  We present an algorithm that identifies the reasoning patterns of agents in a
game, by iteratively examining the graph structure of its Multi-Agent Influence
Diagram (MAID) representation. If the decision of an agent participates in no
reasoning patterns, then we can effectively ignore that decision for the
purpose of calculating a Nash equilibrium for the game. In some cases, this can
lead to exponential time savings in the process of equilibrium calculation.
Moreover, our algorithm can be used to enumerate the reasoning patterns in a
game, which can be useful for constructing more effective computerized agents
interacting with humans.
