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In this paper, with respect to the uncertainty about the individual information, they investigate the relay power allocation problem from the energy-efficient, Pareto optimal, and competitive fairness perspective. At first, they design an easy implementation energy efficiency metric, which aims at striking a balance between the QoS provisioning and the energy consumption. Then, an auction mechanism is proposed for relay power allocation. By transferring the auction mechanism into a game, they prove the existence, uniqueness, and Pareto optimality of the Nash Equilibrium (NE) for their auction game, and show that the allocation strategies from the NE can achieve the energy efficiency in terms of the proposed metric.
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