The explosively growing demands for mobile traffic services bring both challenges and opportunities to wireless networks. Wireless network virtualization is proposed as the main evolution path toward the forthcoming fifth generation (5G) cellular networks. In this paper, we propose a software defined and virtualized (SDV) wireless network architecture for enabling multi-flow transmission with multiple infrastructure providers (InPs) and multiple mobile virtual network operators (MVNOs). In order to ensure the heterogeneity, we formulate the virtual resource allocation problem with diverse QoS requirements as a social welfare maximization problem with distance-related transaction cost. Due to hidden information of InPs and MVNOs for the auctioneer, we introduce a shadow price for ensuring desirable economic properties and total welfare for the system. Simulations are conducted with different system configurations to show the effectiveness and the energy efficiency performance of the proposed SDV wireless network framework and iterative double auction mechanism.