This article investigates game-theoretic approaches in a competitive supply chain model with imperfect production and a two-tier credit facility under the environment of carbon emissions. In this environment, we incorporate a manufacturer and two rival retailers who compete against one another for selling price and advertisement of a product, where the members offer trade credit facilities to the downstream players. We consider that the manufacturer invests in green technology to curtail the emission during the production and rework process. The retailers provide advertisements to expand their businesses, where market demands are dependent on their selling prices, advertisement frequencies, and the green innovation level. Here, we analyze the model under the cap-and-trade policy for various subcases of the centralized and decentralized systems and discuss a solution algorithm for the optimal results. For the practical feasibility test of the model, numerical analysis is examined, and the impact of variations of the critical parameters is studied. The study's primary motive is to figure out the optimal operative strategies and collaborative actions on the decision variables, which leads to the profits of the supply chain to a lofty extent. We observe that the offered credit periods are highly responsive to the profit functions so that the chain members have to be more careful and draw a compact plan for credit policy. Moreover, the manufacturer has to invest in green technology up to a certain level, as, after that level, high investment costs will hamper the optimal profit. Besides, the retailers must have adequate policies for selling prices and advertisement frequencies to acquire a higher yield.

中文翻译：

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两级授信条件下绿色创新和广告在不完善的生产型竞争供应链中的作用

本文研究了在碳排放环境下具有不完善生产和两级信贷机制的竞争供应链模型中的博弈论方法。在这种环境下，我们合并了一家制造商和两家竞争对手零售商，他们在产品的销售价格和广告方面相互竞争，其中成员向下游参与者提供贸易信贷便利。我们认为制造商投资绿色技术以减少生产和返工过程中的排放。零售商提供广告以扩大其业务，其市场需求取决于其销售价格、广告频率和绿色创新水平。这里，我们针对中心化和去中心化系统的各种子案例分析了限额与交易政策下的模型，并讨论了最优结果的求解算法。对于模型的实际可行性测试，进行了数值分析，并研究了关键参数变化的影响。该研究的主要动机是在决策变量上找出最优的操作策略和协作行动，从而在较高程度上导致供应链的利润。我们观察到，所提供的信用期对利润函数具有高度响应性，因此链成员必须更加谨慎并制定紧凑的信用政策计划。此外，制造商必须在一定程度上投资绿色技术，因为在该水平之后，高投资成本将阻碍最佳利润。此外，零售商必须有足够的销售价格和广告频率政策，以获得更高的收益。