In wireless sensor networks (WSNs), effective energy management is vital for extending the network life and improving performance. However, when nodes are densely and randomly distributed over large areas, traditional clustering strategies and routing algorithms often struggle to perform effectively. Clustering strategies face challenges related to cluster head (CH) distribution and cluster radius, which fail to adapt to dynamic node locations, leading to energy distribution imbalance. In routing algorithms, unpredictable path selection for long-distance communication increases energy consumption and leads to the “energy hole” phenomenon. To address these challenges, this study proposes a fuzzy clustering routing protocol for WSNs based on the game model (FBGM). The clustering process integrates a game model with fuzzy logic. Initially, nodes participate in a local election game to select candidate CHs (CCHs). Fuzzy logic then determines the election radius, where CCHs compete to finalize the CH election, thereby forming an unequal clustering structure. The proposed FBGM optimizes the distribution of CHs and ensures load balancing among clusters. For intracluster and intercluster communication, a hybrid routing strategy using a path energy function and fuzzy logic is proposed to optimize the data transmission paths. The experimental results demonstrate that the FBGM protocol dynamically adjusts clustering and routing based on network workloads and topological changes, achieving energy balance while extending the network lifetime and exhibiting commendable dynamic adaptability in large networks.

Energy balance consumption is an important research topic in the field of wireless sensor networks (WSNs). Clustering protocols are widely used to reduce WSN energy consumption. However, this many-to-one cluster head (CH) model can also easily lead to energy exhaustion of some critical nodes near the base station results in the decline of the network quality and lifetime. This article proposes a clustering election game-based and two-level management clustering protocol (CEGT) for WSNs; the network is divided into layers of equal size, and the layer heads (LHs) are selected within the layers based on the location and energy information. Each layer is further divided into clusters of equal size, and the nodes within the clusters undergo a two-stage screening followed by local clustering and multiple rounds of election games to dynamically select the staged CHs. This protocol effectively prevents low-energy nodes from participating in the CH competitions, and selects high-quality nodes through election games which are based on customized qualification values, and ensures reasonable energy utilization as well as efficient network load balancing. Finally, our simulations show that our CEGT protocol outperforms other clustering protocols in terms of the network lifetime, the number of surviving nodes, and the average number of clusters, and the throughput, which also indicate that the CEGT protocol is more suitable for large-scale networks.

In mobile wireless sensor networks, the mobility of nodes imposes heightened energy management demands on the network. This study proposes a game-based dynamic clustering routing (GDCR) protocol for mobile wireless sensor networks. The GDCR protocol employs multidimensional clustering and constructs a mixed strategy game model among heterogeneous nodes. This model considers various factors for cluster head selection, including residual energy, movement, distance to the sink, and node spacing, ensuring comprehensive decision-making. In addition, the protocol incorporates detached node management to ensure network security and stability. Simulation experiments demonstrate that the proposed protocol reduces the average network energy consumption when nodes have unrestricted movements. Furthermore, it effectively curtails fluctuations in energy consumption as the network scales up, thereby prolonging network lifetime and enhancing stability.

Environmental pollution abatement is a complex project. A system dynamics (SD) model is built for studying a mixed-strategy evolutionary game between the government that manages environmental pollution and the firm that generates contamination during their production processes. The stability analysis and SD simulation results show that evolutionary equilibrium (EE) does not exist with a static penalty. Therefore, a dynamic penalty is suggested in the SD model for equilibrium stabilisation and improvement in environmental pollution. Furthermore, a restraining penalty is found, which can not only stabilise the evolutional processes but also ideally influence the environmental pollution control in the simulation result. The stability analysis of the evolutionary game with both the dynamic penalties proves that Nash equilibrium takes the role of EE. The SD model can connect the static concept with dynamic predictions in the evolutionary game theory in a visual and convenient way.