Recycling subsidy and carbon tax policies are ways to achieve energy and environmental sustainability. The implementation of these policies has changed the operating environment of traditional closed-loop supply chains, while the privacy of relevant information increases the difficulty of decision-making. Under the background, this paper considers the green closed-loop supply chain (GCLSC) under the hybrid policy of recycling subsidy and carbon tax where the manufacturer is in charge of recycling and the retailer invests in green marketing. Taking green marketing cost coefficient as the retailerβs private information, this paper explores the influence of information asymmetry on optimal decisions and performance of the GCLSC. By constructing game models of information symmetry and asymmetry, the optimal decisions, economic and environmental performance, and social welfare are provided. Combined with numerical analysis, the influence of uncertainty of the manufacturerβs estimation, subsidies and carbon tax on the GCLSC is proposed. The results indicate that the uncertainty in the manufacturerβs estimation can improve the social welfare under certain conditions, but it cannot reduce carbon emissions. Recycling subsidy and carbon tax policies oppositely affect the manufacturerβs optimal decisions and carbon emissions. Information asymmetry is beneficial to the retailer. However, less uncertainty in estimation is not always better for the manufacturer. The manufacturer needs to proactively adopt strategies to stimulate the retailerβs information sharing.