# A Hybrid Energy Equating Game for Energy Management in the Internet of Underwater Things
## 1 Introduction  
The Internet of Underwater Things (IoUTs) is regarded as a technological revolution of communication and computing and is defined as a network of smart inter-connected underwater objects [1; 2; 3]. To support the idea of IoUT, Underwater Sensor Networks (USNs) are considered an emerging technology, which enables us to monitor the underwater environment, underwater exploration and disaster prevention in real-time [4; 5]. The characteristics of USNs differ from territorial sensor networks in many ways such as transmission media, transmission range, propagation speed, and transmission rate. Most of the recent studies take into account problems like the lack of bandwidth, end-to-end delay and reliability, while a few of them consider dynamic network topology [1; 6]. However, energy limitation is another point of concern for IoUT as the recharging cost of the Field Nodes (FNs) batteries deployed in the underwater environment is very high. Only this limited energy goal can be achieved by designing a protocol, which successfully reduces the number of transmissions and selects a reliable and congestion-free route for data delivery to minimize network energy consumption. Recently, Game Theory (GT) is emerging as an influential tool to solve and investigate the energy management, Cluster Head (CH) selection and routing decisions issues. GT is widely applied in IoUTs algorithms to predict the behavior of FNs and to manage the FNs in USN under critical situations [7; 8]. A two-level classical and evolutionary GT is applied to improve the uneven energy consumption forroute and CH selection [8]. These two-levels are wedge-level and node-level, which are used to balance the energy at CH and node-level, respectively. Each FN is regarded as a rational decision-maker in USN and individually plays its smart game. Each player selfishly makes its decisions, which depends on its own interests. GT is very helpful in finding an equilibrium solution from the available strategies and very suitable for making decisions for the FNs. Each FN can freely make its own decisions for rendering its services as CH/FN or it has a choice to adopt a route because there is no incentive to deviate from the selected strategy [7]. However, achieving an equilibrium strategy and maximizing the payoff for each FN is not completely considered to date. A territory game theoretical clustering protocol is discussed in Reference [9]; the entire sensing field is distributed into four equivalent regions like A, B, C and D. The multi-hop communication is used to forward the data from FNs to the Surface Sink (SS). The FNs in the closer regions have a higher probability to be selected as CHs. The authors tried to optimize the number of CHs from the neighboring region through an evolutionary game. This strategy slightly improves the performance by distributing the energy load on the entire network; however, due to the CH selection limit, the network lifetime is affected badly in dense and large-scale networks. Clustered routing for selfish sensors is discussed in Reference [10], the GT is applied to investigate the behavior of the CHs. As the CHs spend much more energy compared to the FNs, so the FN with low-energy can only render their services as a normal node. However, if each FN declines to be the CH, then limited nodes offer their services as CH. Consequently, these limited selected CHs cannot properly convey the data of all the FNs in the network to the SS, which leads to ending the network lifetime earlier. An algorithm is designed in Reference [11], to tackle the issue that all the FNs in the Network Sensing Field (NSF) can exchange control packets that are not feasible for practical applications. The FNs in Reference [11] are only restricted to play a greedy selfish game with their local neighbors and only a restricted number of CHs are chosen from a certain territory. However, the utility function and a payoff function for adopting different strategies are not defined properly.