Wireless power transfer (WPT) technology enables a cost-effective and sustainable energy supply in wireless networks. However, the broadcast nature of wireless signals makes them non-excludable public goods, which leads to potential free-riders among energy receivers. In this study, we formulate the wireless power provision problem as a public goods provision problem, aiming to maximize the social welfare of a system of an energy transmitter (ET) and all the energy users (EUs), while considering their heterogeneous valuations, private information, and self-interested behaviors. We propose a two-phase all-or-none scheme involving a low-complexity Power And Taxation (PAT) mechanism, which ensures voluntary participation, truthfulness, budget balance, and social optimality at every Nash equilibrium (NE). We propose a distributed PAT (D-PAT) algorithm to reach an NE, and prove its convergence by connecting the structure of NEs and that of the optimal solution to a related optimization problem. We further extend the analysis to a multi-channel system, which brings a further challenge of non-strictly concave agents' payoffs. We propose a Multi-Channel PAT (M-PAT) mechanism and a distributed M-PAT (D-MPAT) algorithm to address the challenge. Simulation results show that, our design is most beneficial when there are more EUs and more homogeneous channel gains.
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