Energy efficiency is an important managerial variable in service business models. Cloud computing advocates the innovation and design of open software services. How the supply of energy-aware software services affects the outsourcing strategies of IT businesses, however, is still not known. This research is concerned with the formation of green virtual organisations (GVOs). Such GVOs foster novel business models to enable the commercialisation of "green" software services. We approach the formation problem from a game-theoretic perspective, which provides well suited models for analysing sourcing strategies of service customers. For analysing the formation, we particularly study the social welfare by examining the economic and ecological efficiency of the GVO as a whole. The contribution of our research is an agent-based GVO formation mechanism that optimises the social welfare of service providers and customers. We demonstrate the efficacy of the proposed artifact in a set of simulation experiments.