We model a closed-loop supply chain, made up of one manufacturer and one retailer, as a stochastic dynamic game. This paradigm allows us to simultaneously capture the strategic interactions between the agents, the intertemporal nature of the return of past-sold products for remanufacturing, and the uncertainty in the parameter values. We characterize and compare the solutions in two scenarios. In the no-sharing scenario, we assume that the manufacturer alone incurs the cost of the green activities aimed at incentivizing consumers to return previously purchased products at the end of their useful life. In the second scenario, namely, revenue and cost sharing contract, the retailer shares the cost of the green activities and the manufacturer transfers part of its revenues to the retailer. Numerical experiments are discussed.