# Game-Theoretic Power and Rate Control in IEEE 802.11\(p\) Wireless Networks
## 2 Related Work  
Vehicular wireless networks have been extensively studied in different contexts, and recently published surveys cover many of their aspects. Game theory has been widely used to analyse the interactions of competitive and cooperative behaviours in wireless networks. The applications of game theory in wireless networks have been generally investigated [7]. With the development of the fifth-generation (5G) communication technology, several recent surveys are mainly concerned with the applications of game theory in the emergingwireless communications such as the multi-access edge computing wireless networks [8] and the UAV-assisted wireless networks [9]. Joint power and rate control have been extensively studied under the game theory framework. In [10], a non-cooperative bargaining game was used for joint power and packet rate adaptation to avoid information congestion. The authors showed that the proposed joint power and rate adjustment congestion control scheme can alleviate the possible packets collisions, thus reducing the average experienced delay in queue and increasing the number of successfully delivered packets on the receiver side. The drawback of this work is that according to their analysis, the more the players, the more the introduced time and computation complexity will be brought, which raises issues of complexity and density. In [11], [PERSON] et al. proposed a power and rate control approach for Vehicle Safety Communications in order to optimise the reception performance between a pair of agents participating in the VANET. To this end, they suggest utilising the average packet Inter-Reception metric. They show that an optimal Tx power can be used for a good reception, which is independent of vehicle density. They provide a simple rate and power control algorithm, which is based on the distance of the communication. In particular, they set the Tx power according to the distance of the vehicle with the receiver, and then, they optimise the rate. Even though this work is simple to be evaluated in practical scenarios, acquiring the distance in wireless networks is ambiguous, and other metrics should replace it. In [12], [PERSON] et al. suggested a joint power and rate adaptation mechanism based on environmental parameters and context. They proposed some form of cooperative communication between vehicles, since a vehicle calculates and receives path loss and neighbouring vehicles' path loss exponents to determine its own power and then utilises the appropriate rate. The proposed algorithm adjusts the transmit power of the messages in order to reach the desired awareness ratio at the target distance. At the same time, the algorithm controls the channel load using an adaptive rate control algorithm. The major problem of this approach is the calculation of the path loss exponent of vehicles. Since we know that it can vary significantly depending on the scenario, it can be risky to make decisions based on this metric. In addition, the neighbouring communication will introduce a significant overhead in the vehicle communication, which may result in a degradation of the desired output. In [13], [PERSON] et al. proposed a joint rate and power adaptation scheme, which takes advantage of the ETSI TS technical specification for minimum beacons transmit frequency. The authors regulate the frequency of beacons and attempt to enhance awareness of the vehicles in close ranges. Moreover, they describe a mechanism to reduce the collision rate and keep the channel in a good state of utilisation. In particular, the presented scheme adapts the rate of transmission to regulate the collision rate and utilisation in terms of the channel being busy. Thereafter, power is adjusted to ensure a high level of awareness for close vehicles considered as neighbours. The binary search employment for the near-optimal channel busy rate is not explained thoroughly, providing evidence in the efficiency of their result analytically. In [14], [PERSON] et al. described an approach of rate and power control in DSRC for VANETS.