Extensive-form level-k thinking

Level-k thinking and Cognitive Hierarchy have been widely applied as a normalform solution concept in behavioral and experimental game theory. We consider the extension of level-k thinking to extensive-form games. Player's may learn about levels of opponents' thinking during the play of the game because some information sets may be inconsistent with certain levels. In particular, for any information set reached, a level-k player attaches the maximum level-l thinking for l < k to her opponents consistent with the information set. We compare extensive-form level-k thinking with other solution concepts such as level-k thinking in the associated normal-form, extensive-form rationalizability, delta-rationalizability, iterated admissibility, and backward induction. We use extensive-form level-k thinking to reanalyze data from some prior experiments in the literature.