In service-oriented environments, reputation-based service selection is gaining increasing prominence. We propose in this paper a social network-based approach to model and analyze trust when a given service, called customer service or customer, should select another service, called provider service or provider, in a composition scenario. Trust is modeled as a game between customer and provider services and represented in the network through two types of nodes and labelled edges linking customer nodes to each other and customer nodes to provider nodes. To analyze the different situations using a game-theoretic and mechanism design representation, each service is associated to a rational agent where decisions are based on the gaining utilities.This allows us to capture, assess and analyze the possible strategies in such a game. An overall trust assessment is provided and some interesting properties are discussed. Some simulation results are also presented.