# Evolutionary Game for Content Cache in a mm-Wave-Based Vehicular Fog
## 5 Experiments
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Freq & 60 & \(\mathrm{GHz}\) \\ BW & 2 & \(\mathrm{GHz}\) \\ \(P_{t}\) & 12 & \(\mathrm{dBm}\) \\ d & 20 & meter \\ NF & 3 & \(\mathrm{dB}\) \\ IL + CB & 27 & \(\mathrm{dB}\) \\ \(L_{w}\) & 3 & meter \\ \(L_{v}\) & 4 & meter \\ Max lanes & 40 & – \\ \(\gamma\) & 0.2 & – \\ \(\alpha_{L}\) & 2 & – \\ \(\alpha_{N}\) & 4 & – \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters. From the above experimental results, we can conclude that narrow beam-forming is helpful for increasing connectivity. More caches can reduce interference, especially for a high SINR threshold. However, both approaches have a limitation in improving connectivity at a given vehicle density. Accordingly, the number of cached vehicles needs to be decided to achieve optimal connectivity within the vehicular fog. In previous experiments, we were not concerned with the cost for content caching. Thus, the utility of cooperative or defective vehicles is investigated in Figure 10. Here the number of sectors, vehicle density and SINR threshold are configured as 12, \(\lambda=\)9 \(\times\) 10\({}^{-4}\) and 12 dB, respectively. For the payoff function of cooperation and defection, cost value is \(\tau=0.5\) and downloading data rate is \(\delta=10\). In Figure 9(a), utility curves of both cooperation and defection are convex with an increasing number of cooperative sectors. Figure 9(b) depicts average utility with normalized \(\delta=1\) defined by Equations (31) and (32), where the number of cooperation sectors is one more than defection. Cooperation utility is little bit higher with low cooperation probability, \(p_{c}\), but lower with high \(p_{c}\) tha  
Figure 8: Connectivity (\(P_{c}\)) versus number of sectors with threshold \(T=10\) dB. Figure 7: Connectivity (\(P_{c}\)) versus vehicle densities with threshold \(T=10\) dB. Figure 9: Connectivity (\(P_{c}\)) versus \(k\) among \(S=12\) sectors. Accordingly, a vehicle probably chooses a cooperation strategy in lower \(p_{c}\) while a defection strategy in high \(p_{c}\). Figure 10c shows comparison of the average utility of defection and cooperation with different costs, \(\tau\). In the figure, the marked line indicates defection utility and other lines are for cooperation. The average utility of cooperation is higher than the defection with a lower cost when the cooperation proportion \(p_{c}\) is low. For instance, if \(\tau<0.7\), the cooperation payoff is higher than defection until \(p_{c}=0.2\). With \(p_{c}=0.3\), the cost \(\tau<0.5\) can be acceptable for vehicles to choose a cooperation strategy. The cooperation strategy is not attractive as the \(p_{c}\) increases since connectivity does not increase notably after a certain number of caches as shown in Figure 9. Accordingly, vehicles prefer to select a defection strategy if either the \(p_{c}\) or cost \(\tau\) is high. Figure 11 shows evolution of \(p_{c}\) into the ESS using global strategy information for the cost \(\tau\) from 0.1 to 0.9 when the payoff of strategy follows the Figure 10c. For this, a vehicle chooses its own strategy based on the global information using the replicator dynamics of Equation (33) and broadcasts its selection as the centralized algorithm. Here, we use two different initial \(p_{c}=0.2\) and 0.8 with evolution speed, \(\eta\) is 1. According to the cost \(\tau\), \(p_{c}\) of the ESS is 1, 0.4, 0.2, 0.1 and 0, respectively. Regardless of the initial \(p_{c}\), \(p_{c}^{*}\) of the ESS is same as shown in Figure 11a,b. Evolution for the cost \(\tau=0.1\) is slower than others since the difference between \(U_{D}\) and \(U_{C}\) becomes smaller as the \(p_{c}\) increases. To exploit strategy convergence with different evolution speed, the \(\eta\) value is configured from 5 to 50 as shown in Figure 11c. The \(p_{c}\) increases faster with the higher \(\eta\) values from the initial \(p_{c}=0.2\).