## 4 Simulation Results and Analysis  
In the analysis of the performance of the EDSAA, it is assumed that there is only one PU system (including one DC and one PU) and two SUs in a region grid of the MCRCS. First, the simulation of the static game is carried out with the specific parameters set as follows:  
1. Set the maximum available spectrum bandwidth of all SUs to 15 MHz; (2) Set the revenue rate of the SU's unit transfer rate \(\tau_{\text{i}}=10\); (3) Set the SNR of each SUs \(\gamma=10\) dB; (4) Set the price evaluation criteria \(\alpha=2\); (5) Set the target of BER \(B_{i}^{tar}=10^{-4}\). The best spectrum allocation curve of each SU is shown in Figure 3. In order to facilitate the comparative analysis, we set the parameter \(\
u\) to 0 to minimize the influence between SUs. As shown in Figure 3, the intersection points of the curve are the Nash equilibrium points in different cases. If there are three SUs in the region, the best spectrum allocation curve for each user is three surfaces and the Nash equilibrium point is the intersection point of the three surfaces [8]. It can be seen that the position of the Nash equilibrium is affected by the SU's detection capability (\(w_{i}\)) and the demand factor (\(\sigma_{i}\)). A stronger detection capability and greater spectrum demand of the SU result in a higher best spectrum allocation curve. On the other hand, when the SU detection capability or the spectrum demand weakens, the best spectrum allocation curve decreases. Second, in order to determine the relationship between learning factors and the convergence of the game results, we propose the corresponding dynamic game simulation verification with the simulation results shown in Figure 4. Under the condition that the detection capabilities of both sides of the game are determined, we propose each learning factor has an upper boundary in order to ensure that the game process finally converges to the stable state. As shown in Figure 4, when the two sides of the game learning factor adjustment have values in the lower left region, the game will eventually converge. However, if the value of the learning factor adjusts over the corresponding region, the game process will not converge. When the detection capability of the game users is weaker, the stability adjustment area of learning factors shrinks accordingly. Therefore, under the condition of different detection capabilities and different spectrum requirements, we analyzed the transient characteristics of the convergence of the game process. According to the above picture, the learning factors of both sides of the game are in the convergence region of \(\beta_{1}=\beta_{2}=0.6\). The simulation results are shown in Figure 5.  
Figure 4: The influence of learning factors on game stability. Figure 3: Best spectrum allocation curve and Nash equilibrium point under the static game. By analyzing the relation between the curves of Figure 5, we can obtain the following conclusions:  
1. Compared with the traditional spectrum allocation algorithm, the EDSAA based on the Cournot model has a higher convergence speed. 2. When the detection capability and the spectrum demand factor of the SUs are the same (\(w_{1}=w_{2}=1.0\) and \(\sigma_{1}=\sigma_{2}=60\)), the spectrum allocated to each user is the same at each stage of the game (represented by the blue curve). 3. When the detection capabilities of SUs are equal and their spectrum demand factors are different (\(w_{1}=w_{2}=1.0\) and \(\sigma_{1}=60,\sigma_{2}=50\)), in the steady state, the bandwidth allocated to each SU is different. The bandwidth of the SU with a large demand factor is wide, while the bandwidth of the SU with a small demand factor is narrow (represented by the red curve). 4. When the SUs' spectrum demand factors are equal and their detection capabilities are different (\(w_{1}=1.0,w_{2}=0.6\) and \(\sigma_{1}=\sigma_{2}=60\)), in the steady state, the bandwidth allocated to the SU is also different.