Sustainability goals are becoming a priority in many societies. An important element in this context is the success of environmentally friendly products. Hence, we consider a manufacturer-retailer vertical supply chain model, managing a green product and its conventional counterpart, designated by brown product. We analyze three kinds of dynamic market scenarios: no market leadership, the manufacturer as the market leader, and the retailer as the market leader. Under each scenario, we determine the equilibrium decisions for pricing and greening investments as well as their dependence on a cost-sharing proportion agreement between the firms. We find that generally both firms have similar pricing trends, where the gap between the two product prices increases with the share of cost carried by the retailer. Moreover, we analyze how these decisions affect the consumer surplus and the performance of the firms. The absence of a market leader leads to higher consumer surplus with the manufacturer investing more in greening. However, cost-sharing may fail if there is no market leader. The retailer has incentive to share the highest proportion of greening costs when it is the leader. When the manufacturer is the leader, the retailer may have incentive to change the cost-sharing proportion over time. Finally, we compare the greening level and learning trajectories for the different scenarios. We provide essential managerial insights on how decisions should be operated, enabling green products to successfully gain a stable market share.