## 6 Results  
The evaluated metrics, such as SINR = and the potential function, align with the proposed work's motivation by directly assessing the impact of interference cancellation in wireless communication systems. The code compares two scenarios, namely one with SIC and the other without SIC. By tracking the evolution of transmission powers and utilities (SINR) over iterations, the metrics provide insight into the system's stability and performance under interference. The game formulations dictate that the devices attempt to maximise their utilities in a competitive manner and the unilateral deviation of the Potential Game ensures the existence of a Nash equilibrium. Interference cancellation in the provided work is demonstrated through the SIC model, where each player decodes only their own signal while treating interference from others as noise. This is reflected in the utility function, where SINR is calculated as the ratio of the player's own signal to the interference and noise. The SIC model leads to higher SINR values compared to the non-SIC model, where interference is not canceled. The implemented code simulates the performance of a multi-player communication network over 300 iterations, where players adjust their transmission powers to optimize their Signal-to-Interference-plus-Noise Ratio (SINR). There are five players with random channel gains ranging from 0.5 to 2.0. Two utility calculation models are implemented, namely, SIC, where players decode only their signals, and non-SIC, where interference from all signals is considered. Players update their transmission powers iteratively using a gradient-based approach, influenced by a step size of 0.1 and bounded within 5 to 15 dB. Random fluctuations are added to transmission powers to introduce variability, and convergence is defined by changes in power levels being below \(10^{-3}\). The potential function depicted in Figure 2 shows the potential function with SIC and non-SIC. It is clear that the potential function is higher when using the SIC-based potential game with the value being 1.72 as opposed to non-SIC, which is 1.26. Thereafter, the transmission power evolution of the players with SIC and non-SIC is illustrated in Figure 3. Nash equilibrium transmission powers that correspond to near-optimal receiver powers are those where no player finds it beneficial to unilaterally deviate from their chosen power level, considering the strategies of the other players. There are cases in which the transmission power level of certain nodes exhibit a higher value with SIC as opposed to non-SIC. Moreover, the opposite is also shown. More specifically, the transmission power levels of each player/node are given in Table 1. The difference is mainly caused by the interference whereby the players increase their transmission power levels to accomplish a higher SINR. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Player** & **SIC (Final Transmission Power)** & **No SIC (Final Transmission Power)** \\ \hline Player 1 & 11.4764 & 12.3867 \\ Player 2 & 12.3635 & 10.8294 \\ Player 3 & 10.7411 & 10.8689 \\ Player 4 & 12.1847 & 11.2238 \\ Player 5 & 9.7110 & 11.0607 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Final transmission powers for each player (linear scale). Figure 2: Potential function value (SIC and non-SIC). The final transmission powers at equilibrium differ, reflecting the sensitivity of the equilibrium to initial conditions and the interaction dynamics among the players. This outcome underscores the complex interplay between the initial power configuration, the iterative optimization process, and the convergence towards a Nash Equilibrium. While the potential function provides a valuable measure of the overall system utility, the Nash Equilibrium captures the strategic stability of the system under the given conditions. In Figure 4, the reader can observe the final utilities based on the SINR over the iterations. It is evident that the SIC method achieves a higher utility.