# A Coalition Formation Game Approach for Efficient Cooperative Multi-UAV Deployment
## 4 Simulation Results and Discussion
### Basic Performance  
In order to better reflect the performance of the proposed approach in UAVs' coverage deployment and coalition formation, we introduce the coverage reward based deployment approach for comparison. In the comparison approach, the coverage utility only depends on the mission reward and there is no coalition formation mechanism. In order to achieve better contrast, we assume that the coverage reward under the comparison approach converges to that of the proposed approach. Under this premise, we evaluate the overall energy consumption and coverage utility for the specific mission area showed in Figure 2a. As mentioned above, the weight coefficient \(\rho\) is the parameter that needs to be calculated and measured from parameters of UAVs and mission environment. For convenience, performance comparisons considering different weight coefficients are paid as reference. To prevent contingency, both algorithms are performed on 100 independent trials; then, the mean results are acquired. Here, we observe some important results from the figures and draw conclusions from the analysis. Figure 3a,b demonstrates the comparison results. In Figure 3a, as the weight coefficient \(\rho\) scales up in the beginning, the overall coverage reward \(U_{\mathcal{N}}\) of the proposed approach decreases due to the increased importance of energy consumption. Meanwhile, the overall reward of comparison approach tends to be the same as \(U_{\mathcal{N}}\), as can be expected. In particular, in the late stage (  
Figure 2: The diagram of 10 UAV deployment and coalition formations under the proposed algorithm: (**a**) Color-coded display of the density map for the mission area; (**b**) UAV deployment and coalition formations with \(\rho=0.1\times 10^{-5}\); (**c**) UAV deployment and coalition formations with \(\rho=1\times 10^{-5}\); (**d**) UAV deployment and coalition formations with \(\rho=2.5\times 10^{-5}\). \(4.5\times 10^{-5}\)), UAVs are no longer keen to cover high-yielding areas since the importance of energy consumption is extremely high, which makes UAVs form a stable deployment state. In Figure 2(b), the comparison result shows that the proposed approach can achieve a lower energy consumption \(E_{0}\). We analyse that the existence of coalition formation mechanism makes the energy consumption of the proposed approach much less than that of the comparison approach. As the weight coefficient scales up, \(E_{0}\) decreases rapidly at first. It suggests that the whole UAV network has a bigger tendency to form coalitions when the weight coefficient increases. Another discovery is that, as weight coefficient \(\rho\) scales up, energy consumption under the coalition formation mechanism tends to be steady due to the limited data traffic UAV collection. According to the above results and Equation (6), the comparison of coverage utility is shown in Figure 4, which is an important indicator of the whole UAV network. This figure shows that coverage utility under all approaches decreases as the weighting coefficient increases in the beginning, while the proposed approach can achieve higher coverage utility under the same weight coefficient. This suggests that, without a guarantee of coalition formation mechanism, the system will obtain a fair reward, but, at the same time, needs more energy consumption, so that the coverage utility is less. Likewise, in the late stage (\(\rho=3.5\times 10^{-5}\sim 4.5\times 10^{-5}\)), the coverage utility of the proposed approach tends to be stable since the coverage reward and energy consumption is in a stable state. Figure 4(a),b shows changes in overall coverage reward and overall coverage utility for different numbers of UAVs, respectively. From the figure, we observe that the coverage performance improves as the number of UAVs increases, which are consistent with the fact that more UAVs are able to collect more data information from the ground. However, when the number of UAVs reaches a certain number, the increase in coverage utility will slow down until eventually declining.