The transport sector is one of the largest contributors to rising greenhouse gas (GHG) emissions in the world. With no tailpipe emissions, electric vehicles (EVs) can be one of the ways to reduce GHG emissions. In recent years, many countries have taken steps to promote the penetration of EVs in the market. Using different policy instruments, in particular, taxes and subsidies are one of the more common approaches. In this paper, using a game-theoretic approach, we study the effect of using a combination of subsidy on EV and green-tax on conventional gasoline vehicles (GV) on overall social welfare, environmental impact, and vehicle stock in monopoly and duopoly forms of market structures. Findings reveal that a combination of subsidy and green-tax can generate higher social welfare as compared to the use of only one of them under both monopoly and duopoly markets. The results provide multifaceted insights for policymakers and governments to design the subsidy and green-tax based on the environmental impact of GVs and EVs along with maximising the social welfare.