# Game Theoretic Solution for Power Management in IoT-Based Wireless Sensor Networks
## 3 The Proposed Mechanism
### Assessment by Nodes
The BS continuously assesses the performance of CHs and designs the revenue for each node to direct them towards the responsibility of CH. The following Figure 2 shows a clear view of our scheme. ### Continual Assessment by the BS

The CHs are always switched with the passage of time due to their degrading performance, caused by either their own energy or by other nodes. The energies and presence of neighboring nodes can also affect the performance of a CH. It is always desired to select the most efficient and economical CHs in each cluster. In our work, the CHs are selected through the evolutionary game, as discussed in the previous section. However, it is the responsibility of BS to keep an eye on the performance of all the CHs throughout the network lifetime. A multi-factor approach similar to a Stackelberg game is designed to evaluate the condition of CHs and CMs in each cluster by the BS. The BS always keeps a list of leading CHs, along with their following CHs. The leading nodes are

\[U_{\alpha(CH)}=\ y\,\Pi\ +\ \Pi+\ 2\ \pi-y\Pi\ -2y\,\pi \tag{15}\]0 Flowchart to clearly show the proposed scheme. considered as the most suitable nodes for cluster headship. Once a leader selected as CH, it is also evaluated again and again and may be switched back to CM by comparing it with the leaders. The key parameters assessed by the BS are: Residual energy, number of closed neighbors, number of neighbors, location of a node, channel quality, and throughput. The residual energy can be seen as the available energy of nodes, which can be used for processing, sensing, and transmission. The closed neighbors can have an adequate impact on the performance on the CH and responsibilities among them can be divided or shared. The number of neighbors can be used to determine cluster size. The higher number of neighbors will lead to a higher level of dependence of CMs or a single CH. In such cases, it is obvious that the CH will exhaust its energy comparatively quickly. The location of the node can also affect the level of energy dissipation on the communication with neighbors. The BS also check the throughputs from different CHs and analyzes their performance according to their inputs in the network. These factors can be represented as:

\[U_{\alpha(CH)}=\ y\,\Pi\ +\ \Pi+\ 2\ \pi-y\Pi\ -2y\,\pi \tag{15}\]1

\[EVAL=\Bigg{\{} \begin{array}{c}Energy,\,Location,\,Neighbors,\\ \lambda i,\,Channel,\,throughput\end{array} \Bigg{\}}. \tag{34}\]

The parameters are then graded into different levels to check their weightage and compared with each other. The levels are as follows:

\[LEVELS=\{1,2,3,\ldots,10\}. \tag{35}\]

Level 1 indicates the worst case or the least value for a grade, while level 10 represents the best case. The nodes that have an aggregate of highest levels for each of their evaluation parameters are considered as the best suitable candidates for cluster-headship. Such nodes are given additional benefits by the BS to make their position stronger for the next rounds of CH selection. It is obvious that the BS cannot investigate all the nodes for these values of parameters periodically. Such types of information exchange can put extra communication overhead on nodes and can reduce the network performance. A probabilistic model is used to determine the energy and \(\lambda_{i}\) values for each node in the network. The DSR protocol is used for routing in the network, therefore, it is easy to extract the IDs of all the involved nodes in a communication session. The BS can easily estimate the energy consumption of each involved node once the list of these nodes and the amount of transmitted data is obtained. ## 4 Simulation Results

A plane domain of the area of \(500\times 500\) is selected to deploy sensor nodes in a random fashion. The list of parameters used is given in the Table 6. This work is cluster-based, therefore, the performance metrics are compared with LEACH and LEACH-C [16]. Moreover, this work mainly depends the evolutionary game, therefore, GEEC [30] and GTEB [31] are also taken for comparative studies.