# A Hybrid Energy Equating Game for Energy Management in the Internet of Underwater Things
## 1 Introduction
To improve the criteria of CHs selection in Reference [11], a hybrid game theory-based distributed algorithm is defined in Reference [12]. The burden on CHs increases when the member nodes are at a longer distance from the SS, so the authors consider the node degree and the node's distance from the SS when describing the payoff function. To overcome the issues of the previously designed schemes, we introduce a novel Hybrid Energy Equating Game (HEEG), which increases the network lifetime by reducing the redundant transmissions over the link while ensuring 99.9% data delivery at the SS. The spatiotemporal multi-cast and dynamic CH selections are capable of easily adjusting the floated nodes due to water current movements across the network. The data-aggregation hierarchy is simple and the data-forwarding routes are congestion free, which also helps to improve the network's lifetime. In our proposed framework, there is no need to employ all the nodes for the sensing and collecting activities. Only the selected nodes from the different directions are chosen to perform the sensing as shown in Figure 1. Consequently, the proposed framework proves to be very energy-efficient with less end-to-end delay and high delivery ratio as compared to the existing schemes. The main contributions of our proposed framework are summarized as:  
* We propose a clustering game to divide the FNs into different clusters by using the social correlation between them, which considers both energy and payoff function. * We design a non-cooperative evolutionary game-based strategy for the best relay selection, which depends upon the set of available hops and strategy space for the players. * We also prove that the next-hop strategy in the relay selection game is not invaded by any other mixed strategies. At each next hop selection, the nodes can modify their strategy until they reach a stable state. * We performed extensive simulations to evaluate the proposed approach and found that the sensor node's life relies completely on the number of transmissions, by avoiding the redundant transmission and controlling the auxiliary information so it does not circulate inside the network, the lifetime of the network can increase by 50-60%. To design HEEG, we considered all the practical aspects and found it suitable for the hardware implementation system. However, the following limitations may occur in a real-time implementation:  
* As the proposed model is redundancy-aware, sometimes the normal data in the overlapping region is considered as redundant and deleted. * In the proposed model, only selected nodes from the different directions are chosen to perform the sensing activity. So, sometimes the information from a particular region may be missed due to this selection criterion. * The proposed model supports the large-scale WSNs; however, the proposed model does not perform persuasively for very large-scale WSNs. The remainder of this paper is organized in the following way: We discuss the current literature on cluster-based schemes for IoUTs in Section 2; in Section 3, the details of energy consumption and the signal-to-noise-ratio calculation models are briefly discussed; in Section 4, each stage of the proposed model, such as the cluster head selection game and the relay selection game, are discussed in detail; in Section 5, the evaluation metrics and comparisons are described to examine our proposed model; and finally, the conclusion is drawn in Section 6.