Radio frequency energy harvesting (RFEH) is a promising technology to charge unattended Internet of Things (IoT) low-power devices remotely. To enable this, in future IoT system, besides the traditional data access points (DAPs) for collecting data, energy access points (EAPs) should be deployed to charge IoT devices to maintain their sustainable operations. Practically, the DAPs and EAPs may be operated by different operators, and the DAPs thus need to provide effective incentives to motivate the surrounding EAPs to charge their associated IoT devices. Different from existing incentive schemes, we consider a practical scenario with asymmetric information, where the DAP is not aware of the channel conditions and energy costs of the EAPs. We first extend the existing Stackelberg game-based approach with complete information to the asymmetric information scenario, where the expected utility of the DAP is defined and maximized. To deal with asymmetric information more efficiently, we then develop a contract theory-based framework, where the optimal contract is derived to maximize the DAP's expected utility as well as the social welfare. Simulations show that information asymmetry leads to severe performance degradation for the Stackelberg game-based framework, while the proposed contract theory-based approach using asymmetric information outperforms the Stackelberg game-based method with complete information. This reveals that the performance of the considered system depends largely on the market structure (i.e., whether the EAPs are allowed to optimize their received power at the IoT devices with full freedom or not) than on the information availability (i.e., the complete or asymmetric information).