<p>This study develops a game-theoretic model for a dual-channel closed-loop supply chain comprising a manufacturer, retailer, and third-party platform, optimizing pricing, green innovation, and promotional effort under centralized, Nash, manufacturer-led, and retailer-led structures to balance profitability and sustainability. The methodology formulates linear demand functions sensitive to price, green innovation, and promotional effort across retail, online, and platform channels, incorporates recovery/ recycling/ remanufacturing costs, and solves equilibria analytically while accounting for platform fees and direct delivery expenses. Numerical illustrations compare scenarios via profits, green innovation levels, and environmental metrics under varying consumer sensitivities. Key findings reveal that moderate green innovation and promotional effort investments maximize system performance, with manufacturer leadership yielding highest sustainability but widest profit disparities; stronger green sensitivity enhances overall profits and recovery rates. Contributions include a unified framework integrating channel coordination with closed-loop dynamics, novel insights on power structures' impacts, and managerial guidance for policies promoting fairness and eco-efficiency in platform-driven closed-loop supply chain.</p>