**Wanqun Zhao**

Rady School of Management, University of California, San Diego, CA 92093, USA; wanqun.zhao@rady.ucsd.edu Received: 30 June 2020; Accepted: 14 September 2020; Published: 22 September 2020

**Abstract:** I designed an experiment to study the persistence of the prevailing levels of reasoning across games. Instead of directly comparing the *k*-level(s) of reasoning for each game, I used cognitive load to manipulate the strategic environment by imposing variations on the subject's cost of reasoning and their first- and second-order beliefs. Subjects have systematic changes in *k*-level(s) of reasoning across games. That finding suggests that subjects are responsive to changes in the strategic environment. Changes in *k*-level(s) of reasoning are mostly consistent with the endogenous depth of reasoning model when subjects are more cognitively capable or facing less cognitively capable opponents. Subjects have cognitive bounds, but often choose a lower-type action due to their beliefs about their opponents. Finally, cognitive ability plays a significant role in subjects making strategic adjustments when facing different strategic environments.

**Keywords:** level-*k* reasoning; guessing game; cognitive load; endogenous depth of reasoning; strategic thinking
