# A Game Theoretic Approach for Balancing Energy Consumption in Clustered Wireless Sensor Networks
## 2 Related Works
For energy saving purposes, a cluster-based topology is constructed in each covered area, and CHs only need to transmit the aggregated data to the corresponding fog node. To select the appropriate CHs from the network, two energy thresholds corresponding to advanced and normal nodes are designed that both initial energy and current average energy of sensor nodes are considered. Then sensor nodes with higher energy level become CHs more frequently if they have more residual energy than the corresponding threshold. Moreover, information about sensor-to-sensor link gains and inter-sensor distances is exploited to find a proper data transmission path from sensor nodes to the log nodes. Simulation results show that P-SEP has improved the network lifetime by 31% compared with SEP. However, only two-levelheterogeneity about initial energy is considered in P-SEP, and pre-deployment of advanced nodes makes it quite limited for execution in practical scenarios. In [26], clustering techniques were used to solve the feedback problem in ultra-wideband systems, where large amounts of feedback are required when transmitting the channel impulse response from receiver to transmitter. By adopting machine learning methods, the estimated channels are clustered into several groups and correspondingly the appropriate channel cluster head (CCH) is selected within each group. Only the label of the most similar CCH to that estimated channel is required for feedback. Thus, the amount of data is reduced significantly across the feedback channel. As an effective way to make decisions for intelligent rational individuals under conflict situations, game theory has been used to solve the data forwarding problem for sensor nodes in WSNs. A game theory protocol named Forwarding Dilemma Game (FDG) was presented in [27] for the purpose of controlling the overhead during data transmission in multi-hop networks. When a sensor node has received a flooding packet, it decides whether to forward this packet by playing the game with other nodes which have received the same packet. Each player has two strategies: One is forwarding the packet and the other is dropping the packet. The mixed NE strategy is adopted in the game and each player acquires a forwarding probability after this game is finished. Then each player decides whether to forward the packet based on this probability so that its payoff can keep a state of equilibrium. In [28], game theory was used to address the issue of energy balancing in cluster-based WSNs for the intruding detection application. When an event is detected by the nodes within a cluster, it should be reported timely to the sink to activate defensive mechanisms. To balance the energy dissipation among sensor nodes, report tasks in the network need to be fairly assigned. Game theory is used to model the report task assignment process, where sensor nodes in the same cluster are considered as the players for event reporter election. The NE solution is finally derived through convex optimization. Each sensor node decides whether to report the intruding event to BS based on the result of the NE solution, so that its payoff can be maximized while the energy balancing objective is also achieved. Recently, game theory was introduced to address the clustering for WSNs. A territory game theoretical clustering protocol (TGCP) was presented in [29], where the whole network is divided into a total of four continuous regions A, B, C and D. To balance energy consumption in multi-hop communication networks, sensor nodes in the region near to BS have bigger probability to be CHs than the ones in the region farther from BS. To determine the limit between neighboring regions, an evolution game is introduced to model neighbor regions as two players for territory size contest. TGCP can effectively improve the network performance compared with LEACH, since it alleviates unbalanced energy dissipation due to asymmetrical distances from CHs to BS. However, only four regions are considered in TGCP making it not very suitable for large-scale networks.