琦文分享（八）学习演化博弈模型的构建

　　01  前情提要
　　上一周的琦文分享，我们学习了引言怎么写，通过引言的撰写，我们要使读者愿意随着我们的文字一步一步读下去，从研究背景到研究的具体问题。引言具体的包含以下截个内容：1）研究问题的背景；2）已有学者对该问题做出的研究；3）指出研究GAP；4）指出该研究具体要解决什么问题；5）指出解决该问题的重要性与现实意义；6）对接下来文章内容规划的概述。
　　接下来，我们将学习演化博弈的模型构建与参数假设。
　　In the Qiwen sharing last week, we learned how to write the introduction. By writing the introduction, we want to make readers willing to read it step by step along with our text, from the research background to the specific problems of the research. The introduction specifically contains the following cut-off content: 1) the background of the research problem; 2) the research on the problem by existing scholars; 3) point out the research GAP; 4) point out the specific problem to be solved by the research; 5) point out the solution The importance and practical significance of this question; 6) An overview of the content planning of the next article.
　　Next, we will learn the model construction and parameter assumptions of evolutionary games.
　　02  模型构建
　　核心企业在供应链中占据主导地位 [14-15]，对促进供应链的绿色化发挥着重要作用。为此， 模型假定涉及消费者和供应链核心企业两类群体，每次都是从两类群体中随机配对进行博弈，双方都是有限理性的并在长期交互影响中不断调整自身策略直至达到演化均衡。 供应链核心企业及消费者在博弈的过程中各有两种行为可选 ：实施绿色供应链和不实施绿色供应链、绿色消费和非绿色消费。具体假设如下 ：
　　Core enterprises occupy a dominant position in the supply chain [14-15] and play an important role in promoting the greening of the supply chain. For this reason, the model assumes that two groups of consumers and core companies in the supply chain are involved. Each time, the two groups are randomly paired to play games. Both parties are boundedly rational and constantly adjust their strategies in the long-term interactive influence until they reach evolution. balanced. During the game, the core enterprises and consumers of the supply chain have two options: implementing a green supply chain and not implementing a green supply chain, green consumption and non-green consumption. The specific assumptions are as follows:
　　然后，得到不同策略选择下的支付矩阵：
　　Then, get the payment matrix under different strategy choices:
　　演化博弈的模型应注意的几点问题：
　　1.在演化博弈模型参数设置之前，先去了解我们撰写的该论文的研究背景。理顺参与主体之间的各种关系。让参数的设置应该贴合现实背景，否则后续模型的分析将会脱离现实意义。
　　2.同时参数的设置也不能过于复杂，会让后续的分析十分困难。
　　Several issues that should be paid attention to in the evolutionary game model:
　　1. Before setting the parameters of the evolutionary game model, first understand the research background of the paper we wrote. Straighten out the various relationships between participating subjects. The setting of parameters should be in line with the real background, otherwise the subsequent model analysis will be out of practical significance.
　　2. At the same time, the parameter setting should not be too complicated, which will make subsequent analysis very difficult.
　　03  模型的分析
　　关于复制动态方程的推导，我们可以用到两种方法:
　　1.基于Malthusianism人口增长模型的推导
　　2.依据收益偏差导致策略转移的推导
　　Regarding the derivation of copying dynamic equations, we can use two methods:
　　1. Derivation based on the Malthusianism population growth model
　　2. Derivation of strategy shift based on income deviation
　　首先计算决策一方（消费者）的平均期望收益：
　　然后计算决策另一方（核心企业）的平均期望收益：
　　Then calculate the average expected return of the other party in the decision (the core company):
　　然后得到系统的复制动态方程组：
　　Then get the system＂s copy dynamic equations:
　　再根据复制动态方程组，得到该系统的雅可比矩阵：雅可比矩阵是一阶偏导数以一定方式排列成的矩阵，其行列式称为雅可比行列式。雅可比矩阵的重要性在于它体现了一个可微方程与给出点的最优线性逼近。
　　Then according to the copy of the dynamic equations, the Jacobian matrix of the system is obtained: the Jacobian matrix is a matrix in which the first-order partial derivatives are arranged in a certain way, and its determinant is called the Jacobian determinant. The importance of the Jacobian matrix is that it embodies the optimal linear approximation between a differentiable equation and a given point.
　　根据detJ>0和trJ<0的判定系统演化点的条件，得到各均衡点的情况，如下图所示：
　　According to the conditions for judging the evolution point of the system according to detJ>0 and trJ<0, the situation of each equilibrium point is obtained, as shown in the following figure:
　　随后，对各均衡点进行分析，先解释其参数代表的表面意义的解释，然后再结合现实背景阐述该稳定点的意义。下面以演化（0，0）点为例。
　　Afterwards, analyze each equilibrium point, first explain the interpretation of the superficial meaning represented by its parameters, and then explain the meaning of the stable point in combination with the realistic background. Let＂s take the evolution point (0, 0) as an example.
　　由此可见，在演化博弈的模型构建中，我们要使我们的模型有意义，一是让模型能顺利的计算下去，得到的可以分析的复制动态方程，二是不仅能顺利计算下去，还能保证让后续我们的分析与现实结合，并提出响应的建议。
　　It can be seen that in the construction of the evolutionary game model, we need to make our model meaningful. First, the model can be calculated smoothly, and the replicated dynamic equation that can be analyzed is obtained. Second, not only can it be calculated smoothly, but also Make sure to combine our subsequent analysis with reality and put forward suggestions in response.
　　参考资料：谷歌翻译
　　参考文献：《政府调控下绿色消费与绿色供应链实施的演化博弈分析》
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