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Game theorists often quote the story of Sherlock Holmes fleeing London by train in direction of Dover, and applying the following recursive reasoning: if he were to continue the journey without giving thought to his pursuers (order-one strategy), then surely Moriarty would find out and follow him to Dover. Knowing his arch-enemy well, Holmes might account for this in a second-order inference and alight at Canterbury to avoid pursuit. However, Moriarty might himself operate on the second-order of reasoning and expect Holmes to do just that, in which case the latter should progress to the third level of recursion and go to Dover. Based on his past experience with Moriarty, Holmes was able to estimate his order of sophistication, k, and optimally respond to it using a k 1 order strategy (otherwise, he could continue the mind game ad infinitum without reaching a decision). In search of the neural underpinnings of such …