# Cooperative Game-Based Energy Efficiency Management over Ultra-Dense Wireless Cellular Networks
## 1 Introduction  
With the growth of wireless cellular communication over the past decade, smart mobile devices, such as smart phones, tablets, and laptops, are being rapidly developed and widely used for bandwidth-hungry mobile Internet applications [1; 2; 3; 4; 5]. There is a broad consensus in the wireless industry that this trend will continue for several years. To support the exponential increase of wireless data traffic, the capacity of wireless cellular networks needs to grow accordingly. The wireless industry has taken on the challenge of cost-effectively supporting a 1000 \(\times\) increase in the wireless capacity demand over the next decade, which is becoming a hot research topic in both industries and academics [6]. In light of the observation by [PERSON]--the pioneer of wireless communications--wireless system capacity can be increased by increasing the wireless nodes, expanding the radio spectrum, and improving the link efficiency [1; 2]. In recent research, millimeter-wave communication was proposed for expanding the system bandwidth and increasing the system capacity [4]. Furthermore, a massivemultiple-input multi-output technology [3] was presented to improve the spectrum efficiency of 5G wireless cellular communication systems. The small-cell conception has been found to increase the throughput and reduce the energy consumption in wireless scenarios [5]. These ingredients for wireless-capacity enhancement may be regarded as having the purpose of \"network densification\" [1]. To realize seamless coverage for future wireless cellular networks, a larger number of small cells must be densely deployed, forming ultradense wireless cellular networks. Initial studies involving ultradense wireless cellular networks are explored in [1; 6; 7; 8; 9]. [PERSON] et al. discussed challenges and opportunities in network densification, which are regarded as the key technology for wireless evolution in the next decade, and analyzed the spatial densification situation and spectrum aggregation situation, i.e., small-cell dense deployment and radio spectrum utilization in diverse bands for 5G networks [1]. On the basis of WiFi and long-term evolution (LTE) technologies, a joint intra-cell and inter-cell resource-allocation coordination scheme is proposed [7]. [PERSON] et al. presented two interference coordination algorithms for the time and frequency domains for LTE-A dense wireless networks [8]. [PERSON] et al. proposed a distributed gateway network architecture for 5G ultra-dense wireless cellular networks, and investigated the backhaul capacity and the backhaul energy efficiency (EE) [6]. The spectral efficiency (SE) and EE of ultra-dense wireless cellular networks under different deployment strategies were investigated in [9]. Future wireless cellular networks should be more environmentally friendly [10; 11]. Hence, the corresponding structural design, operation, and implementation should pursue minimal impacts on the human environment. As observed in [12], energy-efficient wireless communication has recently drawn increasing attention from the research community, especially with the explosive increase of high-data-rate applications. There are adequate energy-efficiency metrics of primary importance, which are directly related to optimization schemes across all the protocol layers. The most popular one is \"bits-per-Joule\", which is defined as the total throughput for unit energy consumption. According to this metric, in [13], EE analysis at the link level is provided, where the transmission power is considered as the primary constraint. In [14], the bits-per-Joule metric at the network level is analyzed, and the number of nodes in the network is proven to be an important factor to increase the EE. Other metrics, such as the SE (Hz/J) and deployment efficiency (DE, bits/\(\ell\)), aim to observe the achieved utility of the different resources. For example, the DE focuses on the financial aspects of the system efficiency [15], which is suitable for a cellular operator concerned about revenue earnings.