## 1 Introduction  
The current capabilities of communication channels, including their maximum bitrate, attempt to meet the needs of modern applications. Advancements in spectral efficiency and noise reduction have facilitated an annual growth in data rates of around 32% [1]. However, these improvements necessitate further investments in technology, costs, and energy consumption. As the demand for data and capacity continues to rise, it is crucial to explore alternative approaches for future networks. One promising avenue is the exploration of new frequencies for data transmission, particularly in the terahertz (THz) range, which spans from 300 GHz to 30 THz. This wide frequency band enables the transmission of extremely high data rates from a single source, thereby significantly improving both energy efficiency and network capacity to meet the evolving needs of communication systems. A rigorous survey regarding THz communications is given in [2]. Moreover, the work in [3] offers an in-depth analysis and technological overview of THz communications and sensing, covering key aspects such as benefits, applications, propagation characteristics, channel modeling, measurement campaigns, antennas, transceiver technologies, beamforming techniques, networking, the convergence of communication and sensing,and experimental testbeds. Furthermore, 6G is addressed with THz communications as the reader can see in [4]. THz waves present notable advantages over microwave and optical signals. They offer significantly greater bandwidth compared to microwave signals and exhibit much lower attenuation due to atmospheric disturbances such as rain and fog than optical links. Specifically, the 300 to 900 GHz frequency range is highly promising for fixed wireless links thanks to its low atmospheric attenuation and the availability of early-stage electronic circuits designed for these frequencies. However, it is important to consider that precipitation droplets and atmospheric molecules can still cause substantial scattering and attenuation of THz waves, potentially limiting the maximum achievable data rates for these wireless links [5]. Multi-hop communication in THz systems [6; 7] offers several benefits, including extended range by using intermediate nodes to relay signals, which counters the high attenuation of THz waves over a distance. It also improves connectivity in obstructed or non-line-of-sight environments, enhances network reliability through multiple data pathways, and reduces power consumption by enabling shorter transmission distances, which is particularly beneficial for battery-operated devices. Multi-hop THz communication presents several challenges and considerations. The complexity of these networks demands sophisticated routing protocols and advanced network management strategies to ensure efficient data transmission. Additionally, managing interference becomes more difficult with multiple nodes transmitting, particularly at THz frequencies where signal interference can significantly impact performance. Synchronizing intermediate nodes for efficient data relay further adds to the complexity of implementing effective multi-hop THz communication systems. In this paper, the implementation of multi-hop THz communications is explored, where multiple relay nodes are used to extend communication distances and improve signal quality. However, multi-hop communication in the THz band faces unique challenges, particularly due to interference from other devices operating in the same frequency range. Hence, interference cancellation is considered. This interference can significantly impact the quality of the communication links and the overall system performance. To address this, the problem of Transmission Power Control (TPC) is formulated using a game-theoretic approach, specifically as a potential game. In this framework, each node acts as a rational player aiming to maximize its own utility, defined in terms of its Signal-to-Interference-plus-Noise Ratio (SINR).