We consider a heterogeneous network (HetNet) in which multiple small cell base stations (SBSs) aim to offload a quantity of macro cell user equipments (MUEs) to reduce the energy consumption of the network while guaranteeing the QoS requirements of all UEs. We design an ascending-bid auction mechanism to achieve this goal. Unique and closed form solutions for the demand and supply quantities of offloading MUEs are derived. When the MBS has knowledge about the utilities and strategies of the

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... , the proposed auction can be formulated as a Stackelberg game where the clinching bid price is obtained in closed form. Numerical results verify the theoretical analysis for different scenarios and show that the proposed auction clinches fast at the unique clinching price, thereby resulting in a win-win solution that improves the energy consumption of the HetNet.