## 经济代写|博弈论代写Game Theory代考|ECON2070

2022年12月29日

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## 经济代写|博弈论代写Game Theory代考|COMBINATORIAL GAMES

We have seen by now that game theory is much more than the study of how to play everyday games like video games, Tic-Tac-Toe, or chess. However, the study of those games also falls within the realm of game theory. Further, since such games almost always require sequential moves by the players, we can use the methods of this chapter in their analysis. Unfortunately, many games, like Monopoly, poker, and soccer, involve chance and/or hidden information, so we exclude them from our analysis for now and focus on combinatorial games.

A combinatorial game is a two-player sequential game that has well-defined positions and alternating moves between players. Further, either (1) one player wins obtaining a payoff of 1 and the other player loses obtaining a payoff of $-1$, or ( 2 ) there is a tie with each player obtaining a payoff of 0 . As usual, we assume that players act to obtain the highest payoff. (Notice that we exclude the possibility that a player may prefer to lose, such as when a parent is playing a game with their young child.)

Perhaps the most well-known combinatorial game is Tic-Tac-Toe which is played on a 3-by-3 grid of squares as shown in the leftmost drawing in Figure 5.13, where the outermost edges are not drawn. The players alternately mark an unmarked square with the first player using ” $\mathrm{X}$ ” and the second player using “O.” The winner is the first player to obtain three of their marks in a row, column, or diagonal. Figure $5.13$ shows one possible play of the game with the player using ” $\mathrm{X}$ ” winning with their fourth mark.

Versions of Tic-Tac-Toe have been played since antiquity although the name we use was not adopted until the twentieth century in the United States [122]. Tic-Tac-Toe is considered a children’s game since it does not take an adult long to realize how to play the game to ensure at least a tie. We examine this game in order to illustrate the strengths and weaknesses of the techniques we have developed. By Zermelo’s Theorem, there is a backward induction equilibrium. Since the only possible outcomes are a win for $\mathrm{X}$ (the player using ” $\mathrm{X}$ “), a win for $\mathrm{O}$ (the player using “O”), or a tie, exactly one of the following must hold: (1) there is a winning strategy for X, (2) there is a winning strategy for $\mathrm{O}$, or (3) there are strategies that ensure at least a tie for both $\mathrm{X}$ and $\mathrm{O}$.

## 经济代写|博弈论代写Game Theory代考|MORAL HAZARD

When we think of risk-aversion and risk-neutrality, we often think about insurance. People who are monetarily risk-adverse often purchase insurance policies to protect themselves or their properties against large losses. Even though the expected value of paying $\$ 100$is the same as having a$1 \%$chance of paying$\$10,000$, for many, paying a guaranteed monthly premium is preferable to having even a small chance of paying a much larger sum. We then wonder if having security against having to pay a larger sum changes people’s behavior in anyway. Insured drivers may not drive as cautiously or may leave their cars unlocked knowing they won’t be responsible for large damages or losses. Insurance companies must take this into account when calculating premiums or must find ways to reduce riskier behavior amongst their insured clients.

The change in behavior produced by passing some of the risk or responsibility from an individual to another player is known in game theory as moral hazard. The individual is called an agent and the other party assuming some of the risk is known as the principal. Insurance is one example with the insurance company acting as the principal for clients who are agents. Another common example studied is that of managers attempting to influence their employees behavior through incentive programs related to sales or profits. In this section, we explore the circumstances under which scholarships, particularly those given out by federal governments, can result in moral hazard.

A key characteristic of a situation that involves moral hazard is that the principal cannot influence the agent’s action in any binding way. In many situations the principal is able to observe only the final results. We can see, then, how a large federal government handing out scholarships to individual students spread out across a country could be in this situation.
We are exploring then, whether the government, in the role of the principal, may enable the student, in the role of the agent, to engage in activities that do not support the intentions of the government. Specifically, rather than working hard to succeed, a student may choose to put minimal effort into their studies and have a higher risk of failure since there is no or little cost to them for the classes.

# 博弈论代考

## 有限元方法代写

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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。