**6. Concluding Remarks**

In this study, I designed a laboratory experiment to examine the consistency of players' strategic sophistication formulated by the level-*k* model. Following the endogenous depth of reasoning framework, I controlled the strategic environment by varying the cost of reasoning for the subjects, and their first- and second-order beliefs about their opponents.

My findings were consistent with the EDR model under some conditions. When the strategic environment was carefully controlled, subjects were very responsive towards the changes in the environment. Subjects who have more cognitive resources (in a low cognitive load treatment) or subjects who are facing opponents with less cognitive resources (in a high cognitive load treatment) change strategies systematically. This behavior can be predicted by the EDR model. Subjects in a strategically disadvantaged situation (high cognitive load treatment) have less room for strategic adjustments. In some of my findings, subjects appeared to try to achieve higher behavioral levels when they were under the high cognitive load treatment. The reason for this is still unclear. It may due to the awareness of the strategic disadvantage and the extra effort of the subjects under such situations, or some other behavioral factors existed that were not captured by the EDR model. The underlying reason needs further investigation. The effect of cognitive ability on the treatments was also captured by the cognitive test. Subjects with higher test scores were more predictable by the EDR model, regardless of the strategic environment. This finding is in line with the asymmetry observed in my results. As the source of asymmetry was mainly the amount of cognitive resources, it is not surprising that subjects with higher cognitive test scores adjusted better in these tasks.

A level of cognitive bound existed for subjects in different strategic situations. When playing games under the same amount of cognitive resources, subjects rarely had behavioral levels that exceeded their respective cognitive bounds for that strategic situation. Significant downward adjustments occurred from the cognitive bound in response to different strategic environments. Overall, when there is a strict control over the strategic environment, changes in *k*-levels across games are systematic. They can be explained by the EDR model to some extent, especially for subjects in a more cognitively advantaged situation. This study only discusses the directional changes in the levels. Further studies could examine the criteria and accuracy of such predictions.

**Funding:** This research received no external funding.

**Acknowledgments:** I would like to thank Charles Sprenger and Vincent Crawford for their valuable feedback and thoughtful suggestions. I am also grateful to the three referees and the editor for their helpful comments.

**Conflicts of Interest:** The author declares no conflict of interest.
