Despite the considerable influence of the governmental regulations on the green supply chain, in the most of the studies in the literature of green supply chain, almost the role of the government and interactions between the government and supply chains members’ decisions are disregarded. In this study, a competitive mathematical model of government as the leader and two competitive green and non-green supply chains as the followers is developed and for the first time in this paper, pricing policies, greening strategies and governance tariffs determining in supply chains competition under government financial intervals are discussed. In the presented framework, the government seeks social benefits and determines subsidy and tax rates for green and non-green products respectively. The sale prices of products and the green degree of the green product are supply chains’ decision variables. In centralized and decentralized models, the optimal values of decision variables are gained and some important sensitivity analyses of governance decisions are done. In the governmental decisions area, it is observed that the impact of raising subsidy rate is significantly more than tax rate and it leads to increase in profits of government and supply chains and sustainability of products. Also among the competition of supply chains, cooperating between members makes more profit for them and leads to produce more eco-friendly products.