The environment is an essential component of multi-agent systems and is often used to coordinate the behaviour of individualagents. Recently many languages have been proposed to specify and implement multi-agent environments in terms of social and normative concepts. In this paper, we first introduce a formal setting of multi-agent environment which abstracts from concrete specification 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 specific normative behaviours can be enforced (or implemented) if agents follow their subjective preferences. We also consider complexity issues of associated problems.