Technology advancements in the era of Industry 4.0 are proposed to shift away from a centralized instance of decision making to a more decentralized one. Critical to the growth of Industry 4.0 is the coordination among supply chain entities, in particular when Industry 4.0 is proposed to improve sustainability efforts. Studies in green supply chain literature have often considered the market expansion effects of greening efforts. However, a number of other factors influence greening efforts, a critical one being the price premium effect driven by the brand building strategy of firms. A principal issue then arises as to which strategy should firms adopt and when does each greening effect benefit firms and supply chains more. We generate several insights into this important issue by developing models considering dyadic settings, competition, and cost-sharing contract. We examine strategic decisions in these channel structures and compare and contrast our results with the market expansion based models. We identify a number of counter-intuitive results, for example, a dyadic channel with high price-sensitive consumers would benefit more from the price premium effect and cost-sharing (when it focusses on building brand) than market expansion. We also conduct intra-channel and inter-channel comparison of outcomes to understand the effect of competition. Among other results, we find that in the presence of a dominant retailer and competing manufacturers, the retailer shares more greening cost with the manufacturer than the corresponding decentralized channel. © 2020 Elsevier B.V.