Abstract: Considering the delay effect of emission reduction and the effect of low-carbon publicity and reference on consumers, a differential game model based on product emission reduction level, low-carbon reputation and reference is constructed for a two-level supply chain composed of manufacturers with single input carbon emission reduction and retailers with single input low-carbon publicity. The optimal effort input strategy of supply chain under decentralized decision and centralized decision is studied, and the influence of delay and reference dual effect related parameters on low-carbon supply chain decision and profit is analyzed. It is found that the optimal effort investment under centralized decision is higher than the corresponding value of decentralized decision, but the overall profit under centralized decision is not always higher than the corresponding value of decentralized decision, the difference of profit depending on the delay time of emission reduction effect and publicity effect. The delay time of emission reduction effect and publicity effect, the memory parameters and sensitive parameters in reference factors, are the main factors for manufacturers and retailers to invest in emission reduction efforts and low-carbon publicity efforts. There are corresponding thresholds for the delay time of emission reduction effect and publicity effect, which affect the strategy selection of product emission reduction, low-carbon reputation and reference, and the profit advantage of supply chain.

Key words: lagged effect, reference effect, emission reduction, low-carbon credit, differential game