*5.4. Result 2: Increasing Cost of Reasoning for Opponent*

To examine the effect of changing the first-order belief on a subject's behavioral level in games, I selected pairs of games with changing cognitive loads for the opponents. For example, a comparison of behavioral levels for games 1 and 4 served the purpose. In game 1 ([LL+]), player 1 has a low cognitive load when facing an opponent with a low cognitive load, and there is full revelation of each other's strategic environment. In game 4 ([LH+]), player 1 has a low cognitive load when facing an opponent with high cognitive load, and again, there is full revelation of the treatments. I found 444 pairs of comparison for the cases wherein the subjects had low cognitive loads, and another 444 pairs of comparison for the cases when they had high cognitive loads. The detailed comparison groups and summary statistics are shown in Table 10. The plotted distribution of behavioral levels is presented in Figure 6.

**Table 10.** The frequency of changing behavioral levels with increasing cost of reasoning for opponent.


**Figure 6.** Level Distribution for increasing cost of reasoning for opponent.

The combined results were the opposite of the theory prediction, with a significant 31.64% of cases of increasing behavioral levels. However, upon further checking, the majority of the increasing cases occurred when subjects are having high cognitive load. When subjects had low cognitive load, 79.73% of the time, they weakly decreased their behavioral levels when their opponents' cognitive loads changed from low to high (23.87% strict decrease). Figure 6a illustrates that [LL+] games had more guesses at higher levels. This result is consistent with the EDR model. When a subject's cost and second-order belief was controlled across the two strategic environments, he was responsive to the changes in his opponent's cost of reasoning. However, some of these adjustments in behavioral levels were not strictly decreasing. If the subject believed that the increased opponent's cost of reasoning was not large enough to decrease the opponent's behavioral level by one, the subject's behavioral level remained the same across the two strategic environments. This partially explains the high percentage (55.86% and 41.44%) of constant behavioral levels in Table 10. When the subject had a high cognitive load and his opponent's cognitive load changed, the result did not comply with the EDR model. A total of 43.02% of the pairs showed increasing behavioral levels across the two strategic environments. The frequency of levels in Table 6 reveals that most subjects had level 1 guesses in games 6 (83.78%) and 13 (70.27%). This gave subjects much less room to adjust their behavioral levels downward compared to another strategic situation. Any behavioral level that was beyond level 1 in games 3 and 12 was considered as moving the behavioral level upward. This was one major limitation in observing the effects of changing the first-order belief when the subject had a high cost of reasoning (i.e., high cognitive load).

The Wilcoxon signed-rank test rejected the null hypothesis that the level distribution was the same for both treatment comparisons ([LL+] to [LH+] and [HL+] to [HH+]). However, the one-tail test suggested that when the subject had low cognitive load, increasing his opponent's cost of reasoning shifted the former's level to the left (to lower levels, significant at the 1% level). However, when the subject had high cognitive load, the level distribution shifted to the right. The regression coefficients suggested that increasing the opponent's cost of reasoning decreased the behavioral level when the subject had a low cognitive load (significant at the 10% level).
