Throughput Maximizing Games in the Two-Hop Relay Channel with Energy Cooperation

In this paper, we study a two-hop network where the source and the relay have data that the destination wishes to receive. The source node is not directly connected to the destination; it can send its data only via the relay. The relay node, on the other hand, does not have an external source of energy, and needs to perform RF energy harvesting from the source to send its and the source's data. Both nodes wish to send as much of their data to the destination as possible. For this setup, we first formulate a noncooperative game and improve upon its equilibrium by using a pricing scheme. Next, we model the communication setup as a Stackelberg game with the relay node as the leader and the source node as the follower of the game. We analyze the resulting equilibrium and interpret how the leader of the game chooses its strategy in order to influence the follower's decision. We provide numerical examples which compare the payoffs achieved by these equilibria. We investigate the impact of the model parameters on the decisions of the two players and the achieved payoffs. We observe that at the Stackelberg equilibrium, the leader of the game can manipulate the follower in order to achieve a higher payoff than it would at the social optimum.