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# 经济代写|微观经济学代考Microeconomics代写|ECON1101 Hybrid models

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## 经济代写|微观经济学代考Microeconomics代写|The interpretation of replicator dynamics

The original interpretation of the replicator dynamics equation is linked with biological reproduction. Let $n^t(x)$ be the number of individuals that use strategy $x$ at date $t$ and let thus $n^t=\sum_{x \in X} n^t(x)$ be the total number of individuals in the population. Suppose that, at date $t$, one individual $i$, using the strategy $x$, is chosen at random in the first population to reproduce (asexual reproduction). This individual is randomly matched with another individual of the other population. Denote by $y$ the strategy used by this other individual. One supposes that the number of offsprings of individual $i$, in the next generation, is proportional to the utility $u(x, y)$ of her strategy in this matching. Utility is here directly the measure of reproductive “fitness”. Under these hypotheses, the probability of a match of type $(x, y)$ is $p^t(x) p^t(y)$ and the number $n^{t+1}(x)$ of $x$-users at date $t+1$ is equal to $n^t(x)$ with the probability $1-p^t(x)$, and to $n^t(x)+\lambda u(x, y)$ with the probability $p^t(x) p^t(y)$, where $\lambda$ is some proportionality constant. On average, one thus has:
$$n^{t+1}(x)-n^t(x)=\lambda p^t(x) \sum_{y \in X} p^t(y) u(x, y)=\lambda p^t(x) u\left(x, p^t\right) .$$

## 经济代写|微观经济学代考Microeconomics代写|A mixed learning model

Consider coordination games in which the individuals (all) prefer to coordinate but in which different conventions for coordination are possible. Such situations are very common: efficiency is improved when technological standards are in place, relations between landlords and exploitants are made easier by the existence of conventional crop sharing rules. When the evolution of such a system is caused by a selection process coupled with a mutation process, one has to compare the time scales needed for these two processes to act. In the long run, when the effect of mutations can be neglected, selection pressure leads to a stable state, even if different stable states can be attained. In the very long run, when the effect of mutations cannot a priori be neglected, they make possible jumps from one stable state to the other, and the behavior of the system depends upon the detail of the mutation process. For instance, it may be the case that in the long run any one of two possible conventions emerges, wheras in the very long run, one of them is selected much more frequently than the other.
In order to analyse this phenomenon, Young (1993a) introduced a stochastic perturbation in the Fictitious Play learning model, together with the consideration of populations of individuals. The following hypothesis are respective applications of the three principles of information, evaluation and decision, to hold at each date $t$ :

1. Each individual has a memory of depth $m$, that is to say that she has no access to events that occurred before period $t-m$.
2. Each individual randomly draws a sample of size $s$ of strategies chosen by the other individuals, among the strategies chosen at dates $t-m, \ldots, t-1$.
3. With probability $1-\varepsilon$, the individual chooses a best response to the static distribution she observed by sampling, and with probability $\varepsilon$, the individual chooses at random her strategy (the number $\varepsilon$ is an error rate).

# 微观经济学代写

## 经济代与写微观经济学代考MICROECONOMICS代写|THE INTERPRETATION OF REPLICATOR DYNAMICS $x$,

$$n^{t+1}(x)-n^t(x)=\lambda p^t(x) \sum_{y \in X} p^t(y) u(x, y)=\lambda p^t(x) u\left(x, p^t\right) .$$

## 经济代写|微观经济学代考MICROECONOMICS代写|A MIXED LEARNING MODEL

1. 每个人都有深刻的记忆 $m$ ，也就是说她无权访问 period 之前发生的事件 $t-m$.
2. 每个人随机抽取一个 size 的样本 $s$ 其他人选择的策略，在日期选择的策略中 $t-m, \ldots, t-1$.
3. 以概率 $1-\varepsilon$ ，个人选择对她通过抽样观䕓到的静态分布的最佳反应，并且概率 $\varepsilon$, 个体随机选择她的策略thenumber\$E\$isanerrorrate.

## 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。