# Context-Aware Caching Distribution and UAV Deployment: A Game-Theoretic Approach
## 3 UAV-Assisted Caching Game
### Log-Linear Caching Algorithm
Here we consider that the number of system files is \(|f|=6\), and there are UAVs available to serve the users, i.e., \(N=8\). Moreover, the cache space of UAVs is \(|c_{n}|=3\). At the end of iteration, the performance of UAV-assisted networks will finally converge. In addition, the final performance is near to the best NE, which is the best one of 1000 independent trials based on the proposed algorithm. The simulation result validates its convergence and the effectiveness of the proposed algorithm. ### Performance Analysis

#### 4.3.1 Performance of UAV-Assisted Networks versus the Number of System Files

Considering the change of the number of system files, we compare the performance of UAV-assisted networks applying four algorithms, i.e., the random selection, best NE, worst NE, and the proposed algorithm. We run the random selection algorithm 1000 times and choose the average value as the final result of the random selection algorithm. Similarly, we carry out 1000 independent trials using the proposed log-linear caching algorithm. Actually, each convergent value is a NE solution. Then the average of values is defined as the final value. In addition, we choose the best one and the worst one of the values as the best NE and the worst NE, respectively. Figure 3 depicts the performance of UAV-assisted networks when varying the number of system files from \(|f|=4\) to \(|f|=8\). Several important observations can be seen in this figure: (1) the performance of UAV-assisted networks decreases as the number of system files increases. (2) Compared with the random algorithm, the log-linear caching algorithm brings the better performance of UAV-assisted networks. (3) As a result of the limited UAVs' processing capacity, when the number of system files increases, users' requests become more complex, which leads to a decline in performance. Figure 3: The performance of UAV-assisted networks versus the number of system files (\(N=8\) and \(|c_{n}|=3\)). Figure 2: The convergence of the proposed algorithm (\(|f|=6\), \(N=8\) and \(|c_{n}|=3\)). #### 4.3.2 Performance of UAV-Assisted Networks versus the Number of Cache Space

We assess the performance of UAV-assisted networks when changing the number of cache space from \(|c_{n}|=3\) to \(|c_{n}|=6\). Figure 4 reflects the final results applying four approaches. The simulation process is similar to Figure 3. From Figure 4, the simulation curves reflect the fact that: (1) The performance of UAV-assisted networks increases as the cache space of UAVs increases. The reason is that greater cache space brings high processing capacity of UAVs, which leads to an increase in performance. (2) The log-linear caching algorithm is close to the best NE and outperforms the random selection algorithm which validate the effectiveness of the proposed algorithm. #### 4.3.3 Performance of UAV-Assisted Networks versus the Number of UAVs

Considering the number of UAVs varying from \(N=5\) to \(N=8\), we compare the performance of UAV-assisted networks. Figure 5 indicates the influence of the number of UAVs on the performance of UAV-assisted networks. The fact is reflected from the simulation curves: in general, as the number of UAVs increases, the performance of UAV-assisted networks increases. The reasonable explanation is that more UAVs yield a larger successful communication probability. Additionally, the final performance of the proposed algorithm is close to the best NE with respect to different numbers of UAVs, which again validates the proposed algorithm. Figure 4: The performance of UAV-assisted networks versus the size of cache space of UAVs (\(|f|=6\) and \(N=8\)). Figure 5: The performance of UAV-assisted networks versus the number of UAVs in service (\(|f|=6\) and \(|c_{n}|=3\)). ## 5 Conclusions

In this paper, the problem of the optimal arrangement for both UAV's caching contents and service locations in UAV-assisted networks was investigated. We modeled the problem as a UAV-assisted caching game with LCA.