Level-k models often assume that individuals employ a fixed depth of reasoning across different games. We study this assumption by having subjects make choices in five classes of games chosen to identify inconsistent depth of reasoning. We demonstrate that depth of reasoning is pervasively inconsistent, changing both within and between classes of games. We show that this cannot easily be explained by factors such as subject confusion, changing beliefs about others' depth of reasoning, stochastic choice, model misspecification, changing incentives, or low cognitive ability. We develop a simple model incorporating ambiguity aversion that predicts inconsistent depth of reasoning.
