## 1 Introduction  
The networks of 5 th Generation Mobile Communication Technology (5G) have developed rapidly in recent years. Due to its characteristics, such as high speed, low latency, and large scale [1, 2], 5G network technology is widely used in all aspects of life, such as healthcare, agriculture, and communication [3, 4, 5, 6]. Wireless sensor networks (WSNs) are the smallest units of networks, and they can support large-scale deployments, high reliability, and high mobility [7]. WSNs are more broadly applied in the 5G network environment [8, 9, 10]. WSNs are increasingly important in the field of communication technology [11]. For example, Internet of Things (IoT) applications of WSNs over 5G infrastructure addressed by [PERSON] successfully reduce the latency of exchanging information between facilities [12]. [PERSON] creates a hybrid clustering and routing strategy for data aggregation in a 5G WSN. This strategy makes the network lifetime longer [13]. Wireless communication has become an integral part of the mobile network. As the demand for 5G mobile wireless networks grows [14], the number of devices and service types is rising. Therefore, the security threat landscape of WSNs in 5G has also grown significantly [15, 16]. [PERSON] discusses the security issues and challenges in WSNs and elaborates on the attack behaviors that WSNs are vulnerable to at the network layer [17]. Currently, many hackers adopt the Advanced Persistent Threat (APT) offense model [18, 19]. Denial-of-service offense mode (DOS) in computer network broadband and connectivity offense [20] attack the target nodes and information transmission paths in the target network. In the face of various offense patterns of hackers, it is particularly important to maintain the security of WSNs. Many scholars apply the offense and defense game model to network security and some information transmission resource allocation problems [21; 22; 23; 24]. Nowadays, many scholars use game theory to solve a series of security problems in WSNs. [PERSON] uses a Bayesian game model to make a secure routing protocol, which can improve the detection accuracy of an intrusion detection system (IDS) in WSNs [25]. [PERSON] combines software-defined networks with Stackelberg games to achieve the optimal data offloading problem in 5G [26]. [PERSON] analyzes the micro-mechanism of malware propagation in WSNs from the perspective of game theory, which can be of guiding significance for inhibiting the spread of malware [27]. The combination of game theory methods and WSNs can better address a series of security problems existing in WSNs. However, with the development of large-scale and high-performance 5G, the development and extension of WSNs have diversified. The existing attack methods and scale of offense and defense are no longer sufficient for the environment in which they are located. The offense and defense strategies in WSNs under the 5G environment are no longer in a singular form but rather align with the characteristics of large-scale deployments in 5G. Regarding offense and defense of WSNs in 5G, most of the attack methods are to attack the target node while ignoring the attack on the information transmission link. The problem of how to analyze the large-scale offense and defense confrontation behaviors of WSNs in 5G has become an important issue to be studied. Therefore, the main contributions of this paper are as follows. 1. A network topology diagram based on WSNs is constructed. The nodes and the transmission links in the WSN are abstracted as nodes and edges in an undirected graph. The scale of the offense and defense confrontation is expanded, and the adversarial game is carried out on the graph structure. 2. A complete information static game model is established for the offense and defense problem in WSNs. And the existence of Nash equilibrium in the model is proved. Therefore, offense and defense game behaviors of WSNs in the 5G environment can be analyzed more clearly and intuitively. 3.