Does Level-k Behavior Imply Level-k Thinking?

I design an experiment to interpret the observed Lk behavior. It distinguishes between the “Lkb” players, who have high ability and best respond to Lk belief, and the “Lka” players, who could use, at most, k steps of reasoning, and thus could not respond to L(k+1) or higherorder belief. The separation utilizes a combination of simultaneous and sequential ring games. In the sequential games it requires more than k reasoning steps to respond to Lk belief, so Lkb players still best respond but Lka would fail. I find that around half of the L2 and L3 subjects are best responding to L2 or L3 belief, while the rest have reached their upper boundaries of reasoning. Additionally, subjects’ CRT scores, a measure of their cognitive ability, support the separation of the two types. The findings suggest that both belief and reasoning ability could be the decisive factors of players’ observed levels.