*5.2. Distribution of Levels*

From the preview of results from raw guesses in the previous subsection, changing the strategic environment appeared to lead to some structured changes in the depth of reasoning. However, only about half of the guesses were type-exact guesses. To better understand the treatment effects of the other half, I used maximum likelihood estimation to assign types, and then conducted analyses based on the estimated levels.

There were a total 1998 observations of guesses. As discussed in the previous section, I assigned a behavioral level for each observation. Surprisingly, a few guesses corresponded to exact level 4 and level 5 guesses in my data. Therefore, I included levels 1 to 5 and the Nash equilibrium type in my estimation. Of all the observations, 1167 guesses were estimated. The distribution of estimated levels for these guesses is shown in Table 5. The majority of the guesses were assigned to level 1 guesses. The level distribution for all the guesses is shown in Table 6. The game number is referred to the game number list in Table 1. Since all the subjects played each game exactly once, for each game listed, there were 111 observations.


**Table 5.** Summary of estimation results.


**Table 6.** The frequency of levels by game.

The distributions of the levels were fairly similar to the results in CGC06, except that levels 4 and 5 were then included. Level 1 was the most prominent behavioral level. Of 1998 observations, 60.26% were level 1 guesses. In some games, level 1 was even more frequently observed. For example, in game 1, about 70% of the guesses were classified as level 1. A number of observations were levels 2 and 3 and Nash guesses. In my data, the occurrence of level 3 was more frequent in a few games. For example, in game 2 and game 3, more than 20% of observations were assigned to level 3. Although some observations corresponded to exact level 4 or level 5 guesses, the overall frequency of these two higher levels was much lower. In about one-third of the games, no guesses were classified into these two levels.

As shown in Table 6, there are a pair of games that have almost identical level distribution, game 3 and game 12. These two games have identical parameters and treatments (as shown in Table 1). Besides these two games, the frequency of levels in other games differed considerably. In some games, behavioral levels congregated toward levels 1 or 2, for example, games 1 and 6. In some games, such as games 2 and 9, behavioral levels spread out across the six categories. The variations in the distribution of levels across games could be due to the differences in the cognitive load tasks. The exact impact of the memorization tasks is discussed in detail in the following subsections.
