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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写博弈论Game Theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写博弈论Game Theory代写方面经验极为丰富，各种代写博弈论Game Theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 经济代写|博弈论代写Game Theory代考|Adaptive Dynamics

In Box $4.1$ we examined how the mutant proportion of a resident population changes with time. There are in principle three possibilities for the fate of a mutant. It can either fail to invade by approaching zero representation (which was examined in Box 4.1), take over the population by instead approaching fixation, or remain in the population over the longer term by forming a polymorphism with the former resident. A simple conceptualization of evolutionary change is as a sequence of successful mutant invasions and fixations, which we refer to as adaptive dynamics. In reality evolutionary change need not follow such a simple scenario, but can instead proceed with substantial ongoing polymorphism, as well as with different types of genetic determination of strategies (e.g. diploid, multi-locus genetics), but the study of simple adaptive dynamics is useful for game theory in biology. In fact, the study of the invasion of an initially rare mutant into a resident population has proven to be a very productive link between game theory and evolutionary dynamics.

For games where strategies or traits vary along a continuum, it is of particular interest to examine if a mutant strategy $x^{\prime}$ in the vicinity of a resident $x$ can invade and replace the resident. The sign of the strength of selection $D(x)$ is key to this issue. For $x^{\prime}$ in the vicinity of $x$ we have the approximation
$$W\left(x^{\prime}, x\right)-W(x, x) \approx\left(x^{\prime}-x\right) D(x) .$$
Suppose now that $D(x)$ is non-zcro for a resident strategy $x$, so that $W\left(x^{\prime}, x\right)>W(x, x)$ for an $x^{\prime}$ close to $x$. Then the mutant $x^{\prime}$ can invade the resident $x$ (i.e. when the mutant is rare it will increase in frequency). It can also be shown that the mutant $x^{\prime}$ keeps increasing in frequency and will eventually replace the resident $x$.

## 经济代写|博弈论代写Game Theory代考|Convergence Stability

Any resident trait value $x^{}$ that is an equilibrium point under adaptive dynamics must satisfy $D\left(x^{}\right)=0$. Such a trait value is referred to as an evolutionarily singular strategy (Metz et al., 1996; Geritz et al., 1998). But what would happen if an initial resident trait is close to such an $x^{}$ ? Would it then evolve towards $x^{}$ or evolve away from this value? To analyse this we consider the derivative of $D(x)$ at $x=x^{}$. Suppose that $D^{\prime}\left(x^{}\right)<0$. Then for $x$ close to $x^{}$ we have $D(x)>0$ for $x}$ and $D(x)<0$ for $x>x^{}$. Thus by the conditions in (4.6) $x$ will increase for $x}$ and decrease for $x>x^{}$. Thus, providing the resident trait $x$ is close to $x^{}$, it will move closer to $x^{}$, and will converge on $x^{}$. We therefore refer to the trait $x^{}$ as being convergence stable if $$D^{\prime}\left(x^{}\right)<0 .$$ We might also refer to such an $x^{*}$ as an evolutionary attractor. Conversely, if $D^{\prime}\left(x^{*}\right)>0$, then any resident trait value close to (but not exactly equal to) $x^{}$ will evolve further away from $x^{}$. In this case we refer to $x^{}$ as an evolutionary repeller. Such a trait value cannot be reached by evolution. Figure $4.4$ illustrates these results. If $x^{}$ is a Nash equilibrium value of the trait, then $W\left(x^{\prime}, x^{}\right)$ has a maximum at $x^{\prime}=x^{}$. Thus if $x^{}$ lies in the interior of the range of possible trait values we must have $\frac{\partial W}{\partial x^{}}\left(x^{}, x^{}\right)=0$; i.e. $D\left(x^{}\right)=0$. Thus $x^{}$ is an equilibrium point under adaptive dynamics; i.e. it is an evolutionarily singular strategy. Since every ESS is also a Nash equilibrium, every internal ESS is also an evolutionarily singular strategy. The above analysis of the convergence stability of an ESS was originally developed by Eshel and Motro (1981) and Eshel (1983).

## 经济代写|博弈论代写Game Theory代考|Adaptive Dynamics

$$W\left(x^{\prime}, x\right)-W(x, x) \approx\left(x^{\prime}-x\right) D(x) .$$

## 经济代写|博弈论代写Game Theory代考|Convergence Stability

$$D^{\prime}(x)<0 .$$ 䖸们也可以参考这样的 $x^{*}$ 作为进化吸引子。相反，如果 $D^{\prime}\left(x^{*}\right)>0$ ，然后任何接近 (但不完全等于) 的常驻特征值 $x$ 将进一步远离 $x$. 在这种情况下，我们指 $x$ 作为进 化的排斥者。进化无法达到这样的特征值。数字4.4说明了这些结果。如果 $x$ 是特征的纳什均衡值，则 $W\left(x^{\prime}, x\right)$ 有一个最大值 $x^{\prime}=x$. 因此，如果 $x$ 位于我们必须具有 的可能特征值范围的内部 $\frac{\partial W}{\partial x}(x, x)=0 ; \mathrm{IE} D(x)=0$. 因此 $x$ 是自适应动力学下的平衡点；即，它是一种进化上的单一策略。由于每个 ESS 也是一个纳什均衡，每个 内部 ESS 也是一个进化上的单一策略。ESS 收敛稳定性的上述分析最初是由 Eshel 和 Motro (1981) 和 Eshel (1983) 提出的。

## 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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师