  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 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 due to the
non-strict concavity of the 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 with more homogeneous channel gains.
