Directional wireless power transfer (WPT) technology provides a promising energy solution to remotely recharge the Internet of things sensors using directional antennas. Under a harvest-then-transmit protocol, the access point can adaptively allocate the transmit power among multiple energy directions to maximize the social welfare of the sensors, i.e., downlink sum received energy or uplink sum rate, based on full or quantized channel gains reported from the sensors. However, such power allocation can be challenged if each sensor belongs to a different agent and works in a competitive way. In order to maximize their own utilities, the sensors have the incentives to falsely report their channel gains, which unfortunately reduces the social welfare. To tackle this problem, we design the strategy-proof mechanisms to ensure that each sensor’s dominant strategy is to truthfully reveal its channel gain regardless of other sensors’ strategies. Under the benchmark full channel gain reporting (CGR) scheme, we adopt the Vickrey-Clarke-Groves (VCG) mechanism to derive the price functions for both downlink and uplink, where the truthfulness is guaranteed by asking each sensor to pay the social welfare loss of all other sensors attributable to its presence. For the 1-bit CGR scheme, the problem is more challenging due to the severe information asymmetry, where each sensor has true valuation of full channel gain but may report the false information of quantized channel gain. We prove that the classic VCG mechanism is no longer truthful and then propose two threshold-based price functions for both downlink and uplink, where the truthfulness is ensured by letting each sensor pay its own achievable utility improvement due to its participation. The numerical results validate the truthfulness of the proposed mechanism designs