Does level-k behavior imply level-k thinking?

The level-k literature classifies subjects into different Lk types by their observed levels of reasoning in games. However, it remains unclear whether the observed level-k behavior is determined by belief or reasoning ability. This study proposes a strategy to identify the ability-bounded Lk subjects, who could not reason more than k steps of iterated best responses and thus have reached the upper bounds of their reasoning capacity. The identification utilizes a combination of simultaneous and sequential ring games. In the sequential games, it requires an extra step to best respond as Lk, and thus the ability-bounded ones would fail the task. Results show that more than half of the L2 and L3 subjects are ability-bounded. Additionally, subjects’ CRT scores, a measure of their cognitive ability, support the separation of the ability-bounded types. The findings suggest that both belief and reasoning ability could determine the observed levels, and thus one must be cautious when trying to infer belief or ability from the existing level-k data.