## 3 Verification and Analysis
### Typical Scenario Analysis
This frequency was interfered with only 50 times by the blue team agent, yielding an interference probability of 22.73%. From the above statistical analysis, it is evident that the red team agent, using the  
Figure 5: Detailed working status of game adversarial agents. MCCFR algorithm in 100 simulation runs, can avoid interference from the frequency bands selected by the blue team attacking agents, thereby reducing the probability of interference. Figure 6: Comparison of interference counts for red team defensive agents based on the MCCFR and MC strategy. Figure 7: Comparison of jamming failures for blue team attacking agents based on the MCCFR and MC strategy. Figure 9 illustrates the number of times the blue team agent selecting specific frequency bands for interference and the number of successful interference events for those bands. It can be observed that the blue team agent most frequently selects the 300 MHz to 1000 MHz band for interference, with a total of 346 selections, accounting for 43.25% of all frequency band choices. Successful interference occurs 135 times in this band, resulting in an interference percentage of 39.02%. The next most frequently selected band is 1000 MHz to 3000 MHz, chosen 264 times, representing 33.00% of all selections. Successful interference in this band occurs 99 times, yielding an interference percentage of 37.5%. The blue team intelligent agent selects the 30 MHz to 300 MHz band for interference the least frequently, with only 190 selections, which accounts for 23.75% of all frequency band choices. Successful interference in this band occurs 64 times, resulting in an interference percentage of 33.69%. The statistical results indicate that there is a direct proportionality between the number of times the blue team intelligent agent selecting a frequency band for interference and the interference percentage, demonstrating that the MCCFR algorithm effectively optimized the choice of interference bands. Figure 8: Histogram of frequency selection counts and interference counts for red team agents based on the MCCFR strategy. Figure 9: The statistics of frequency selection counts and successful interference counts for the blue team agent based on the MCCFR strategy. Figure 10 displays the statistics of interference and interference probability for both the red team defense and the blue team attack in a multi-player incomplete information game. It can be observed that the probability of interference experienced by the red team defensive agent is 32.5%, which is lower than the interference probability of the attacking agents at 37.3%. This discrepancy is primarily due to the overlap in frequency band selections among the eight attacking agents on the blue team, leading to two or more attacking agents interfering with the same defensive agent. Table 7 presents a comparison of convergence times. It can be observed that the simulation time for a multi-player incomplete information game, the single simulation time is 6.28 s, and the average time for 100 iterations of the algorithm is 3.06 s. This indicates that the MCCFR-based mixed strategy game algorithm exhibits the advantage of faster convergence. The reason why the time for a single simulation is longer than running 100 simulations is mainly because the program needs to be initialized and third-party libraries need to be loaded before the simulation starts, which consumes a lot of time. In multiple simulations, the program and third-party libraries only need to be initialized and loaded during the first simulation, so the average time for multiple simulations is less than that for a single simulation.