Level-k thinking in the extensive form

Level-k thinking has been widely applied as a solution concept for games in normal form in behavioral and experimental game theory. We consider level-k thinking in games in extensive form. 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-\(\ell \) thinking for \(\ell < k\) to her opponents consistent with the information set. We compare our notion of strong level-k thinking with other solution concepts such as level-k thinking in the associated normal form, strong rationalizability, \(\Delta \)-rationalizability, iterated admissibility, backward rationalizability, backward level-k thinking, and backward induction. We use strong level-k thinking to reanalyze data from some prior experiments in the literature.