In this paper, an auctioning strategy is proposed for cellular networks that ensures net energy savings. The pricing scheme, in conjunction with a two dimensional bid structure, incentivizes cooperation at the terminal nodes for better interference management at receivers and for cooperative relaying. It is shown that, for the proposed auctioning strategy, network operators are guaranteed revenue gains, mobile nodes' dominant strategy is to bid their true valuation of their energy resources, and overall effective energy gains occur under the assumption of a reserve price for bidding. Simulation results show that significant energy savings can be achieved by employing this auctioning mechanism for a 3G cellular set-up.