Abstract The environment is an essential component of multi-agent systems and is often used to coordinate the behaviour of individual agents. Recently many languages have been proposed to specify and implement multi-agent environments in terms of social and normative concepts. In this paper, we ?rst introduce a formal setting of multi-agent environment which abstracts from concrete speci?cation languages. We extend this formal setting with norms and sanctions and show how concepts from mechanism design can be used to formally analyse and verify whether speci?c normative behaviours can be enforced (or implemented) if agents follow their subjective preferences. We also consider complexity issues of associated problems.