We investigate the impact of information asymmetry regarding the producer of remanufactured products on the decisions of a manufacturer and an authorized remanufacturer (AR) in a competitive closed-loop supply chain. Information asymmetry affects consumers' perceived value of new and remanufactured products, thereby influencing market dynamics. In our model, the manufacturer licenses the AR to remanufacture products, with both parties independently setting prices and deciding on the policy of information disclosure about the remanufactured products' producer. The analysis shows that information symmetry generally results in higher prices for new products and lower prices for remanufactured products. However, when the AR's remanufacturing capacity is bound, there is a threshold in consumer recognition of remanufactured products (net gain value of product perceived value under information symmetry) which alters the price relationship. When the AR employs a partial remanufacturing strategy, information symmetry leads to a reduction in the manufacturer's licensing fee. Additionally, we find that information symmetry can cause the AR to adjust its remanufacturing strategies under certain conditions. Due to the perceived value effects, sometimes there is no threshold for product cost that can cause changes in the information disclosure policies. Furthermore, the independent decision-making of supply chain members sometimes can allow the manufacturer to benefit as a free rider. These findings highlight the complex interplay between information asymmetry, remanufacturing strategies, and remanufacturing licensing.