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|DYNAMIC OLIGOPOLY AND COLLUSION

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## 经济代写|博弈论代考Game theory代写|DYNAMIC OLIGOPOLY AND COLLUSION

Consider the Cournot duopoly model in Chapter 10, with two firms that each produce at zero cost (which I assume just to make the computations easy), and suppose the market price is given by $p=1-q_1-q_2$. Firm $i$, which produces $q_i$, obtains a payoff of $\left(1-q_i-q_j\right) q_i$. Note that the Nash equilibrium of this game is $q_1=q_2=1 / 3$, yielding a payoff of $1 / 9$ for each firm. As noted in Chapter 10, this outcome is inefficient from the firms’ point of view; they would both be better off if they shared the monopoly level of output by each producing $1 / 4$. Sharing the monopoly output yields each firm a payoff of $1 / 8$, which is greater than the Nash equilibrium payoff of $1 / 9 .^1$ In the static game, therefore, the firms would like to collude to set $q_1=q_2=1 / 4$, but this strategy profile cannot be sustained because it is not an equilibrium.

In most industries, firms do not interact in just a single point in time. They interact every day, potentially forever. To model firms’ ongoing interaction, we can examine an infinitely repeated version of the Cournot duopoly, where the stage game is defined as the Cournot game described in the preceding paragraph. Analysis of the infinitely repeated game demonstrates that collusion can be sustained in equilibrium, using the reputation mechanism. In particular, let us evaluate the following grim-trigger strategy profile: Each firm is prescribed to select $1 / 4$ in each period, as long as both firms did so in the past; if one or both players deviates, the firms are supposed to play the stage Nash profile $(1 / 3,1 / 3)$ forever after.

## 经济代写|博弈论代考Game theory代写|ENFORCING INTERNATIONAL TRADE AGREEMENTS

Whereas self-enforced contracts between colluding firms is undesirable, the opposite is true of contracts between countries. International trade agreements can be very beneficial, but, because there is no strong external enforcement institution for interaction between countries, nations must rely on self-enforcement. The reputation mechanism is used to enforce trade agreements.

For example, a significant fraction of the world’s nations have agreed to set low tariffs on imports (a reduction from the high tariffs that existed decades ago). Low tariffs are generally efficient in that countries are better off when they all set low tariffs than if they all set high tariffs. However, as you have learned by analyzing the equilibrium of the static tariff game in Chapter 10, low tariffs cannot be sustained as a self-enforced contract when the countries rely on shortterm incentives. In other words, low tariffs do not constitute a Nash equilibrium in the static game. Instead, nations utilize the repeated nature of their interaction. They often agree to trigger-strategy equilibria, whereby low tariffs (cooperation) are sustained by the threat of reverting to the high-tariff stage Nash profile. That is, if one country cheats by unilaterally raising a tariff, then it and its trading partners expect low value in the future as play turns to the stage Nash profile.
Self-enforced contracts between countries are quite explicit-they result from active, sometimes intense, negotiation. International institutions facilitate trade agreements by bringing the nations’ representatives together, by providing them with a language that fosters mutual understanding, by recording agreements, and by disseminating information. The World Trade Organization (WTO) and its predecessor, the General Agreement on Tariffs and Trade (GATT), have been the focal point for achieving dramatic tariff reductions in the past century.

# 博弈论代写

## 经济代写|博弈论代考Game theory代写|ENFORCING INTERNATIONAL TRADE AGREEMENTS

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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。