## 经济代写|博弈论代写Game Theory代考|ECON6025

2022年10月7日

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## 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).

# 博弈论代考

## 经济代写|博弈论代写博弈论代考|差异选择社会敏感性

Johnstone(2001)考虑了一个模型，在这个模型中，大量人口的成员进行了一系列的竞争回合。在每一轮中，每个人口成员与不同的随机选择的对手配对，两人争夺有价值的资源$V$。在这场比赛中，每个人都可以玩老鹰或鸽子。收益与标准的鹰鸽博弈(第3.5节)相同。假设$V<C$。种群中有三种可能的策略:(i)总是玩老鹰，(ii)总是玩鸽子，(iii)偷听。采用后一种策略的人观察了上一轮比赛的结果。如果他们当前的对手在上一轮获得了资源(游戏邦注:即通过使用Hawk或Dove)，他们便选择了Dove，如果对手未能获得资源，他们便选择了Hawk

## 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。