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The deployment of heterogeneous networks (HetNets) can significantly boost the network capacity. However, the large number of small cell base stations (SBSs) deployed in HetNets can result in an increased total energy consumption. One of the promising techniques to reduce the energy consumption of networks is base station (BS) ON/OFF switching (sleeping) approaches. Due to device lifetime and energy waste by unnecessary switchings, the number of switchings is considered as an important problem. In this paper, we formulate the ON/OFF switching problem as a satisfaction game, where BSs seek to meet certain performance constraints in order to avoid the frequent BS switchings. Furthermore, BSs can choose their transmission power levels according to the network conditions in a distributed manner. The proposed satisfaction game involves a multi-step process. In the first step, we aim at satisfying the …