In this paper we propose and evaluate an auction-based resource allocation mechanism in a cloud-based radio access network (C-RAN), where the spectrum is managed by several mobile virtual network operators (MVNOs) and the physical resource is owned by the C-RAN operator. Technically, our approach consists of two coupled auctions in a hierarchical way: the lower-level auction between end users and the virtual operators and the higher-level one between MVNOs and the C-RAN operator. The proposed auction-based approach satisfies fundamental economic properties such as truthfulness. We also numerically analyze the auction results in several typical network settings, considering both homogeneous and heterogeneous resource demands