Relay Incentive Mechanisms Using Wireless Power Transfer in Non-Cooperative Networks

The advances of 6G systems have prompted the study of new communication paradigms, including relay networks enabled by wireless power transfer (WPT). While existing literature focuses on the cooperative case, this paper examines a non-cooperative scenario in which a source must incentivize one of several battery-powered user equipments (UEs) to act as a relay by offering payment in the form of WPT, while the utility-maximizing UEs seeking to extract as much energy from the source as possible. We propose a protocol based on a reverse auction that enables the source to determine which candidate UE to select as the relay and the amount of energy to be transferred as payment, even when the channel quality between the candidates and the destination is unknown to the source. We first examine the performance of the system under the classical Vickrey auction. We prove that our protocol achieves the best possible outage probability and point out ways to mitigate the gap in energy efficiency when compared to a cooperative baseline. We then analyze system performance under a Myerson auction, which maximizes the auctioneer’s utility. To ensure computational tractability, we extend the forward auction regularity condition to the reverse setting, providing a mathematical characterization of regularity and the associated pricing mechanism. We then prove the regularity of the WPT-based auction under both lognormal and Rayleigh fading. To validate our analytical findings, we present extensive numerical results demonstrating how system parameters affect energy efficiency and outage probability. Our results show that auction-based protocols can reduce both outage probability and communication energy by more than 50% with as few as two relay candidates, compared to direct transmission by the source. Additionally, they demonstrate exponential convergence to the cooperative lower performance bound and indicate conditions under which one auction type is preferred over the other. Overall, the auction-based system offers a foundation for improved energy efficiency and communication reliability in non-cooperative environments.