Relay-Centric Two-Hop Networks with Asymmetric Wireless Energy Transfer: Stackelberg Games

This paper studies two-hop networks with wireless energy transfer (WET) consisting of one source and multiple relay-destination pairs. We focus on relays' primary interest of sending their own messages to the associated destinations. As an incentive for relaying, WET is offered by the source to relays who forward source data as a return. We propose an asymmetric WET (AWET) model, where relays receive source signals one by one but those waiting longer are able to accumulate more energy by harvesting from earlier signals. We also consider symmetric WET, broadcast WET, and independent WET for comparison, where source signals can either be harvested by all relays via time-division, or via broadcasting, or harvested by intended relays exclusively. We adopt the framework of Stackelberg game to capture the self-interest and hierarchically competing nature of nodes. The relay-destination pairs play as leaders and the source-destination pairs as followers. The existence and the uniqueness of the Stackelberg equilibrium (SE) are shown, and a best-response-based algorithm that achieves the SE is provided. Simulation results demonstrate that the AWET protocol outperforms the others.