Game Development Reference
In-Depth Information
FIGURE 6.3
Each group of people will take into account the groups before them.
For example, the index 1 group will assume the index 0 people are guessing randomly.
The index 2 group will assume the index 1 people are basing their guess on
index 0, and so on.
If some people take the level-two guessers into account and base their own
guesses on that (i.e., 15), we would give them a rationality index of 3. Again, as be-
fore, they performed three layers of calculation, in that they are assuming that
plenty of levels twos exist based on the level twos' belief about the level ones which
are, in turn, based on the assumption of the level zeros.
If you were to proceed all the way down to the bottom, you would get to a guess
of
one
at rationality index 10. That is, someone would have to assume that level
nines exist who are basing their own guess on the assumption that level eights exist,
and so on.
How Low Will You Go?
So, how many iterations are people either capable of doing, willing to do, or believe
is appropriate to do? Separating out those three reasons for not proceeding further
is a little difficult, but coming up with how many iterations of logic people do is eas-
ily measured. As we saw in the Danish example, if a significant number of people
“get it,� it tends to show up on the histogram of the results. In this case, there were
plenty of index 0 people, about 6.5% were index 1 (guessing 33), and about 6%
were index 2 (guessing 22). After that, things tend to blur out and are no longer
apparent from the histogram. This is not a coincidence.
Many researchers have toyed with the game and found that those patterns re-
peat. By changing the game to “guess 70% of the average,� for example, you would
