# A Game Theoretic Approach for Balancing Energy Consumption in Clustered Wireless Sensor Networks
## 6 Performance Evaluations  
In this section, the performance of our proposed protocol GTAB will be evaluated via simulations executed by using MATLAB. Since LEACH is one of the most famous cluster-based routing protocols, and CROSS and LGCA are game theoretical cluster-based routing protocols, we will evaluate the performance of GTAB by comparing it with these three protocols. The parameters that adopted in our simulations are given in Table 2.  
Besides, the expected proportion of CHs is set to be 0.05 for LEACH. Since the predefined parameter \(w\) has important influence on the performance of the network in CROSS and LGCA, we find its optimal value 0.02 that can maximize the network lifetime through plenty of experiments. And we set \(w\) to be 0.02 in our following simulations. To evaluate the performance of GTAB comprehensively, we will conduct the simulations under various network conditions. Firstly, different network sizes are considered during the simulation to \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Basic energy \(E_{b}\) (J) & 0.5 \\ Random energy exponent \(\alpha\) & 0.1 \\ Packet size \(q\) (bits) & 3000 \\ Control packet size (bits) & 300 \\ \(\zeta\) (n/bit) & 50 \\ \(\varepsilon_{m}\) (pl/bit/m\({}^{4}\)) & 0.0013 \\ \(\varepsilon_{f}\) (pl/bit/m\({}^{2}\)) & 10 \\ \(E_{DA}\) (n/bit/message) & 5 \\ Radius adjustment factor \(\varepsilon\) & 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter setup. find the effect of network scale on the network lifetime, round until the last node dies, average number of packets per node and average number of CHs per round; then, different communication radiuses of sensor nodes are considered in the simulation to find the influence of communication radius on network lifetime; At last, to find the effect of node density on the network lifetime, the simulation is performed for the networks with different node densities. In the rest of this section, we begin our simulations under the case that network size ranges from 100 \(\times\) 100 to 200 \(\times\) 200 m\({}^{2}\), node density is 1 node/100 m\({}^{2}\) and communication radius is 35 m.  
The most important criterion for performance evaluation in clustering is network lifetime, which is defined as the lifespan of the node which first exhausts its energy in the network. Figure 4 gives the comparison of network lifetime versus different network sizes among LEACH, CROSS, LGCA and GTAB. From Figure 4, we can see that our proposed protocol GTAB outperforms other three protocols regarding the network lifetime for all network size cases. This is because GTAB has integrated with our proposed clustering model and game theoretical model. Specifically, by playing our clustering game each node not only acquires the equilibrium between energy cost and benefit from data transmission, but also achieves its own maximum payoff. To analyze the degree of improvement to the network lifetime for our proposed clustering model and game theoretical model, Table 3 lists the network lifetimes of LEACH, routing scheme which only using our proposed clustering model (Only-clustering) and GTAB under the case that the network size is 100 \(\times\) 100 m\({}^{2}\). From Table 3 we can find that compared with LEACH, the routing scheme that only utilizing our proposed clustering model has improved the network lifetime by 15%. After the game theory is introduced into our clustering model, the network lifetime has been improved by 26%. In addition, Figure 4 also shows that all the four protocols have reduced network lifetimes when the network size increases. This is because the average distance between CHs and BS increases with the increase of network size. We can find that the network lifetime in LGCA is shorter than that in CROSS when the network size is smaller than 150 \(\times\) 150 m\({}^{2}\), but the opposite is true when the network size is larger than 150 \(\times\) 150 m\({}^{2}\).