Consistent Depth of Reasoning in Level-k Models

The level-k model is often implemented with an assumption that individuals employ a fixed depth of reasoning across different games. To study the validity of this assumption, we have subjects make choices in a series of games designed to identify inconsistent depth of reasoning without relying on the results of an econometric model. Most subjects’ choices are not consistent with them having a fixed depth of reasoning even in extremely closely related games. Econometric analysis verifies that this result is quite robust and illustrates the nature of the inconsistency. The likelihood of inconsistency increases with cognitive ability, suggesting that it is not solely due to confusion. Higher optimization premiums are correlated with greater depth of reasoning, but do not reduce the likelihood of inconsistency per se. We argue that depth of reasoning, like many other varieties of individual choice, is subject to stochastic choice.