Abstract: Focusing on low-carbon collaboration in complex product supply chains under the "dual carbon" goals, this study constructs a Stackelberg game model led by a dominant manufacturer. The model incorporates a transfer payment contract based on the supplier's low-carbon effort level and introduces the Cobb-Douglas function to characterize the nonlinear relationship between collaborative low-carbon efforts and market demand. This framework enables the analysis of how the manufacturer's altruistic preference influences supply chain decisions and facilitates the design of a corresponding coordination contract. The results show: (1) a critical threshold exists for the impact coefficient of low-carbon efforts on demand, beyond which equilibrium values increase; (2) the altruistic preference improves both parties' effort levels, market demand, supplier profit, and total supply chain profit, but reduces the main manufacturer's profit; (3) the proposed bargaining-based coordination strategy optimizes profit allocation, alleviates the main manufacturer's profit loss, and achieves Pareto improvements; (4) the main manufacturer's share of surplus profit depends on its bargaining power. This study not only deepens the understanding of the mechanisms behind low-carbon supply chain collaboration from a behavioral motivation perspective but also provides a concrete decision-making framework and managerial insights for enterprises to design incentive-compatible low-carbon cooperation mechanisms.