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# 经济代写|微观经济学代考Microeconomics代写|The satisfaction principle

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## 经济代写|微观经济学代考Microeconomics代写|The satisfaction principle

The satisfaction principle is the only principle common to both evolutionist and classical game theory. It requires that, in addition to the set of players, the set of strategies available to each of them, one specifies for each player a utility function, which defines his payoff at each issue of the game (which may be repeated). It specifies the set of players, the set of strategies available to each of them as well as his utility function, i. e. his payoff at each issue of the stage game. The opportunities and preferences of the players are supposed to be given (to the modeller) at the beginning of the game and stay unchanged.

The standard illustration, systematically used in the future, is the “technology game”. It represents the coordination problem faced by two firms, 1 and 2 , which have to choose among two technologies, A and $\mathrm{B}$. The technology B, in contrast to the technology A, is a state-of- the-art- tech-nology: both firms, if they both choose B, better perform -they both get 4 than if they both choose A -they both get 2. When one firm uses technology A and the other technology B, the first firm gets $b$ and the second $c$, these parameters being further specified. Note that this game is symmetric whatever the values assigned to $b$ and $c$ (firms A and B have the same strategy set and achieve the same payoffs in symmetric issues). The corresponding game matrix, a symmetric matrix, is the following:

In a first variant of the technology game, looking like Rousseau’s stag hunt game, one states $b=1$ and $c=0$. It means that the inferior technology $\mathrm{A}$, better mastered than technology B, can be used alone (with a reduced payoff). Conversely, the superior technology $\mathrm{B}$, which needs to develop, is bad when used alone. In this variant, the technology $A$ is less risky than technology B, in that it yields a payoff which less depends on the choice of the other firm (the payoff is between 1 and 2 for technology A, in contrast to 0 and 4 for technology B). The corresponding matrix is the following (variant 1):

The stage game may be isolated or part of a bigger game, which is potentially much more complex. A stage game is isolated when the payoffs of the confronted players at a given period are independent of the behavior of all other players, which potentially play the same game, at the present (and preceding) periods. Some degree of isolation is necessary for a game to be studied in an evolutionist way; more precisely, in case of lack of the isolation assumption, it is possible to address the game only if the stage game smoothly changes from one period to the other, due to the evolution of the global game, whose impact is felt only progressively. So the technology game is perhaps not necessarily an isolated game: the prices of both technologies A and B, and therefore the benefits achieved with each of them, may depend on the behavior of other firms having to choose among the technologies A and B (and possibly other technologies), as well as on the behavior of consumers supposed to buy the product produced by means of the different technologies.

## 经济代写|微观经济学代考Microeconomics代写|The confrontation principle

Players play repeatedly, a finite or infinite number of times, a $n$-player stage game. The stage game is a non cooperative game in the usual sense, in normal or extensive form. The payoffs of the players are aggregated thanks to some discount rate (see chapter 1).

The $n$-player stage game is supposed to be played by $n$ players or, more usually in evolutionist games, by $n$ populations of agents, each agent of the population $i$ playing the role of player i. In each period, several $n$-uplets of individuals are randomly drawn from the $n$ populations (or subsets of these $n$ populations), one agent from each population, and each $n$-uplet of agents plays the game. The interactions may be more or less numerous at each period. On one side, a single $n$-uplet is constituted in a random way. On the other side, all possible $n$-uplets are formed. In the technology game, if each firm is represented by an equal number of agents (each agent having a given technology), each agent of one population may meet one firm of the other population or many combinations can be sorted out.

A usual distinction about meetings concerns the “multi-population” or the “mono-population” approach. The multi-population approach is available for any game and corresponds to differenciated players. Agents from a given population meet agents from the other populations. By contrast, the mono-population approach is reserved to symmetric games when players are considered as interchangeable. Agents form a unique population and meet any agents from that population. For a symmetric game, the two approaches are then available while only the first is available for non symmetric games. For example, one may study the technology game with two populations of agents, namely if the two firms are not located in the same place and if the game can only confront firms not located in a same place, but also with only one population of agents if the firms are interchangeable.

A second distinction about meetings makes a difference between “global interaction” and “local interaction”. In a local interaction model, the agents which an agent may meet in a given period belong to subsets of the other population(s). These subsets figure agent’s local “interaction neighborhood”. For example, in some traditional evolutionist games, agents are located on a one or two dimensional space, like a circle or a torus, and the interaction neighborhood spontaneously includes agents who are physically near them. By contrast, in a global interaction model, each agent may meet any agent in the opponent population(s). Global interaction is just a special case of local interaction (the size of the subsets is the cardinality of the populations). For instance, the technology game may be played by firms situated on a circle and a firm meets only the firms at its right and left.

# 微观经济学代写

## 经济代写|微观经济学代考Microeconomics代写|The confrontation principle

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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。