

## 经济代写|微观经济学代考Microeconomics代写|Finding the Nash Equilibrium for a Game Tree

To find the Nash Equilibrium for a game tree, we compare all different combinations of strategies. In the example in Section 13.4, E has two strategies and $\mathrm{J}$ has two. It is then possible to “translate” the game tree to a game on matrix form, as in Figure 13.3. Each strategy is translated into a row or a column. It now looks similar to the game from Section 13.2, but with other payoffs and strategies.

Note that in the case when E chooses “not enter”, it does not matter what J chooses. Looking at the game tree in Figure 13.2, this is obvious since the game ends after such a choice and $\mathrm{J}$ never gets to choose. In the matrix, this translates into identical payoffs in all columns of the corresponding row, i.e. $(50,100)$

To find the Nash equilibrium, we use the same method as in the last section and check each square separately. E chooses in the vertical direction and $\mathrm{J}$ in the horizontal. In Figure 13.3, we have inserted arrows from squares that have a better alternative to that alternative. Squares that have no arrows going out will then be Nash equilibria. In this case, there are two Nash equilibria:

• E chooses “enter” and $\mathrm{J}$ chooses “accept.” If $\mathrm{E}$ unilaterally changes her strategy, she will diminish her payoff from 75 to 50, and if $\mathrm{J}$ does so, she will diminish her payoff from 75 to 50 .
• E chooses “not enter” and J chooses “price war.” If E changes her strategy, she will diminish her payoff from 50 to 25 , and if $\mathrm{J}$ does so, she will get the same as before, i.e. 100 . The latter is due to the fact that it does not matter what $\mathrm{J}$ chooses when $\mathrm{E}$ has chosen “not enter.”

# 微观经济学代写

## 经济代写|微观经济学代考Microeconomics代写|A Monopoly with No Barriers to Entry

• 玩家们; 现任者 $(J)$ 和新入者 (E)。
• 动作；E：选择“进入”或“不进入”；对于 J：选择“价格战”或“接受”。
• 信息; $\mathrm{E}$ 知道斿戏结构是什么样的，但不知道如何 $\mathrm{T}$ 稍后再决定。J，相反，在她选择的时候知道E是如何 选择的。J因此有更多的信息比E.
• 策略。对于 $\mathrm{E}$ 有两种策略：
1. 选择“进入”。
2. 选择“不输入”。 对于J，也有两种策略:
3. 选择“价格战”。
4. 选择“接受”。

## 经济代写|微观经济学代考Microeconomics代写|Finding the Nash Equilibrium for a Game Tree

• E选择“进入”和J选择“接受”。如果E单方面改变她的策略，她会将收益从 75 减少到 50 ，如果 $\mathrm{J}$ 这样做，她会将收益从 75 减少到 50。
• E选择“不进入”，J选择“价格战”。如果 $\mathrm{E}$ 改变她的策略，她会将她的收益从 50 减少到 $25 ，$ 并且如果 $\mathrm{J}$ 这样做，她将得到与以前相同的值，即 100 。后者是因为不管怎样 $\mathrm{J}$ 选择什么时候 E选择了”不进入”。

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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。