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“小宇分享（十一）：

精读《上下游联合减排与低碳宣传的微分博弈模型》算例分析

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Xiaoyu's Sharing (11):

In-depth reading of the case analysis of "Differential Game Model of Upstream and Downstream Joint Emission Reduction and Low-Carbon Promotion"

一、思维导图（Mind mapping）

二、精读内容（Intensive reading content）

引入参数

Introducing parameters

制造商和零售商在3 种联合减排与低碳宣传的微分博弈中，各自的最优决策和利润以及供应链系统的利润依赖于模型中参数的选择．算例相关参数如下: γ = 2、δ = 1、α = 5、β = 2、θ = 3、πM = 6、πＲ = 5、ρ = 0． 9、ηM= 15、ηＲ= 12、τ0 = 0．

In three differential games involving joint emission reduction and low-carbon promotion, the optimal decisions and profits of manufacturers and retailers, as well as the profits of the supply chain system, depend on the parameters selected in the model. The relevant parameters for this example are as follows: γ = 2, δ = 1, α = 5, β = 2, θ = 3, πM = 6, πR = 5, ρ = 0.9, ηM = 15, ηR = 12, and τ0 = 0.

将相关参数代入命题 1、命题 2、命题 3 及推论1 所给的解析式，利用 matlab 可以给出成本分担前后制造商和零售商利润对比关系图( 图 2) 、3种情况供应链系统利润对比关系图( 图 3) 、参数β 对成本分担契约 Pareto 改善效果的影响( 图4) 、参数 ηＲ对成本分担契约 Pareto 改善效果的影响(图5)

Substituting the relevant parameters into the analytical expressions given in Propositions 1, 2, and 3, and Corollary 1, Matlab can produce a graph comparing the profits of manufacturers and retailers before and after cost sharing (Figure 2), a graph comparing the profits of the supply chain system under the three scenarios (Figure 3), the effect of parameter β on the Pareto improvement of the cost-sharing contract (Figure 4), and the effect of parameter ηR on the Pareto improvement of the cost-sharing contract (Figure 5).

MATLAB绘图分析

MATLAB Plot Analysis

成本分担契约的改善

Improvements to cost-sharing contracts

从图2 可以看出，利用成本分担契约可以达到制造商和零售商利润的 Pareto 改善，且对零售商利润的改善效果优于对制造商利润的改善效果．由于制造商分担了零售商的低碳宣传成本，零售商会付出更大的努力进行低碳宣传，从而带来更多的市场需求，市场需求的增加最终将增加制造商和零售商的利润，因此使双方的利润都能达到 Pareto 改善; 同时由于零售商成本的降低和需求的增加两者都会增加零售商的利润，而制造商只有需求的增加会带来利润的增加，分担的零售商的低碳宣传成本反而使成本上升，因此，成本分担契约对零售商利润的改善效果要优于对制造商利润的改善效果，图中在成本分担前后制造商和零售商利润变化的垂直距离也可以反映这一点.

Figure 2 shows that cost-sharing contracts can achieve a Pareto improvement in the profits of both manufacturers and retailers, with the improvement in retailer profits being greater than that of manufacturers. Because manufacturers share the retailer's low-carbon promotion costs, retailers will invest more in low-carbon promotion, generating more market demand. This increased market demand ultimately increases the profits of both manufacturers and retailers, thus achieving a Pareto improvement in profits for both parties. Furthermore, since both reduced retailer costs and increased demand increase retailer profits, while for manufacturers, only increased demand leads to increased profits; sharing the retailer's low-carbon promotion costs actually increases costs, the cost-sharing contract improves retailer profits more than it does manufacturer profits. This is also reflected in the vertical distance between the changes in manufacturer and retailer profits before and after cost-sharing.

协同控制的集中式决策的改善

Improved centralized decision-making for collaborative control

从图 3 可以看出，3 种情况下供应链系统最优利润情况是: 协同控制的集中式决策时最大、无成本分担的分散式决策时最小，有成本分担契约时可以达到供应链系统利润的 Pareto 改善．制造商和零售商协同控制的集中式决策时供应链系统的总利润远大于两种非协同控制的分散式决策时系统的总利润，验证了理论推导的结果．且协同控制的集中式决策情形下供应链系统的总利润增长迅速，而两种非协同控制的分散式决策情形下供应链系统的总利润增加缓慢，这充分说明协同控制的集中式决策优于非协同控制的分散式决策，可以为上下游联合减排与低碳宣传提供参考，剩余利润根据双方的讨价还价能力进行分配．

Figure 3 shows that the optimal profit of the supply chain system under the three scenarios is: maximum under coordinated centralized decision-making, minimum under decentralized decision-making without cost sharing, and a Pareto improvement in the supply chain system's profit can be achieved with a cost-sharing contract. The total profit of the supply chain system under coordinated centralized decision-making by manufacturers and retailers is significantly greater than that under the two decentralized decision-making scenarios without coordinated control, validating the theoretical results. Furthermore, the total profit of the supply chain system under coordinated centralized decision-making grows rapidly, while the total profit of the supply chain system under the two decentralized decision-making scenarios without coordinated control increases slowly. This clearly demonstrates that coordinated centralized decision-making is superior to decentralized decision-making without coordinated control, providing a reference for joint emission reduction and low-carbon promotion between upstream and downstream parties. The remaining profit is distributed based on the bargaining power of both parties.

成本分担契约的敏感性

Sensitivity of cost-sharing contracts

从图4 可以看出，随着消费者对零售商低碳宣传敏感性的增加，成本分担契约对制造商和零售商利润的 Pareto 改善效果越明显．消费者对零售商低碳宣传的敏感性越大，零售商单位低碳宣传努力的增加越能带来更多的市场需求，制造商通过成本分担契约激励零售商进行低碳宣传的效果就越明显． 这可以为制造商的决策提供参考依据，制造商可以通过调查零售商的影响力决定是否为零售商提高补贴以及补贴的额度．

Figure 4 shows that as consumers' sensitivity to retailers' low-carbon promotion increases, the Pareto improvement effect of cost-sharing contracts on manufacturers' and retailers' profits becomes more pronounced. The greater consumers' sensitivity to retailers' low-carbon promotion, the more market demand each retailer's unit of low-carbon promotional effort generates, and the more effective manufacturers' cost-sharing contracts are in incentivizing retailers to promote low-carbon products. This can provide a reference for manufacturers' decision-making, allowing them to determine whether to increase subsidies for retailers and the amount of subsidies they provide by investigating their influence.

成本分担契约的改善效果

Improvement Effects of Cost-Sharing Contracts

从图5 可以看出，成本分担契约对制造商和零售商利润的 Pareto 改善效果随零售商低碳宣传努力成本系数的降低而提高．零售商低碳宣传努力成本系数越大，零售商进行低碳宣传需要付出的成本越多，制造商对零售商的激励的效果越不明显，因此制造商进行决策时也要综合考虑零售商的低碳宣传成本问题，对于零售商进行低碳宣传越容易的情况给予较高的补贴，对于零售商进行低碳宣传越难的情况给予较少的补贴或者不给补贴．

Figure 5 shows that the Pareto improvement effect of the cost-sharing contract on manufacturer and retailer profits increases as the retailer's low-carbon promotion effort cost coefficient decreases. The larger the retailer's low-carbon promotion effort cost coefficient, the more it costs the retailer to conduct low-carbon promotion, and the less effective the manufacturer's incentives are. Therefore, manufacturers should also consider the retailer's low-carbon promotion costs when making decisions. They should provide higher subsidies when retailers find it easier to conduct low-carbon promotion, and lower or no subsidies when retailers find it more difficult.

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翻译：谷歌翻译

资料来源：ChatGPT、百度百科

参考文献：[1]徐春秋,赵道致,原白云,等.上下游联合减排与低碳宣传的微分博弈模型[J].管理科学学报,2016,19(02):53-65.

本文由LearningYard学苑整理并发出，如有侵权请后台留言沟通。

文案：qiao

排版：qiao

审核：李杰

来源：LearningYard学苑