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How Many Levels Do Players Reason ? An Observational Challenge and Solution ∗

How many levels do players reason about rationality? In simultaneous-move games, there is a wellunderstood methodology for identifying reasoning about rationality—one based on iterated dominance. However, there is a challenge in porting that methodology to extensive-form games: It would appear to require that the researcher have information about the hierarchies of beliefs that players consider possible. Moreover, imposing (potentially incorrect) assumptions about those beliefs can have non-trivial implications for identification—implications that do not arise in simultaneous-move games. We provide a novel methodology to identify reasoning in a generic class of extensive-form games. Importantly, the methodology does not require information about the hierarchies of beliefs players consider possible. The centipede game illustrates that the methodology has non-trivial implications for experimental design.