# A Game Theoretic Approach for Balancing Energy Consumption in Clustered Wireless Sensor Networks
## 2 Related Works  
Clustering techniques for WSNs have been widely studied recently for the goal of prolonging the network lifetime. In this section, we will provide a review of some clustering schemes most related to our work. Low Energy Adaptive Clustering Hierarchy (LEACH), one of the most famous traditional clustering protocols, was presented in [21]. All sensor nodes in the network are clustered into some groups. A CH is selected in each cluster with the responsibilities of receiving, aggregating and forwarding data from other normal nodes distributed in the same cluster. Since CHs have more data traffic and consume much more energy than normal sensor nodes, the CH role must be rotated among nodes to balance the energy. Then a random CH rotation mechanism is introduced so that a sensor node can serve as the CH once within a specific time interval. This mechanism can balance the energy dissipation among sensor nodes, but it may result in an uneven distribution of clusters. Another famous clustering protocol called Hybrid Energy-Efficient Distributed clustering (HEED) was presented in [22]. CHs are periodically selected by adopting an iterative CH rotation mechanism. The residual energy of nodes and communication cost within a cluster are considered when selecting the suitable CHs. Then sensor nodes which possess more energy have bigger probabilities to be CHs, and each one prefers to join the cluster with smaller communication cost. Furthermore, this CH rotation mechanism can assure that no more than two sensor nodes within a close neighborhood will be selected as the CH simultaneously. Finally, HEED acquires a more even distribution of clusters than LEACH, but it needs extra energy for the iterative CH election process. Inspired by behavior of honeybee swarms, a cluster-based routing algorithm for WSNs named queen-bee evolution algorithm (QEGA) was presented in [23]. The queen-bee algorithm has a high execution rate that results in premature convergence. Two mutation rates are introduced to solve this problem, which can increase the diversity of children. QEGA has enhanced energy efficiency and network lifetime compared with genetic algorithm-based clustering, but it does not consider sensor nodes' residual energy, which is the most important factor in routing protocols for WSNs. A novel ring-based clustering method called Efficient Cluster-Based Communication Protocol (ECOMP) was proposed in [24]. Each cluster consists of some normal sensor nodes, a CH node and a cluster sender node. A bidirectional ring is constructed by normal nodes and the cluster sender node within each cluster. The cluster sender node starts data collection from the normal sensor nodes in a clockwise or anticlockwise direction around the ring in turn. Each normal sensor node aggregates its previous neighbor node's data with its own, and then forwards the data to its next neighbor. Finally, the cluster sender node has received the data of all normal sensor nodes on the ring, and it transmits the data to a BS by single or multi-hop forwarding with the CHs in the network. ECOMP liberates the CHs from heavy data receiving and aggregating for normal sensor nodes, as each normal node only transmits the data to its near neighbor. Thus the energy dissipation of nodes can be effectively reduced. However, extra costs have to be paid for ring construction, since sensor nodes exchange some information with BS and get locations by GPS. To prolong the stable period of Fog-supported WSNs, a modified Stable Election Protocol (SEP) which is called Prolong-SEP (P-SEP) was proposed in [25]. The whole sensor field is covered by some fog nodes which have the responsibility of forwarding data to the internet gateway. Sensor nodes with two-level heterogeneity about initial energy are pre-placed or randomly deployed into each fog node covered area, and they can be classified into advanced nodes and normal ones.