Higher Orders of Rationality and the Structure of Games

Identifying individual levels of rationality is crucial to modeling strategic interaction and understanding behavior in games. Nevertheless, there is no consensus on how to best identify levels of higher order rationality, and the identification of an empirical distribution remains highly elusive. In particular, the games used for the task can have a huge impact on the identified distribution. To tackle this fundamental problem, this paper introduces an axiomatic approach that singles out a simple class of games that minimizes the probability of misidentification errors. It then shows that the axioms are empirically meaningful in a within subject experiment that compares the distribution of orders of rationality across different games, including standard games from the literature. The games singled out by the axioms exhibit the highest correlation both with the distribution of the most frequent rationality level a subject has been classified with and with an independent measure of cognitive ability. Finally, there is no evidence in our sample of within subject consistency of identified rationality levels across games.