## 1 Introduction  
The next generation of electrical power grids is known as Smart Grid [1], which is characterized by high security, intellectuality, autonomy, and efficiency. To achieve intellectuality and autonomy in Smart Grids, an integrated, high-speed communication system with a real time two-way transmission network is crucial [2]. As shown in Figure 1, the communication system of the Smart Grid is a three-layer architecture, which includes home area network (HAN), neighborhood area network (NAN), and wide area network (WAN), respectively.  
At present, the wire transmission method remains widely used in NAN and WAN communication systems because of the method's wide transmission range and outstanding transmission reliability [3]. However, with the increase in the demand for automatic distribution networks and smart work environments, the wireless sensor network would gain more attention depending on its speed deployment, lower cost, and excellent expansibility in HAN. The IEEE 802.15.4g suggested that a home area network can utilize a 900 MHz frequency band as its wireless channel [4]. However, with the growing number of existing wireless sensors, this working band will become increasingly crowded. Thus, cognitive radio (CR) has been regarded as an effective solution for extending the utilization of wireless spectrum resources [5]. CR technology dynamically changes the transmission frequency of the transceivers by sensing the variations in the ambient environment. Therefore, a CR user can communicate with a gateway and other users through the free primary channel at a different frequency [6].  
In CR technology, the allocation of licensed free channels to unlicensed users is a primary concern. Recently, a competitive method is proposed to solve this problem. That is, the users should contend for the limited free licensed transmission channels based on the needful target. This idea resembles game theory in mathematics [7]. Hence, the application of game theory used in the spectrum allocation model is proposed. In [8], [PERSON] _et al_. have introduced a CR spectrum allocation algorithm based on the potential game theory. In this algorithm, potential function is used to achieve the optimization of the spectrum allocation problem. In [9], a CR spectrum allocation model based on prisoner's dilemma has been proposed to analyze the spectrum sharing problem in competing channels. Additionally, the literature [10] has analyzed the performance of the CR spectrum allocation algorithm based on  
Figure 1: Three-layer architecture of the Smart Grid communication system.  
non-cooperative game theory. However, both these existing algorithms have calculated without the multi-Nash equilibrium, which may cause misconvergence in the CR network. In this article, a modified CR spectrum allocation algorithm based on [PERSON] _et al._ non-cooperative game theory in Reference [10] will be proposed. Subsequently, a micro smart grid spectrum allocation model will be built. The computing simulation consequence by testing software is used to demonstrate that this modified algorithm can achieve stable spectrum allocation strategies and avoid the appearance of multi-Nash equilibrium at the expense of certain sacrifices in the system utility in the smart grid communication system.