Future wireless networks are expected to be highly heterogeneous with the co-existence of macrocells and small cells and they will also provide support for device-to-device (D2D) communication. In such muti-tier heterogeneous systems, centralized radio resource allocation and interference management schemes will not be scalable. In this work, we propose an auction-based distributed solution to allocate radio resources in a muti-tier heterogeneous network. We provide the bound of achievable data rate and show that the complexity of the proposed scheme is linear with the number of transmitter nodes and the available resources. The signaling issues (e.g., information exchange over control channels) for the proposed distributed solution is also discussed. Numerical results show the effectiveness of the proposed solution in comparison with an optimal centralized resource allocation scheme.