Abstract: Against the backdrop of economic digital transformation, live-streaming e-commerce has become a dominant channel for online shopping. As an emerging e-commerce format, its operational management has increasingly attracted attention from both academia and industry; however, existing studies mainly focus on static analyses, with limited research on the dynamic operation of live-streaming e-commerce. This paper investigates a live-streaming e-commerce supply chain composed of a platform, a streamer, and a manufacturer. By incorporating factors such as the average number of online viewers, reference price, conversion rate, product quality goodwill and streamer influence, a demand function for live-streaming e-commerce is constructed. Under four decision-making scenarios involving consumer returns and platform cost-sharing, a differential game model is employed to characterize the dynamic operational process of the live-streaming e-commerce supply chain, and the dynamic equilibrium strategies and performance levels across different scenarios are comparatively analyzed. The results indicate that: (1) both the reference price effect and the average number of online viewers positively affect the profits and effort levels of supply chain members; (2) consumer returns cause significant profit losses for supply chain members, and reducing related effort inputs may lead to long-term losses that outweigh short-term cost savings; (3) when the platform’s unit revenue is relatively high, sharing the manufacturer’s quality control costs can achieve a Pareto improvement for the entire live-streaming e-commerce supply chain; and (4) under centralized decision-making, all decision variables attain their maximum levels, whereas only when the cost-sharing ratio is sufficiently high do the manufacturer’s quality control effort and product reputation under the cost-sharing mode exceed those under the centralized decision-making mode.