Differential Game Model for a Dual-Channel Supply Chain’s Optimal Strategy under the Reference Carbon Emission Effect

Taking into account the impact of time factors on emission reductions and brand reputation, the reference carbon emission effect and dual-channel supply chain are incorporated into a unified analysis framework. We applied differential game theory to build models under centralized decision-making and decentralized decision-making. The aim of the research is to explore the strategies of a single manufacturer and a single retailer on product pricing, low-carbon production, and advertising. The research analyses the impact of reference carbon emission effects, cost coefficients, and interchannel substitutable coefficients on profits. In order to alleviate the double marginal effect brought about by decentralized decision-making, a cost-compensation coordination mechanism is proposed. The conclusions are as follows. First, centralized decision-making is the optimal decision-making mode, but further consultation is required to implement it voluntarily by both parties. Second, a cost-recovery contract occurs when the fixed fee that the retailer gives the manufacturer meets certain conditions. The contract can make the retailer’s advertising investment reach the level of centralized decision-making and improve the member’s profit under the decentralized decision-making. The coordination mechanism is effective. Third, the reference carbon emission effect can bring about an increase in the manufacturer’s low-carbon production input and profits. The retailer’s advertising investment is not affected by the reference carbon emission effect. Fourth, wholesale prices and online or offline retail prices are all positively correlated with the market share of the channel. The price-substitution coefficient between channels is positively correlated with both low-carbon inputs and profits.