Recent advance of Network Function Virtualization (NFV) enables deployment of NFV-based network services on a cloud-base infrastructure. Meanwhile, edge computing provides cloud infrastructure on the the edge of access network to serve end user. This paper proposes a decentralized market-based framework that matches independent network service providers (NSPs) with independent edge service providers (ESPs) for possible deployments of network services with associated payments. The framework benefits all participants by guaranteeing that the results are profitable for all participants: no NSP or ESP can be better off by dropping out of the match result. Simulation results indicate that the proposed approach had the highest average number of deployed network services compared with counterparts.