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|ECO467 Does randomizing make sense?

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## 经济代写|博弈论代考Game theory代写|Does randomizing make sense?

A mixed strategy requires that players randomize their choice of pure strategy. It is natural to object that only crazy people make serious decisions at random, but mixed strategies are used all the time without anyone realizing it.

My favourite example arose when I was advising a package holiday company on a regulatory matter. Game theory predicts that such a company will use a mixed strategy in the pricing game it has to play when the demand for vacations proves to be unexpectedly low. However, when I asked a senior executive whether his company actively randomized their prices last year, he reacted with horror at such an outlandish suggestion. So why were his prices for similar vacations so very different? His answer was instructive: ‘You have to keep the opposition guessing.’

His answer shows that he understood perfectly well why game theory sometimes recommends the use of mixed strategies. What he didn’t want to face up to is that his company’s method for setting prices was essentially a randomizing device. Nobody cut any cards. Nobody rattled a dice box. But from the point of view of a rival trying to predict what his company would charge for two weeks in the Bahamas, they might as well have done so.

## 经济代写|博弈论代考Game theory代写|Mixed Nash equilibria

The use of mixed strategies isn’t at all surprising in Matching Pennies, where the whole point is to keep the opponent guessing. As every child knows, the solution is to randomize between heads and tails. If both players use this mixed strategy, the result is a Nash equilibrium. Each player wins half the time, which is the best that both can do given the strategy choice of the other.
Similarly, it is a Nash equilibrium in the Driving Game if both players choose left and right with equal probability, which therefore has three Nash equilibria, two pure and one mixed. The same is also true in both Chicken and the Battle of the Sexes, but the mixed Nash equilibrium in the Battle of the Sexes requires more of the players than that they simply make each of their pure strategies equally likely.

In the Battle of the Sexes, Bob likes boxing twice as much as ballet, and so Alice must play box half as often as ball to ensure that he gets the same payoff on average from his two pure strategies. Since Bob doesn’t then care which of his pure strategies gets played, all of his strategies are then equally good – including the mixed strategy which makes ball half as likely as box. But the use of this mixed strategy makes Alice indifferent between her two pure strategies. So all of her strategies are then equally good – including the mixed strategy which makes box twice as likely as ball. This completion of the circuit shows that we have found a mixed Nash equilibrium in which Alice and Bob each play their more favoured strategy two-thirds of the time.

# 博弈论代写

## 经济代写|博弈论代考Game theory代写|Mixed Nash equilibria

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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。