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Resource orchestration has a major impact on improving the performance of network services and reducing the system cost composed of both capital expenditures and operational expenses in network functions virtualization (NFV). In this paper, we consider the optimal resource orchestration problem in a multi-domain NFV system under the competition among multiple NFV service providers (NSPs). In particular, we analyze a game on an NFV platform where an NSP can reserve different types of resources, including the virtual computing, storage, and network resources, and the non-virtualized resources allocated by various NFV domains, for optimizing the utility in an individual manner. We also derive a necessary and sufficient condition for equilibrium under the competition among NSPs. We further investigate the equilibrium in a scenario of cooperation where NSPs build their own NFV infrastructure and join together to create a federation. Our numerical results illustrate the best response in resource reservation of a provider with respect to the strategy of other providers and the effect of the number of domains on the utility obtained by NSPs in the competition. Importantly, we demonstrate that an NSP is able to make a profit when the number of domains in an NFV infrastructure increases until a threshold, beyond which the utility of an NFV provider falls down, which is useful for designing a multi-domain NFV platform, especially in a multiprovider scenario. Another observation is that the best strategy of the NSPs in the competition is opposite to that in the scenario of cooperation, which is significant for the NSPs in the optimization of their utility.

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