*5.6. Result 4: Cognitive Bound*

In block 2 of the experiment, the subjects played against the computer. They were told that the computer was playing a Nash equilibrium strategy, and the equilibrium concept was explained. However, they were not taught the method to derive the equilibrium. The behavioral levels from the guesses in these two games should be considered as the highest levels they could achieve under each cognitive load treatment. I selected all the games with the same cognitive load treatment, either low cognitive load or high cognitive load, and pooled the results. A pairwise comparison between the pooled data and behavioral level obtained from games 17 and 18 allowed me to examine the existence of cognitive bounds. There were 888 pairs of comparison for each type of cognitive load, and the summary statistics are shown in Table 13.


**Table 13.** The frequency of changing behavioral levels comparing to cognitive bound.

The result for low cognitive load treatment was interesting: 48.20% of the guesses from block 1 games had behavioral levels lower than the subject's respective cognitive bound (level in game 17). Less than 20% of guesses had higher behavioral levels. This suggested that in many block 1 games, subjects purposely adjusted their behavioral levels downward due to different strategic situations, even though they had reached higher levels. For high cognitive load treatment, about 30% of behavioral levels increased from block 1 games to game 18. However, about 50% of the guesses had the same behavioral level across the two situations. Since high cognitive load inherently restricts the subject's cognitive ability, there may have been less room for downward adjustments for block 1 games. Due to the large percentage of weakly increasing levels from block 1 to block 2 games, I concluded that cognitive bound existed in most cases. In some situations, cognitive bound was strictly higher than the subject's behavioral levels in games. In some situations, cognitive bound was the same as the behavioral levels. Such cases were largely observed in the high cognitive load treatment.

To examine whether high cognitive load had a lower level distribution, I conducted a Wilcoxon signed-rank test on the estimated behavioral levels of games 17 (low load) and 18 (high load). Table 8 shows that the distributions of levels for the two treatments were significantly different at the 1% level. The one-tailed test indicated that the distribution of low load cognitive bound levels was to the right of

the distribution of high load cognitive bound levels. This finding indicated that subjects had a higher cognitive bound when receiving low cognitive load treatment (memorizing a string of three letters) compared to receiving a high cognitive load treatment (memorizing a string of seven letters).
