经济代写|博弈论代写Game Theory代考|ECON6025

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Doug I. Jones

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  • 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|ECON6025

经济代写|博弈论代写Game Theory代考|Differences Select for Social Sensitivity

If there is no variation in a population there is no advantage in observing the past behaviour of others. Once there is variation it can be advantageous to be socially sensitive, and observe the past behaviour of others in order to predict their current behaviour. However, the value of social sensitivity depends on the usefulness of the information obtained, which often depends on the amount and type of variation in the population. Thus when there are costs of sensitivity the range of behaviours in a population affects the optimal degree of sensitivity. Conversely, increasing the degree of sensitivity increases the importance of reputation and hence affects the range of behaviours. This section concerns this two-way interaction in models of the co-evolution of behaviour and social sensitivity.

Johnstone (2001) considers a model in which members of a large population play a long series of competitive rounds. In each round each population member is paired up with a different randomly selected opponent and the two contest a resource of value $V$. In this contest each can either play Hawk or Dove. Payoffs are as in the standard Hawk-Dove game (Section 3.5). It is assumed that $V<C$. There are three possible strategies in the population: (i) always play Hawk, (ii) always play Dove, and (iii) Eavesdrop. Individuals following the latter strategy have observed the outcomes of contests in the last round. If their current opponent gained the resource in the last round (either by playing Hawk or Dove) they play Dove, and if the opponent failed to gain the resource they play Hawk.

Let the frequency of pure Hawks, pure Doves, and Eavesdroppers in the population be $f_H, f_D$, and $f_F$, respectively. Johnstone (2001) shows that the proportions of these three types that gained the resource in the last round, $p_H, p_D$, and $p_E$, tend to limiting values that depend on the frequencies of the three strategies. This then allows the mean payoffs under the three strategies to be evaluated. Johnstone (2001) analyses the evolutionary outcome using replicator dynamics (Section 4.4), showing there is a unique stable attractor of the dynamics. At this equilibrium all three strategies co-exist.

If an opponent has gained the resource in the last round, this opponent is more likely to be a Hawk than the population frequency of Hawks. Thus by playing Dove against such an opponent an Eavesdropper avoids a costly Hawk-Hawk fight. Similarly, an opponent that failed to gain the resource in the last round is more likely to be a Dove than the population frequency of Doves, so that an Eavesdropper gains by playing Hawk. Eavesdroppers are inconsistent in their actions. Thus Eavesdroppers do not spread to fixation because as their proportion increases reputation becomes less predictive, so that eavesdropping becomes less valuable.

经济代写|博弈论代写Game Theory代考|Markets

Organisms often exchange commodities or services. Such biological markets have been highlighted by Ronald Noë and his co-workers (Noë and Hammerstein, 1994; Bshary and Noë, 2003; Hammerstein and Noë, 2016). A market often consists of two distinct trader classes, and this is the situation we consider in this section. For example, aphids and ants may form two classes in a market in which aphids provide ants with sugar-rich exudate and in exchange the ants provide the aphids with protection against predation. Cleaner fish and their clients trade with each other; the cleaner fish benefit by feeding on the ectoparasites of their clients and the client fish gain by having these parasites removed. Insects pollinate plants in exchange for nectar. Usually, the members of one class (or both classes) would benefit if they could get away with providing as poor service as possible. So for example, cleaner fish prefer to feed on the mucus of their clients rather than the ectoparasites, and do so if they can. A flowering plant would do better to produce less nectar if that did not affect the behaviour of pollinating insects. In such situations, whether it is possible to get away with poor service depends on the market setting. In this section and the following two sections we explore market forces and their consequences. As we will show the mean level of service given by one class is usually important. In many cases the variation in the quality of service is also important as the choosiness of recipients of service can be strongly affected by the range of options available.

Members of each trader class provide services to members of the other class. Figure $7.8$ summarizes the relationship between the service given by members of one trader class and the response to this service of members of the other class. This dependence can be described as follows.

Choosiness of recipients. Recipients of service can be choosy about the individuals that service them in a number of ways. (i) They might recognize those who would give poor service in advance and avoid these servicers. So for example, if a client fish has observed that a previous interaction between a cleaner and another client has ended in conflict, the cleaner is avoided (Bshary and Noë, 2003). (ii) Recipients may provide less in exchange or break off their interaction sooner if the service is poor. For example, a client is liable to terminate the interaction with a cleaner fish that feeds on mucus. An insect will tend to leave a flower earlier if there is little nectar. (iii) A recipient may avoid a servicer in the future if they have previously experienced poor service.

The degree to which recipients should be choosy depends on the costs and benefits of choosiness. Often recipients may be receiving positive benefits from a servicer, but these benefits are too few and the recipient should break off the interaction or avoid the servicer in the future in an attempt to find a better servicer. In the case of a foraging insect drinking the nectar from a flower, the rate at which it gains nectar will typically decrease as the amount of nectar remaining decreases. At what point should it leave the current flower and seek a new one? In the model we present below, this depends on the mean rate at which it can gain nectar from other flowers in the environment, which depends on the amounts of nectar in these flowers and the time taken to move between flowers. In the case of a client fish receiving bad service from a cleaner fish, should the client return to this cleaner the next time it requires cleaning, or should it seek a different cleaner? If all cleaners are the same there is clearly no point in being choosy. Thus choosiness is advantageous only if there is variation, so that there is a significant possibility of finding a better cleaner. The costs of rejecting a cleaner is also central. Finding a better cleaner may take time and involve energetic or mortality costs. Overall, the benefits of seeking a better partner must be weighed against the costs (e.g. Exercise 7.6).

经济代写|博弈论代写Game Theory代考|ECON6025





设种群中纯鹰派、纯鸽派和纯偷听者的频率分别为$f_H, f_D$和$f_F$。Johnstone(2001)表明,这三种类型在最后一轮($p_H, p_D$和$p_E$)中获得资源的比例倾向于限制值,这取决于三种策略的频率。这样就可以评估三种策略下的平均收益。Johnstone(2001)使用复制因子动态分析了进化结果(第4.4节),表明动态存在一个独特的稳定吸引子。在这种平衡状态下,三种策略同时存在 如果一个对手在上一轮获得了资源,那么这个对手更有可能是一个鹰,而不是鹰的人口频率。因此,通过让鸽子对抗这样的对手,窃听者避免了一场代价高昂的鹰鹰大战。同样地,在上一轮中未能获得资源的对手更有可能是鸽子,而不是鸽子的人口频率,所以窃听者通过扮演鹰而获得资源。偷听者的行为前后不一。因此,窃听者不会扩散到固定的程度,因为随着他们所占比例的增加,声誉的可预测性变得越来越低,因此窃听的价值就变得越来越低


生物经常交换商品或服务。Ronald Noë和他的同事强调了这种生物市场(Noë和Hammerstein, 1994;Bshary和Noë, 2003;汉默斯坦和Noë, 2016)。一个市场通常由两种不同的交易者阶层组成,这就是我们在这一节中所考虑的情况。例如,蚜虫和蚂蚁可以在市场中分成两类,蚜虫为蚂蚁提供富含糖分的渗出物,作为交换,蚂蚁为蚜虫提供保护,使其免受捕食。清洁鱼和它们的客户之间进行贸易;清洁鱼通过捕食它们的客户鱼的体外寄生虫而获益,客户鱼通过清除这些寄生虫而获益。昆虫为植物授粉以换取花蜜。通常情况下,如果一个阶层(或两个阶层)的成员能够提供尽可能差的服务,他们就会受益。例如,清洁鱼更喜欢以它们的客户的粘液为食,而不是体外寄生虫,如果可以的话,它们会这样做。如果不影响授粉昆虫的行为,开花植物会更好地减少花蜜。在这种情况下,是否有可能摆脱糟糕的服务取决于市场环境。在本节和接下来的两节中,我们将探讨市场力量及其后果。正如我们将要展示的,一个班级提供的平均服务水平通常是重要的。在许多情况下,服务质量的变化也很重要,因为服务接受者的选择性会受到可用选项范围的很大影响 每个交易者类的成员为其他类的成员提供服务。图$7.8$总结了一个交易员类的成员提供的服务与另一个类的成员对该服务的响应之间的关系。这种依赖性可以描述为:

收件人的挑剔。服务的接受者可以通过多种方式选择为他们服务的人。(i)他们可能会提前发现那些服务质量差的人,并避开这些服务人员。因此,例如,如果一条客户端鱼观察到清洁鱼和另一条客户端之前的交互以冲突告终,清洁鱼就会被避开(Bshary和Noë, 2003)。(ii)如果服务差,接受者可能提供较少的交换,或更早地中断他们的互动。例如,客户有可能终止与以粘液为食的清洁鱼的互动。如果花蜜很少,昆虫会倾向于提前离开花朵。(iii)如果接受者以前经历过糟糕的服务,将来可能会避开服务提供者


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术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


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。


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