In some multi-agent scenarios, identifying observations that an agent can safely ignore reduces exponentially the size of the agent's strategy space and hence the time required to find a Nash equilibrium. We consider games represented using the multi-agent influence diagram (MAID) framework of Koller and Milch [2001], and analyze the extent to which information edges can be eliminated. We define a notion of a safe edge removal transformation, where all equilibria in the reduced model are also equilibria in the original model. We show that existing edge removal algorithms for influence diagrams are safe, but limited, in that they do not detect certain cases where edges can be removed safely. We describe an algorithm that produces the "minimal" safe reduction, which removes as many edges as possible while still preserving safety. Finally, we note that both the existing edge removal algorithms and our new one can eliminate equilibria where agents coordinate their actions by conditioning on irrelevant information. Surprisingly, in some games these "lost" equilibria can be preferred by all agents in the game.
