# Cooperative Game-Based Energy Efficiency Management over Ultra-Dense Wireless Cellular Networks
## 1 Introduction
This metric contains a careful treatment of the capital expenditure (CapEx) and operational expenditure (OpEx) of the wireless network. For a core network, which cares more about the capacity, the SE is more suitable for explaining the relationship between the capacity and the energy consumption [16]. In ultra-dense wireless cellular networks, the small cell is a general term adopted in LTE standards, which refer to picocells and femtocells in a coverage radius of 10-300 m [17]. Compared with orthogonal deployment, spectrum sharing deployment between multiple small cells and macro cells is more attractive owing to its easier implementation and more efficient utilization of the frequency band [18]. As a result, the network SE is improved with frequency reuse and spectrum sharing. At the same time, with the coexistence of multiple small-cell base stations (SeNBs) and macro-cell base stations (MeNBs), the path loss between a user and its base station is reduced, which increases both the signal power and the inter-tier interference, and effectively dwarfs the effect of thermal noise. Thus, interference mitigation is essential for network efficiency management in ultradense wireless cellular networks, which requires adaptive resource coordination among the whole network. According to [19; 20], interference-aware power coordination among SeNBs and MeNBs is a critical issue for mitigating both inter-tier and intra-tier interference and achieving good SE. The conventional power coordination schemes use a central controller to realize convex optimization by a complex signaling overhead, which is not suitable for a distributed ultra-dense wireless cellular network. Game theory provides a natural model for handling multiple interactively interfering entities to seek a solution for maximizing the utility of every entity [21; 22]. Many studies on power coordination and SE optimization have adopted a non-cooperation Nash game-theoretic approach. In [23],the non-cooperative power allocation considering the signal-to-interference-plus-noise-ratio (SINR) is proposed to relieve the interference from femtocells to macro cells. In [24], a power control scheme based on the Stackelberg game is formulated to maximize the capacity of femtocells under an inter-tier interference constraint. A non-cooperative power and subchannel resource allocation scheme for co-channel femtocells is presented with transmitting protection for macro-cell users [25]. Although the aforementioned power-coordination strategies based on the strategic non-cooperative Nash game could simply reflect the hierarchical relationship between MeNBs and SeNBs, they are unable to capture the inherent coordination actions among different base stations. Moreover, players in a non-cooperative game act rationally and selfishly to maximize their individual utility [26], which might introduce additional interference to other cells. The strategies fail to guarantee fairness among different small cells, where the Nash equilibrium is not always efficient. To improve the Pareto-optimality of the non-cooperative game, schemes have been introduced such as pricing of the interference [27], the virtual referee [28], uniform and differential pricing game of resource scheduling [29], and repeated game [30]. However, backhauls are necessary for massive information exchange or aggregation to achieve accurate pricing. Furthermore, pricing scheme may lead to a slow convergent or even divergent power-control algorithm. On the other hand, the cooperative game model [31; 32] is more suitable for resource allocation in ultra-dense wireless cellular networks, which has been proven in the economic field. A cooperative bargaining game was demonstrated to achieve the optimal social solution by maximizing a Nash-product utility function [33]. Moreover, game theory-based energy-efficient resource allocation has been studied for wireless networks [11; 32; 34]. In [34], the Nash equilibrium of a power-control game was proposed to enhance the EE.