The traditional representations of games using the extensive form or the strategic (normal) form obscure much of the structure that is present in real-world games. In this paper, we propose a new representation language for general multiplayer games -- multi-agent influence diagrams (MAIDs). This representation extends graphical models for probability distributions to a multi-agent decision-making context. MAIDs explicitly encode structure involving the dependence relationships among variables. As a consequence, we can define a notion of strategic relevance of one decision variable to another: