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|Who should do how much housework?

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## 经济代写|博弈论代考Game theory代写|Who should do how much housework?

Newspapers like to stoke the gender wars when short of copy.
Here is a typical quote: ‘Men pay lip service to equal rights in the home while letting women do three quarters of the household chores.’ Other things being equal, the fact that wives do more housework than husbands would indeed show that the balance of power within marriages is biased in favour of men, but are other things equal?
Alice and Bob are getting married. They have no interest in enjoying any of the benefits of marriage other than sharing the housework. In the modern style, they agree on a binding marriage contract that specifies how many hours a week of housework each will contribute. What deal does the Nash bargaining solution predict that they will reach?
In a toy version of the problem, Alice thinks a household should devote two hours a day to housework; Bob thinks one hour a day is adequate. Each player derives a benefit of 100 utils a week if at least the number of hours they think appropriate is worked; otherwise they see no benefit at all in any housework being done.

Neither Alice nor Bob likes doing housework. Alice loses 5 utils a week for each hour of housework that she does. Bob loses 10 utils per hour, because he dislikes doing housework more than Alice. In the status quo situation before the marriage, Alice therefore does 14 hours of housework a week from which she derives a utility of 30 utils; Bob does 7 hours of housework from which he also derives a utility of 30 utils.

The Coase theorem says that the bargaining outcome will be efficient, which means that Alice will get her way over the number of hours that the new household will spend on housework. To find the Nash bargaining solution, we need to find the extreme outcomes that just make the marriage worthwhile for both partners. One extreme arises when Alice does all the housework; she will then get 30 utils and Bob will get 100 utils. The other extreme arises when it is Bob who gets only 30 utils. He will then do one hour of housework a day. Alice must do the other hour of housework to make up the two hours a day she thinks necessary. Her utility will then be 65 utils.

Because the model has been fixed to make Alice and Bob risk neutral, the Nash bargaining solution is found by averaging the two extremes. So Alice will end up with 47.5 utils and Bob with 65 utils a week. To make this happen, Alice will have to work $10 \frac{1}{2}$ hours a week and Bob only $3 \frac{1}{2}$ hours a week.
The Nash bargaining solution therefore says that if Alice and Bob bargain on an equal basis, then Alice will get her way on the number of hours worked a week, but she will have to do three-quarters of the work. If it is indeed true that wives do three times as much housework as single women, then our toy model shows that it doesn’t necessarily follow that the balance of power within marriages is biased in favour of men. Who would do how much housework if all the factors left out of the toy model were taken into account? Even if I knew, I wouldn’t say!

## 经济代写|博弈论代考Game theory代写|Rubinstein’s bargaining model

In accordance with the Nash program, Nash defended his bargaining solution with a noncooperative bargaining model in which Alice and Bob each simultaneously commit themselves to take-it-or-leave-it demands. However, Schelling was later successful in casting doubt on the realism of attributing commitment power to the players in negotiation games.
For example, if Bob were able beat Alice to the draw when making an irrevocable commitment in Divide-the-Dollar, then he could scoop the pot by demanding 99 cents, leaving Alice with a choice between one penny or nothing. But how does Bob convince Alice that he is truly committed – that nothing she might do can make him revise his demand? Who believes someone who claims he is now making his ‘last and final offer’? Even prices posted on expensive items in fancy stores are seldom final. The seller will try to make you feel like a cheapskate for challenging the price, but folk wisdom is right for once. Everything is negotiable. Never take no for an answer.

It is genuinely hard to establish commitments. People sometimes make a career of building up a reputation for being stubborn or stupid for this purpose. Trade unionists occasionally succeed in committing themselves by voting for intransigent leaders. But outside such special circumstances, the vocabulary of commitment is usually just so much cheap talk. But if all threats must be credible, we have seen that we need to look at subgame-perfect equilibria.
So what happens when anything a player says has to be credible before the other player will believe it? This question led Ariel Rubinstein to make the most important of all contributions to the Nash program. In the most natural noncooperative model of bargaining, Alice and Bob alternate in making offers to each other until they reach agreement. If they are assumed to prefer making any particular deal now rather than later, then Rubinstein showed that the alternating-offers model has a unique subgame-perfect equilibrium.
My own contribution was to show that the unique subgame-perfect equilibrium outcome approximates an asymmetric version of the Nash bargaining solution when the time interval between successive offers becomes sufficiently small. In the symmetric version of the Nash bargaining solution, the ratio $N B / A N$ in Figure 33 is equal to one. In the asymmetric version $N B / A N$ equals the ratio of the rates at which Alice and Bob discount time.

# 博弈论代写

## 经济代写|博弈论代考Game theory代写|Rubinstein’s bargaining model

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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。