In the context of carbon trading policy, a supply chain consisting of manufacturers who invest in carbon emission reduction technology and retailers who invest in blockchain technology is used as the research object. A centralized decision model, a decentralized decision model and a vertical cooperation decision model based on technology investment are developed, and a differential game approach is applied to study the problem of technology investment decision and the vertical cooperation strategy of the supply chain, and a two-way cost-sharing contract is designed to coordinate the supply chain. The results show that: Retailers will choose to cooperate with manufacturers only when their marginal profits meet certain conditions, and the existence of carbon trading policies will make the conditions for vertical cooperation more stringent; Vertical cooperation can achieve the double dividend of “emission reduction and efficiency enhancement” in the supply chain; When the price of carbon trading is higher than a certain threshold, consumers' green preferences and green information sensitivity will not be affected; When the price of carbon trading is above a certain threshold, the increase in consumer green preferences and green information sensitivity will reduce the level of technology investment by supply chain members; Under certain conditions, two-way cost-sharing contracts can fully coordinate the supply chain.