Level-$k$ thinking and Cognitive Hierarchy have been widely applied as a normal-form solution concept 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.

翻译：层级思维（Level-$k$）与认知层级作为行为与实验博弈论中的标准型解概念已被广泛应用。我们研究扩展形式博弈中的层级思维。在博弈进行过程中，玩家可能了解到对手的思维层级，因为某些信息集可能与特定层级不一致。具体而言，对于任何到达的信息集，层级-$k$ 玩家为其对手赋予与信息集一致的最大层级-$\ell$ 思维（其中 $\ell < k$）。我们将强层级思维概念与标准型中的层级思维、强理性化、$\Delta$-理性化、迭代可接受性、后向理性化、后向层级思维及逆向归纳等其他解概念进行比较。我们运用强层级思维重新分析文献中若干先前实验的数据。