We introduce the notion of strategic awareness in experimental games which captures the idea that subjects realize they are playing a game and thus have to form beliefs about others' actions. The concept differs from both, rule understanding and rationality. We then turn to experimental evidence from a beauty contest game where we elicit measures of cognitive ability and beliefs about others' cognitive ability. We show that the effect of cognitive ability is highly non-linear. Subjects' behavior below a certain threshold choose numbers in the whole interval and does not correlate with beliefs about others ability. In contrast, choices of subjects who exceed the threshold avoid choices above 50 and react very sensitively to beliefs about others' cognitive ability. (author's abstract)
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