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Network function virtualization is an emerging network resource utilization approach which decouples network functions from proprietary hardware and enables adaptive services to end-user requests. To accommodate the network function requests, network function instances are created and deployed at runtime. In this paper, we study a network virtualization scheme to orchestrate and manage networking and network function services. We propose an integrated design for network function instance allocation and end-to-end demand realization sharing the same physical substrate network and demonstrate that the corresponding network design problem is NP complete. A mixed-integer programming formulation is proposed first to find its optimal solution, followed by a two-player pure-strategy game model which captures the competition on physical resources between network function instance allocation and …