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(5):表示成员收入,Shapley所给出的局中人i的收入称作 Shapley值;











[2]张伸, 孟庆春, 安国政. 电商平台扣点率影响下的双渠道供应链协调定价研究[J]. 中国管理科学, 2019, 27(10): 44-55.

[3]马士华,王鹏. 基于Shapley值法的供应链合作伙伴间收益分配机制[J]. 工业工程与管理,2006,(04):43-45+49.

[4]刘浪,唐海军,陈仲君. Shapley值在动态联盟利益分配博弈分析中的应用[J]. 工业工程,2006,(06):118-121



Hello, everyone. This is leanringyard college. Today is the second day of the new year. Xiaobian is here to wish you all the best in the new year.

In this festive moment, Xiaobian will not forget to bring you new knowledge, so today we continue to bring you a series of articles on Mathematica introductory tutorial. Todays theme is Shapley value method.

1. Executive summary

In the last issue, I combed the theories, unfamiliar terms and concepts used in the study on coordinated pricing of dual channel supply chain under the influence of discount rate of e-commerce platform (authors: Zhang Shen, Meng Qingchun, an Guozheng), as well as the ideas and methods of constructing the model in the paper. At the end, I mentioned the coordination scheme, which is based on Shapley value, And Xiaobian also knew this method for the first time, so he made a simple study a few days ago. In this issue, well take a look at what Shapley value is and how it is used in the article.

2. Shapley value method

Originally, I wanted to Baidu, but what Baidu said was a little unclear, so I went to HowNet to find relevant papers to study. This article describes the definition of Shapley value method in detail, and shows how to use it in supply chain coordination through a simple and specific numerical example.

Purpose: Based on my own understanding, there are multiple participants engaged in an economic activity. Under the optimal combination strategy, this activity will produce a maximum total benefit. They will adopt the optimal distribution scheme to maximize their benefits. This distribution scheme is the Shapley value method.

Definition: the above figure illustrates the definition of Shapley value method. First, the following conditions must be met: when there are no members, the income is zero; Overall rationality and individual rationality. Then, list the possible Federation sets. Finally, the income distributed by each member is calculated according to the formula.

I didnt explain too much about the parameters, so I referred to another article and explained each formula:

(1) : indicates that when there is no enterprise, the whole activity income is 0;

(2) : indicates super additivity, similar to 1 + 1 > = 2, indicating that the total income of enterprises in alliance is greater than or equal to the sum of their respective income when enterprises are not in alliance;

(3) : indicates the overall rationality. The sum of the income allocated by each member from the total income of the alliance is equal to the total income of the alliance;

(4) : indicates individual rationality. The income allocated by an individual from the alliance cannot be lower than the income completed alone.

(5) : represents the income of members. The income of player I given by Shapley is called Shapley value;

(6) : final weight calculation formula.

This is the whole Shapley value method model. The proof process will not be explained in the small series.

3. Practical application

After knowing the basic principle of Shapley value method, lets take a look at its specific application in this paper.

The supply chain in this paper only includes two decision makers, manufacturer and retailer. First, determine the income allocated by the manufacturer, and the alliance set I = {manufacturer, (manufacturer, retailer)}. First, determine the specific values of each parameter according to the income calculation formula, as shown in the table, and then calculate the results. The last row in the table in the figure below represents the income that the manufacturer can allocate under each alliance.

Adding the income distributed under the two alliances represents the manufacturers profit after coordination. Similarly, the profit of retailers can be calculated.

After determining the profit expression after coordination, make it equal to the profit expression during decentralized decision-making, and use the software to calculate the corresponding wholesale price.


This issue of sharing is over. We have learned all the theoretical knowledge, modeling ideas and methods of the article. In the next issue, we will start to use Mathematica for practical exercises. Lets look forward to it.

Those who are interested in Shapley value method can search for more materials and learn by themselves. You are also welcome to leave messages and communicate with Xiaobian!

Finally, I wish you a happy new year and new harvest in the New Year!