Evidence shows that when engaged in game-playing tasks, individuals think about what other individuals are thinking. Presumably, though, cognitive limits prevent individuals from entertaining indefinite levels of thinking about what other players are thinking about what other players are thinking, etc.. Drawing on neural evidence, we propose a procedure by which a player builds such levels of thinking. The number of possibilities that a player must consider at each level m in this procedure grows exponentially with m. We argue that this feature may help explain why a cognitive bound has been found in game-theory studies to come into effect at a small finite number of levels of thinking about thinking.