Hi，大家好，我是编程小6，很荣幸遇见你，我把这些年在开发过程中遇到的问题或想法写出来，今天说一说知识打卡（8）：Mathematica学习5,希望能够帮助你!!!。

分享知识、传播快乐、增长见闻、留下美好，大家好，这里是Leanringyard学院。今天小编将继续为大家带来Mathematica入门教程系列文章，今天的主题就是：Mathematica学习5。

Share knowledge, spread happiness, increase knowledge and leave beauty. Hello, everyone, this is leanringyard college. In today's and later articles, Xiaobian will continue to bring you a series of Mathematica introductory tutorials. Today's topic is: getting started with Mathematica tutorial 5.

01.内容概述

Content overview

在前面我们已经学习了有关Mathematica的基础运算，矩阵命令，基本括号的使用规则以及对变量赋值，自定义函数。基于以上单个知识点，我们可以将其进行综合运用，完成一套完整的计算代码。今天了，我们将以一篇具体的论文，来对前面的知识进行运用，同时也帮助大家了解演化博弈。

本文将以学者郑克俊和张利深的文章《逆向物流中的企业和政府博弈及对策研究》为例。

Previously, we have learned about the basic operations of Mathematica, matrix commands, the use rules of basic parentheses, variable assignment and user-defined functions. Based on the above single knowledge point, we can use it comprehensively to complete a complete set of calculation code. Today, we will use a specific paper to apply the previous knowledge and help you understand evolutionary game.

This paper will take the article "Research on the game and Countermeasures between enterprises and government in reverse logistics" by scholars Zheng Kejun and Zhang Lishen as an example.

02.问题描述

Problem description

此文以政府和企业角度出发，对政府是否对电子企业是否构建逆向物流系统进行监督管制和电子企业是否构建逆向物流系统构建演化博弈博弈模型，探讨政府与电子企业各自应该采取的策略，政府与电子企业演化博弈的收益矩阵如下表所示。

From the perspective of government and enterprises, this paper discusses whether the government supervises and regulates whether electronic enterprises build reverse logistics system and whether electronic enterprises build reverse logistics system, constructs evolutionary game model, and discusses the strategies that the government and electronic enterprises should adopt. The income matrix of evolutionary game between government and electronic enterprises is shown in the table below.

03.模型构建

Model Building

1.政府监管与不监管两种决策行为的期望收益以及平均收益：

Expected return and average return of government supervision and non supervision decision-making:

2、求政府的策略复制动态方程，（复制动态方程：一种策略的适应度或支付比种群的平均适应度高, 这种策略就会在种群中发展, 体现在种群中使用某个策略的个体在种群中所占比例的增长率大于零）：

Find the government's strategy replication dynamic equation (replication dynamic equation: if the fitness or payment of a strategy is higher than the average fitness of the population, this strategy will develop in the population, which is reflected in that the growth rate of the proportion of individuals using a strategy in the population is greater than zero):

3.同理，我们可以计算出电子企业的各策略下的期望收益，平均收益以及复制动态方程：

Similarly, we can calculate the expected return, average return and replication dynamic equation under each strategy of the electronic enterprise:

4.基于以上模型构建，我们最终得到动态复制方程式：

Based on the above model, we finally get the dynamic replication equation:

04.演化博弈分析

Evolutionary game analysis

1.使用Solve函数，对电子企业和政府的复制动态方程求解a,k的值，可以得到五个均衡点：

Using the solve function to solve the value of a and K for the replication dynamic equation of electronic enterprises and government, five equilibrium points can be obtained:

五个均衡点（k,a）：(0,0)，(0,1)，(1,1)，(1,0),（k0,a0)。

Five equilibrium points (k, a): (0,0), (0,1), (1,1), (1,0), (K0, A0).

2.演化稳定性分析，输入雅可比矩阵,并将矩阵元素化简：

For evolutionary stability analysis, input Jacobian matrix and simplify matrix elements:

3.将五个稳定点代入矩阵，求取不同取值下的行列式值以及矩阵的迹。下面小编以(1,0)和（0,1）为例，说明计算过程。首先要将矩阵定义为关于k,a的函数：

Five stable points are substituted into the matrix to obtain the determinant value under different values and the trace of the matrix. The following compendium takes (1,0) and (0,1) as examples to illustrate the calculation process. First, the matrix should be defined as a function of K and a:

然后分别计算a,k取不同值的行列式式值以及迹：

Then calculate the determinant value and trace of different values of a and K respectively:

最终，基于上面计算的结果，我们就可以进一步对稳定性进行分析。感兴趣的同学可以去知网下载原文阅读，这里重点分析Mathematica的计算过程。

Finally, based on the above calculation results, we can further analyze the stability. Interested students can go to HowNet to download the original text for reading. Here we focus on the analysis of Mathematica's calculation process.

今天的分享就到这里了，如果您对今天的文章有独特的想法，欢迎给我们留言，让我们相约明天，祝您今天过得开心快乐！

That's it for today's sharing.If you have unique ideas about today’s article, please leave us a message,Let us meet tomorrow,I wish you a happy day today!

参考资料：

[1]谷歌翻译、百度百科.

[2]付小勇,朱庆华,窦一杰. 中国版WEEE法规实施中政府和电子企业演化博弈分析[J]. 管理评论,2011,23(10):171-176.

[3]田琦.Mathematica入门学习.

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