Relay-centric two-hop networks with asymmetric wireless energy transfer: A multi-leader-follower stackelberg game

This paper studies a two-hop network with wireless energy transfer consisting of one source, multiple relays, and multiple destinations. The relays' main objective is to communicate their own messages to their own destinations. The message of each relay is transmitted to its associated destination along with the source's information that is intended for the same destination. As an incentive for relaying, the source offers wireless energy transfer to the relays via radio frequency signals. The relays harvest energy and receive information one by one. The relays that are further down in the order in which they are powered incur delay, but are able to harvest from previous time slots and thus are able to accumulate more energy until it is their turn to transmit, thus establishing an energy-delay trade-off. We formulate a multi-leader-follower Stackelberg game to capture the self-interest and hierarchically competing nature of the nodes. The relay-destination pairs play as leaders and the source-destination pairs as followers. We incorporate data rate, energy cost and delay in the utility functions. The existence and the uniqueness of the Stackelberg equilibrium (SE) are proved, and two algorithms that achieve SE in centralized and distributed fashion are provided. Numerical results verify analytical findings.