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“小宇分享（七）：
精读《上下游联合减排与低碳宣传的微分博弈模型》成本分担下的分散式决策模型与均衡结果”
Share interest, spread happiness,
Increase knowledge, leave a beautiful!
Dear, this is LearningYard Academy.
Today, the editor brings you an article.
Xiaoyu's Sharing (Ⅶ):
A Closer Look at "A Differential Game Model for
Upstream and Downstream Joint Emission Reduction and Low-Carbon Promotion":
Decentralized Decision-Making Model and Equilibrium Outcomes Under Cost Sharing"
一、思维导图（Mind mapping）
二、精读内容（Intensive reading content）
成本分担契约下的分散式决策意义
The significance of decentralized decision-making under cost-sharing contracts
进一步分析成本分担契约对均衡解及供应链绩效的影响，研究成本分担契约能否使供应链达到协调或者能多大程度上改善供应链绩效． 在有成本分担契约的分散式决策时，假设制造商在联合减排与低碳宣传问题中处主导地位，为激励零售商进行低碳宣传，制造商给零售商提供一定比例的补贴． 从长期、动态的角度考虑，制造商与零售商之间关于减排努力与低碳宣传努力的决策构成了上下游之间的 Stackelberg 微分对策模型( 用上标 Y 表示有成本分担契约的情况)
We further analyze the impact of cost-sharing contracts on equilibrium solutions and supply chain performance, examining whether they can achieve supply chain coordination and to what extent they can improve supply chain performance. In decentralized decision-making with cost-sharing contracts, we assume that manufacturers play a dominant role in joint emission reduction and low-carbon promotion. To incentivize retailers to engage in low-carbon promotion, manufacturers provide retailers with a certain percentage of subsidies. From a long-term, dynamic perspective, the decisions between manufacturers and retailers regarding emission reduction efforts and low-carbon promotion constitute a Stackelberg differential game model between upstream and downstream players (superscript Y denotes the presence of cost-sharing contracts).
成本分担契约下的分散式决策问题
Decentralized decision-making problem under cost-sharing contracts
制造商和零售商独自决策以最大化各自的利润，第 1 阶段，制造商决定自身的减排努力程度EYM(t)和为零售商承担的低碳宣传成本比例X(t);第2 阶段，根据给定EYM(t)，X( t)，零售商决策自身的低碳宣传努力程度 EYＲ( t)．由假设 6) 可知，在无限时间区间内制造商和零售商的利润具有相同的贴现因ρ，于是可以得到制造商决策问题和零售商的决策问题,如下图所示：
The manufacturer and retailer make independent decisions to maximize their respective profits. In the first stage, the manufacturer determines its own emission reduction efforts, EYM(t), and the proportion of low-carbon promotion costs it will bear for the retailer, X(t). In the second stage, given EYM(t) and X(t), the retailer determines its own low-carbon promotion efforts, EYR(t). Assumption 6 shows that, over an infinite time interval, the manufacturer and retailer's profits have the same discount factor, ρ. This allows us to formulate the manufacturer's and retailer's decision problems, as shown in the following figure:
成本分担契约下的分散式决策的均衡结果
Equilibrium outcomes of decentralized decision-making under cost-sharing contracts
为了得到成分担契约决策下供应链各成员的反馈均衡策略，与无成本分担决策时的情况相同，采用HJB方程进行求解．求解结果如下：
To obtain the feedback equilibrium strategy of each supply chain member under the cost-sharing contract decision, the HJB equation is used to solve the problem, similar to the situation when there is no cost-sharing decision. The solution is as follows:
制造商单位产品减排量的最优轨迹计算结果如下图所示：
The calculation results of the optimal trajectory of emissions reduction per unit product of manufacturers are shown in the figure below:
制造商和零售商的微分博弈均衡策略计算结果如下图所示：
The calculation results of the differential game equilibrium strategies of manufacturers and retailers are shown in the figure below:
制造商和零售商各自的利润最优值函数分别计算结果如下图所示：
The calculation results of the optimal profit value functions of manufacturers and retailers are shown in the following figure:
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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
