## 8 Conclusions  
This paper investigates the field of multi-hop Terahertz (THz) communications, focusing on its integration into modern communication networks while addressing its inherent challenges, particularly the susceptibility to interference from neighboring devices operating within the same frequency spectrum. As multi-hop THz communications are expected to play a critical role in future wireless networks due to their potential for ultra-high-speed data transmission, managing interference becomes a pivotal challenge in ensuring reliable and efficient communication over multiple hops. A key issue addressed in this context is the Transmission Power Control (TPC) problem, which directly influences the Signal-to-Interference-plus-Noise Ratio (SINR) and, consequently, the overall network performance. To effectively address this challenge, the paper introduces an innovative approach that leverages game theory to model TPC as a potential game. This game-theoretic formulation offers several advantages, including the ability to represent the network as a system of rational players (nodes) that individually aim to maximize their utility (SINR). Through this approach, it is guaranteed that the system will converge to a Nash equilibrium, a stable state in which no node has the incentive to unilaterally alter its transmission power. The convergence to Nash equilibrium, coupled with the potential game framework, ensures that the network collectively optimizes power allocation, thus enhancing overall performance. We also give bounds for the PoA and PoS. The effectiveness of this proposed approach is thoroughly validated through a series of comprehensive simulations, which provide evidence of its ability to improve the performance and reliability of multi-hop THz communication networks. The results show that the system not only achieves higher power allocations but also effectively accomplishes higher utilities with SIC, leading to enhanced SINRs and a more efficient use of network resources. The simulations further highlight the potential of this approach in future multi-hop THz deployments, particularly in scenarios where interference management is critical for maintaining high data rates and low latency. In terms of future work, several key directions are proposed to extend and refine the current methodology. One of the primary objectives is to introduce discrete strategies into the current TPC problem, transitioning from continuous to discrete action spaces, which may more accurately reflect real-world constraints in THz communications. In discrete strategies, the problem becomes more challenging due to the nature of the mathematical formulation. The utilization of Schur concavity may be utilized to provide an optimal solution. Also, as the strategies increase, the problem may become intractable or insufficient for practical implementations. Additionally, the use of concavity in the utility functions will be explored to provide tighter bounds on the solution space, ensuring more robust guarantees for system performance. Another important aspect of future research is the investigation of compact strategy spaces, which could simplify the analysis and computation of equilibria. Finally, the paper aims to investigate the conditions for equilibrium uniqueness in the current framework, ensuring that the Nash equilibrium is not only stable but also unique, which would further solidify the predictability and reliability of the proposed TPC solution. Moreover, a more inclusive utility function will be considered, incorporating energy-efficiency and fairness in the given problem. This may give significant insights into the continuation of the proposed scheme. Moreover, an additional stability analysis, considering varying interference intensities and node densities, could further validate the robustness and adaptability of their approach under diverse network conditions. Methodology, E.D.S. ; Software, E.D.S. ; Validation, E.D.S. ; Formal analysis, E.D.S. ; Writing - original draft, E.D.S. ; Writing - review & editing, V.K. and C.S.