Multi-Agent Influence Diagrams for Representing and Solving Games

Daphne Koller, Brian Milch

Abstract: 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: D′ is strategically relevant to D if, to optimize the decision rule at D, the decision maker needs to take into consideration the decision rule at D′. We provide a sound and complete graphical criterion for determining strategic relevance. We then show how strategic relevance can be used to detect structure in games, allowing a large game to be broken up into a set of interacting smaller games, which can be solved in sequence. We show that this decomposition can lead to substantial savings in the computational cost of finding Nash equilibria in these games.