The closed-loop supply chain for new energy vehicles involves a power battery supplier, a new energy vehicle manufacturer, and an echelon utiliser. The power battery supplier invests in blockchain technology to ensure whole life cycle traceability of the power battery in a dynamic environment. This portrays the dynamic evolution of the traceability level of the power battery. Four differential game models for power battery recycling are constructed based on two channel rights and two recycling channels of power battery suppliers and new energy vehicle manufacturers. The feedback equilibrium solutions of the four models are solved to compare the state variables, decision variables and feedback profits of the system in the steady state situation. The numerical examples further verify the dynamic operational strategy of the closed-loop supply chain for new energy vehicles. The results indicate that the highest levels of traceability for power batteries and blockchain technology in the system are achieved when the power battery supplier leads the supply chain and is responsible for battery recycling. Conversely, the lowest levels are achieved when the new energy vehicle manufacturer acts as the leader and is responsible for battery recycling. Both power battery suppliers and new energy vehicle manufacturers generate higher profits when they lead the supply chain, regardless of who is responsible for recycling. For echelon utiliser, their profits are higher when the power battery supplier is in charge of recycling, rather than the new energy vehicle manufacturer. The findings offer a point of reference for participants in the closed-loop supply chain of new energy vehicles with regards to blockchain technology application, channel rights allocation, and battery recycling strategies.