# 经济代写|博弈论代写Game Theory代考|Games with Overlapping Generations of Players

#### Doug I. Jones

Lorem ipsum dolor sit amet, cons the all tetur adiscing elit

couryes™为您提供可以保分的包课服务

couryes-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。

## 经济代写|博弈论代写Game Theory代考|Games with Overlapping Generations of Players

Crémer (1986) considcred a repeated game in which overlapping generations of players live for $T$ periods, so that at each date $t$ there is one player of age $T$ who is playing his last round, one player of age $T-1$ who has two rounds still to play, and so on down to the new player who will play $T$ times. Each period, the $T$ players simultaneously choose whether to work or to shirk, and their choices are revealed at the end of each period; players share equally in the resulting output, which is an increasing function of the number who chose to work. ${ }^{13}$ The cost of effort exceeds a $1 / T$ share of the increases in output, so shirking is a dominant strategy in the stage game, which has the flavor of a $T$-player prisoner’s dilemma. Payoffs in the repeated game are the average of the per-period utilities.
Suppose that the efficient outcome is for all players to work. This outcome cannot occur in any Nash equilibrium, since the age- $T$ player will always shirk. Nevertheless, there can be equilibria where most of the players work. This will be easicst to sec if we further specialize the model. Let $T=10$. Suppose that if $k$ players work the aggregate output is $2 k$, and that the disutility of effort is 1 . Then if preferences are linear in output and effort, the payoff to working when $k$ opponents work is $2(k+1) / 10-1$, and the payoff to shirking is $2 k / 10$. The efficient outcome is for all players to work, with resulting utility of 1 per player.

Now consider the following strategy profile: “Age-10 players always shirk. So long as no player has ever shirked when his age is less than 10, all players of age less than 10 work. If a player has ever shirked when his age is less than 10 , then all players shirk.” If all players conform to this profilc, each player reccives $18 / 10-1=4 / 5$ in the periods he works and $9 / 5$ in the period he is of age 10. Clearly, no player can gain by deviating when he is of age 10 . If a player of age 9 deviates, he receives $8 / 5$ the period he deviates, and 0 the next period, which is less than $4 / 5+9 / 5$; younger players lose even more by deviating. Thus, these strategies are a subgameperfect equilibrium.

Kandori (1989b) and Smith (1989) have generalized this type of construction and provided conditions for the folk theorem to obtain.

## 经济代写|博弈论代写Game Theory代考|Randomly Matched Opponents

Another variant of the repeated-games model supposes that there are $a$ many players, each of whom plays infinitely often but against a different opponent each period. More precisely, fix a two-player stage game, and suppose that there are two populations of players of equal size, $N$. Each period, every player 1 is matched with a player 2 . The probability of being matched to a particular player 2 is $1 / N$, and matching in each stage is independent. $^{14}$

In the first analyses of this sort of random-matching model, Rosenthal (1979) and Rosenthal and Landau (1979) assumed that when the players in each pair are matched, their information consists of the actions that the two of them played in the previous period. Thus, if the stage game is the prisoner’s dilemma, where C is “cooperate” and D is “defect,” there are four possible “histories” a pair of players can have, namely $(C, C),(D, C),(C, D)$, and (D, D), and consequently each player has $2^4=16$ pure strategies. (Note that players do not have perfect recall!)

With this information structure, the strategy “cooperate if and only if my opponent cooperated last period,” or “tit for tat,” is feasible. More generally, the action a player chooses in period $t$ can have a direct effect on his opponent’s play in period $t+1$.

If the player expects to face the same opponent in period $t+1$ and in period $t+2$, he may anticipate an additional indirect effect of his period- $t$ action on his opponent’s play in periods after $t+1$. For example, if the opponent’s strategy is to cooperate only if the history is (C,C), defecting in period $t$ will not only make the opponent defect in period $t+1$; it will also make the opponent defect in every period thereafter.

# 博弈论代考

## 经济代写|博弈论代写Game Theory代考|Games with Overlapping Generations of Players

crsammer(1986)考虑了一种重复游戏，在这种游戏中，重叠的几代玩家生活$T$周期，所以在每个日期$T$有一个年龄$T$的玩家玩最后一轮，一个年龄$T$的玩家还有两轮，以此类推，新玩家将玩$T$次。每一时段，$T$参与者同时选择是工作还是逃避，他们的选择在每一时段结束时揭晓;玩家平均分享产出，这是选择工作的人数的递增函数。${}^{13}$努力成本超过产出增加的1美元/ T美元份额，因此逃避是阶段博弈中的主导策略，这有点像$T$参与人的囚徒困境。重复博弈的收益是每时期效用的平均值。

Kandori (1989b)和Smith(1989)对这种构造进行了推广，并为民间定理的获得提供了条件。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

Days
Hours
Minutes
Seconds

# 15% OFF

## On All Tickets

Don’t hesitate and buy tickets today – All tickets are at a special price until 15.08.2021. Hope to see you there :)