This paper discusses how managers adjust their strategies to allocate relevant resources more effectively and maximize economic benefits when major technological changes are predicted for the future. For a supply chain system consisting of a single manufacturer and two competing retailers as the research object. First, random stop model is applied to portray the impact of technological innovation on the decision-making of supply chain members. On this basis, differential game models for supply chain members are constructed based on different cooperation modes, including centralized, decentralized, and retailers alliance. Second, we solve and compare the optimal decision-making, emissions reduction, low-carbon goodwill, and profit levels before and after technological innovation in different modes. Finally, we design a bilateral cost-sharing contract to achieve coordination. Results demonstrate that: (1) Before the success of technological innovation, when a higher probability of success and uplift rate is predicted can incentivize supply chain members' emissions reduction and low-carbon promotion inputs; (2) In the presuccess period of technological innovation, members' independent decision-making (decentralized decision-making) can optimize the retailer's low-carbon promotional inputs under certain conditions. In contrast, the optimality of decentralized decision-making after technological innovation depends only on the influence of competition intensity. (3) The bilateral cost-sharing contract designed in this paper can optimize supply chain-related inputs and performance levels to achieve perfect coordination within the supply chain system, given that specific preconditions are satisfied.