We consider a Closed-loop supply chain (CLSC) with a single manufacturer and a single retailer. We characterize and compare the feedback equilibrium results in two scenarios. In the first scenario, the manufacturer invests in green activities to increase the product-return rate while the retailer controls the price. A Nash equilibrium is sought. In the second scenario, the players implement a cost-revenue sharing contract (CRS) in which the manufacturer transfers part of its sales revenues, and the retailer pays part of the cost of the manufacturer's green activities program that aims at increasing the return rate of used products. A feedback-Stackelberg equilibrium is adopted, with the retailer acting as the leader. Our results show that a CRS is successful only under particular conditions. While the retailer is always willing to implement such a contract, the manufacturer is better off only when the product return and the remanufacturing efficiency are sufficiently large, and the sharing parameter is not too high.