A multi-leader stackelberg game for two-hop systems with wireless energy transfer

We study a two-hop network with wireless energy transfer (WET) from the source to multiple energy harvesting relays. Both the source and relays intend to transmit dedicated information to the destination. The source, without direct reliable channels to the destination, needs the relays to forward signals, while the relays are short of energy and have to harvest energy from the source to transmit their own data and relaying the source's data. Relays use time division to harvest then transmit. For the multiple access channel (MAC) from the relays to the destination, we consider both time division multiple access (TDMA) between the relays and simultaneous transmission (ST) by all relays. The source and the relays are all selfish and aim to maximize their own utility. We take a game theoretic viewpoint to model the hierarchical competition between the source and the relays. In particular, multi-leader Stackelberg games are formulated where the relays play as the leaders and the source plays as the follower. The existence and the uniqueness of Stackelberg equilibrium (SE) are analyzed, based on which algorithms are proposed to achieve the SE. The numerical results verify that the proposed algorithms improve the system performance comparing to the baseline scheme.