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 Monopoly

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## 经济代写|博弈论代考Game theory代写|Dynamic Monopoly

Retail firms frequently adjust prices. Sometimes price adjustments are due to changes in wholesale prices, but more often the adjustments have to do with customer demand. Consider the market for 3D television monitors. Not all consumers have the same interest in buying such a product; in other words, demand is differentiated. The “high-value” customers are people who either have a real need for the $3 \mathrm{D}$ technology or just love to buy the newest gadget on the market. “Low-value” customers would be interested in purchasing 3D monitors but only if these are priced to compete with standard displays.

Facing this heterogeneous consumer population-as is the case in most markets-retailers wish to extract a high price from the high-value customers and a lower price from the low-value customers. Although legal constraints and arbitrage force retailers to charge the same price to all people, a retailer can use time to its advantage. A common scheme is to initially set a high price that is intended to attract only the high-value customers. Then, after selling to the highvalue folks, the retailer will drop the price in the hopes of capturing the demand of low-value customers.

Superficially, this scheme appears to give the retailer a very high profit by allowing it to extract the surplus of trade from both the high- and the lowvalue customers. In other words, the retailer gets both types of customers to pay the most that they are willing to pay for the product. But the retailer does face some constraints. First, competition with other retailers may exert downward pressure on prices. Second, the retailer must realize that customers will behave strategically-in particular, high-value customers may delay their purchase of 3D monitors if they anticipate that the price will fall over time. In this section, I sketch a simple model that helps us explore the second strategic aspect. ${ }^3$ The model focuses on a monopoly setting (where a single firm is in the industry), and therefore it ignores the matter of competition between irms.

## 经济代写|博弈论代考Game theory代写|Price Guarantees as a Commitment to High Prices

As described earlier, under some conditions retail firms have an incentive to decrease prices over time to extract surplus from customers with different valuations. You might think that such a pricing policy is good for a firm-it helps the firm obtain profit from each type of customer. In fact, the incentive to decrease prices over time may actually have the opposite effect on profit. To make sense of my claim, let us continue with the dynamic monopoly example.
Consider again the optimal pricing scheme, C. Recall that when selecting the period 1 price $p_1$, Tony must consider the customers’ strategic calculations. In particular, all of the players know that if the low-type customers do not purchase and at least one of the high types does purchase a monitor in period 1 , then in period 2 Tony will have the incentive to select $p_2=200$. (You will recall that this is the “useful fact” noted on page 212.) Tony’s scheme C pricing policy is therefore a balancing act. On one hand, Tony wants to deal only with Hal and Hilbert in period 1, raising the price as high as they are willing to pay. On the other hand, once Hal and Hilbert have purchased monitors, Tony wants to decrease the price and sell two more units to Laurie and Lauren. Because Hal and Hilbert anticipate the second-period price, Tony can get them to pay only $\$ 1400$in period 1 . By comparison, consider how much Tony would make if he could somehow commit never to deal with Laurie and Lauren. For example, suppose that in period 1 Tony could make a legally enforceable promise not to sell monitors in period 2. Then suppose Tony chose a period 1 price of$p_1=1700$, or just below this amount. In this case, Hal and Hilbert would purchase monitors in period 1 . (By purchasing a monitor, a high type’s payoff would be$1700-p_1$; if he did not purchase a monitor, then the high type would get 0 , because no monitors would be sold in period 2.) Laurie and Lauren would not purchase at this high price. However, Tony’s payoff would be$\$3400$, which is greater than the payoff he would get without the ability to commit. Thus, commitment helps Tony.

# 博弈论代写

## 经济代写|博弈论代考Game theory代写|Price Guarantees as a Commitment to High Prices

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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。