In the future connected societies, everyone and everything will be inter-connected, under the umbrella of the Internet of Things, where tens to hundreds of devices will be serving every single citizen. However, connecting this massive number of energy-constrained devices pose a serious challenge on the wireless networking paradigm; energy efficiency still represents a major challenge within the design of the future generation of wireless networking (5G). In this paper, we address reducing energy consumption of energy-constrained wireless devices, through energy-aware cooperative relaying in future heterogeneous networks (HetNets). Using game theory concepts, we formulate the problem as an assignment game. In the first stage of the game, the optimal relay selection is formulated as a linear programming problem, whose solution assigns suitable relays to their perspective sources. In the final stage, the core solution is derived, which guarantees fair distribution of the payoff among players, to keep them satisfied and discourage them from quitting the coalition. Our solution also proposes a credit based system to reward cooperative players; hence possibly excluding selfish users from cooperative coalitions. The proposed relay selection algorithm is evaluated using extensive NS2 simulations. The simulation results show significant energy savings using cooperative relaying, reaching up to 22%, with extensive increase in battery lifetime.