###### Abstract  
Energy limitation is one of the intrinsic shortcomings of wireless sensor networks (WSNs), although it has been widely applied in disaster response, battlefield surveillance, wildfire monitoring, radioactivity detection, etc. Due to the large amount of energy consumed for data transmission, how to prolong the network lifespan by designing various hierarchical routing protocols has attracted more and more attention. As a result, numerous achievements have emerged successively. However, these presented mechanisms can rarely guarantee the satisfactory quality of service (QoS), while lowering the energy cost level of WSNs. Meanwhile, invulnerability is undoubtedly an excellent quantitative index to assess QoS. Therefore, it is critical to develop a practical routing method to optimize network lifetime by considering both invulnerability and energy efficiency. Game theory is suitable for such a critical problem as it can be used in node or at network level to encourage the decision-making capabilities of WSNs. In this paper, a novel invulnerability-aware clustering routing algorithm (IACRA) using game-theoretic method is proposed to solve the predicament. The core features of the addressed game-theory-based routing protocol include integral invulnerability awareness, optimal cluster head selection in hierarchical routing, distance-aware cluster head discovery, and cluster rotation update mechanism for lifetime optimization. Particularly, the integral network invulnerability based on weighted fusion is constructed for further defining the profit model by combining the invulnerability indicators used to evaluate the local and whole network. Meanwhile, the optimal probability function of every node elected as CH in per cluster is established through the game between invulnerability and node energy consumption. In addition, the cluster update mechanism base on cluster rotation is proposed to avoid the rapid death of nodes with large energy consumption for maximizing network lifetime. The experimental results indicated a significant improvement in energy balance as well as in invulnerability compared with the other three kinds of well-known clustering routing protocols including GEEC (Game-theory-based energy efficient clustering routing protocol), HGTD (Hybrid, game-theory-based distributed clustering protocol), and EEGC (Efficient energy-aware and game-theory-based clustering protocol). Concretely, at the 400 communication rounds, the invulnerability of IACRA was higher than that of GEEC, HGTD, and EEGC by 77.56%, 29.45% and 15.90%, respectively, and the average residual energy of IACRA was 8.61%, 18.35% and 6.36% larger than that of GEEC, HGTD, and EEGC, respectively. Based on these results, the proposed protocol can be utilized to increase the capability of WSNs against deterioration of QoS and energy constraints. wireless sensor networks; clustering routing protocol; lifetime; game theory; invulnerability; average residual energy +
Footnote †: journal: Sensors  
20222227936202222279362022222279362  
processing, and communication transmission in various application scenarios [1; 2]. Due to the harsh deployment environment, the node energy cannot be replenished in time and effectively, leading to the energy hole problem in the data collection and transmission procedure and significantly reducing the network lifetime [3]. The network routing protocol can balance the difference in network energy consumption, improve the survival rate of nodes, and boost the network lifetime by optimizing the network topology and data transmission links without increasing hardware cost [4]. Compared with other protocols, the hierarchical routing protocol exhibits considerable advantages in improving energy utilization, reducing transmission delay and packet loss rate, and alleviating the energy hole issue [5]. Inspired by the high reliability and centralized management of hierarchical network architecture, a large number of researchers have extensively investigated cluster head (CH) selection for hierarchical routing protocol.