Abstract-In heterogeneous ultra-dense networks (HetUDNs), the software-defined wireless network (SDWN) separates resource management from the geo-distributed resources belonging to different service providers. Through a centralized SDWN controller, the operation of the entire network can be managed in a global manner. In this work, we focus on mobile traffic offloading and resource allocation in the SDWN-based HetUDNs, which is constituted of heterogeneous macro base stations (MBSs) and small-cell base stations (SBSs). We explore a scenario where the capacity of the SBSs is accessible, but their expected performance for offloading cannot be known to the SDWN controller, which is the information asymmetric case. To address this asymmetry, a bundle of incentive traffic offloading contracts is designed, to encourage each SBS to select the contract specifically designed to achieve its own maximum net utility. Meanwhile, the MBS utility and social welfare can also be optimized, in comparison to the situation without information asymmetry. To aggregate the characteristics of large numbers of SBSs in HetUDNs, we develop an analytical model that characterizes the SBS type based on different contracts which can be designed with individual rationality and incentive compatibility. This leads to an analytical expression in closed-form for SBS type which we validate mathematically and by simulations, and observe that the monotonicity and incentive compatibility of contracts are ensured. The effectiveness and efficiency of the contract-based traffic offloading mechanism that we design, and the overall system performance are also validated with simulation results.