We establish dynamic game models in a low-carbon supply chain consisting of a single manufacturer and a single retailer with social preference. This study investigates the complex dynamic characteristics of pricing decision and carbon abatement strategy in the supply chain and focuses on the impact of the retailer's social preference on pricing decision, carbon emission abatement strategy, profits, supply chain coordination, and complexity of dynamic models. We find that adjustment parameters of pricing and carbon emission abatement should be maintained in a certain range; otherwise, the system will be unstable and even chaotic through period double bifurcation or wave shape chaos. A higher social preference of the retailer is always beneficial to carbon abatement and the manufacturer and helps maintain the stability of the supply chain system. However, the impact on the long-term profitability of the supply chain is related to the state of the system. Compared with the setting of a centralized decision, the optimal carbon abatement strategy and supply chain profit in a decentralized decision are always less than those in a centralized setting, regardless of whether the retailer has social preference. Therefore, a side-payment self-executing contract is designed to coordinate the supply chain and achieve Pareto improvement. The coordination mechanism proposed in this study not only leads to Pareto improvement but also increases the stability of the supply chain system. Finally, this study enlightens management in operating a low-carbon supply chain.

我们在由具有社会偏好的单一制造商和单一零售商组成的低碳供应链中建立动态博弈模型。本研究考察了供应链中定价决策和碳减排策略的复杂动态特征，重点关注零售商的社会偏好对定价决策、碳减排策略、利润、供应链协调和动态模型复杂性的影响。我们发现定价和碳减排的调整参数应该保持在一定范围内；否则，系统会因周期双分岔或波形混沌而不稳定甚至混沌。零售商较高的社会偏好总是有利于碳减排和制造商，有助于维持供应链系统的稳定性。但是，对供应链长期盈利能力的影响与系统状态有关。与集中决策的设置相比，无论零售商是否具有社会偏好，分散决策的最优碳减排策略和供应链利润总是小于集中决策。因此，设计了一个侧付自执行合约来协调供应链，实现帕累托改进。本研究提出的协调机制不仅导致帕累托改进，而且增加了供应链系统的稳定性。最后，本研究对运营低碳供应链的管理有所启发。与集中决策的设置相比，无论零售商是否具有社会偏好，分散决策的最优碳减排策略和供应链利润总是小于集中决策。因此，设计了一个侧付自执行合约来协调供应链，实现帕累托改进。本研究提出的协调机制不仅导致帕累托改进，而且增加了供应链系统的稳定性。最后，本研究对运营低碳供应链的管理有所启发。与集中决策的设置相比，无论零售商是否具有社会偏好，分散决策的最优碳减排策略和供应链利润总是小于集中决策。因此，设计了一个侧付自执行合约来协调供应链，实现帕累托改进。本研究提出的协调机制不仅导致帕累托改进，而且增加了供应链系统的稳定性。最后，本研究对运营低碳供应链的管理有所启发。侧付自执行合约旨在协调供应链并实现帕累托改进。本研究提出的协调机制不仅导致帕累托改进，而且增加了供应链系统的稳定性。最后，本研究对运营低碳供应链的管理有所启发。侧付自执行合约旨在协调供应链并实现帕累托改进。本研究提出的协调机制不仅导致帕累托改进，而且增加了供应链系统的稳定性。最后，本研究对运营低碳供应链的管理有所启发。