Network function virtualization (NFV) has been a promising approach to flexible and scalable deployment of network services. In NFV management and orchestration (NFV-MANO) architectural framework, VNF managers (VNFMs) should be deployed to manage the lifecycle of virtualized network functions (VNFs). VNFM placement problem (MPP) is to deploy VNFMs that minimizes overall operational cost while meeting performance requirements. The only existing approach to MPP is centralized and does not well adapt to network dynamics (e.g., VNFM failures, ups and downs of VNF instances, etc.) We leverage game theory to achieve distributed solutions to the MPP, which are self-adaptive in the sense that each VNFM locally and autonomously adapts to network dynamics without a central control. Simulation results show the proposed approaches can adapt to network dynamics and have lower total cost than the counterpart in large-scale NFV systems.