## 4 Results and Discussions  
Having investigated the game theoretical aspect of the proposed schemes in Section 2, let us now evaluate our simulation results. The first set of simulations consider \(N=3\) CJs, where the positions of \(CJ_{2}\) and \(CJ_{3}\) are fixed, while the impact of changing the location of \(CJ_{1}\) (mobile jammer) is investigated. The (\(x\), \(y\)) location coordinates of of \(S\), \(R\), \(CJ_{2}\), \(CJ_{3}\) and \(D\) are given at the caption of the figures. In this scenario, the pathloss exponent was chosen to be \(\rho=4\), with \(P_{s}/N_{0}=\overline{P}_{CJ_{i}}=10\) (mW) and \(c=0.25\) (bit/s/Hz/mW). The jammers' destinations are considered to be a fraction of the distance between the \(S\) and \(D\), i.e., \(d_{j}=d_{sd}/4\) from its jammer transmitter location, where \(d_{sd}\) is the distance between \(S\) to \(D\) and is measures in meters. In order to compare UR-MCJST and UR-MCJTDT scenarios when the \(\alpha\) and \(\beta\) values are fixed, we set the \(\alpha\) and \(\beta\) values to 0.65 and 1, respectively, in this first set of simulations. Figure 4 illustrates the secrecy rate and the corresponding utility rate for the sender \(S\) and the cooperative jammer \(CJ_{i}\) in the case of the UR-MCJST scenario employed by the jammers. On the other hand, Figure 5 shows the secrecy rate and the corresponding utility rate when the jammers adopt the UR-MCJTDT scenario. We found from Figure 4a that the secrecy rate drops to 1.2042 (bit/s/Hz) and 1.43 (bit/s/Hz) when \(CJ_{1}\) gets closer to \(CJ_{2}\) at (22,43) and \(CJ_{3}\) at (26,50), respectively, in the UR-MCJST scenario. This is due to high interference levels at the jammers' destination, i.e., when the interference matrix \(\mathbf{H}\) is no longer strictly diagonally dominant. Since the power used during the third phase has to be small when two CJs are close to each other, the jamming power used during the first phase also needs to be small because we have \(\beta=1\). When the jamming power used during the first phase is small, the achievable rate by the untrusted relay would be higher, which would result in a low secrecy rate for the PU. Similarly, the utility rate of \(CJ_{1}\) also drops when it is closer to \(CJ_{2}\) or \(CJ_{3}\) due to the use of lower power during the third phase. As expected, this effect is mitigated in the UR-MCJTDT scenario, as seen in Figure 5a, because the transmission power of each CJ causes no interference to other CJs during the third transmission phase. Note that there is another drop in the secrecy rate when \(CJ_{1}\) gets closer to \(R\), which gives a secrecy rate of 1.3951 (bit/s/Hz) and 1.3983 (bit/s/Hz) at location (25,25) for Figures 4a and 5a, respectively. However, after considering all factors including the effect of the locations of CJ's destination nodes, a local minimum of the secrecy rate (of value 1.3883 (bit/s/Hz)) is located at (23,23) in Figure 4a. Similarly, Figure 5a also shows a minimum value of 1.3901 (bit/s/Hz) at location (23,23). This is due to the fact that the jamming signals would form part of the amplification factor, as seen in (10), which will be forwarded to the destination node, as shown in (13). As we note from the secrecy rate region of the UR-MCJTDT scenario depicted in Figure 5a, the best location for \(CJ_{1}\) is farther away from the relay node, while the effect of the other CJs' locations is negligible compared to that of the UR-MCJST scenario shown in Figure 4a. Furthermore, the utility rate of the UR-MCJTDT scenario is not affected by the relay location because the relayed signal during the second phase is independent of the third-phase transmission. Note that the utility rate of \(CJ_{1}\) in the UR-MCJTDT scenario is constant and is higher than that of the UR-MCJST scenario, as seen in Figures 4b and 5b. Our second set of simulations explores the effect of increasing the number of CJs, i.e., \(N\), when both the Stackelberg game and power control game were invoked for optimal performance.