Achieving greening in a supply chain substantially depends on the structure of the channel and the efforts of independent members of the chain whose incentives may not be aligned. To investigate these two critical factors, we study a two-echelon green supply chain composed of a single supplier and a single buyer using a game-theoretical approach. We particularly consider the case where the demand is unilaterally dependent on the greening efforts of both parties. We investigate equilibrium decisions on pricing and greening effort under three different decentralized channel structures and analyze the outcomes from the perspective of the players as well as the overall channel. In the first scenario, the supplier moves first and sets her wholesale pricing and greening effort decisions followed by buyer's decisions on the resale price and greening effort. In the second scenario, the supplier and the buyer move simultaneously and set their own effort levels in the first stage. The supplier sets her wholesale price and the buyer responds with her resale price in the second and third stages respectively. In the third scenario, parties set their decisions in four stages that follow supplier's effort, buyer's effort, supplier's wholesale pricing, and buyer's resale pricing decisions. We compare our results with the previous literature that focuses on bilateral impact of efforts on demand. In contrast to the cases with bilateral effect, we observe that stronger leadership role given to the supplier in the first scenario results in higher levels of greening for the supply chain.