In this paper, we aim to reduce the power expen-diture in the reverse link during low network load periods, by allocating extra resource blocks (RBs) to the mobile users. Thereby, the user's rate demands are split among its allocated RBs in order to transmit in each of them by using a low level modulation order. We model the bandwidth expansion (BE) process by a game theory framework derived from the concept of stable marriage with incomplete lists (SMI). We focus on the optimization of the circuit consumed power rather than on the transmitted power. Thus, the power consumption of the radio frequency (RF) circuits and the base band (BB) system module is taken into account. Our proposed framework works in a distributed way, hence each RB and mobile user in the system are considered as an independent entity which takes an active role in the decision making process. Additionally, we show that when circuit power consumption is used as an optimization metric, transmitting in more than one RB may not become an energy efficient solution for users experiencing favorable propagation conditions in the reverse link.