Game Development Reference
In-Depth Information
expect the most popular guesses to change accordingly. It turns out that this was,
indeed, the case. Most people were random (index 0), many people guessed 70% of
the expected average of 50, or 35 (index 1), and another large batch guessed 70%
percent of 35, or 24 (index 2). Just like in the Danish example, index 3 either didn't
show up or was diffused enough that it blended into the background.
Changing the game to other rules provided similar results. When various stud-
ies around the world have been run with multipliers such as 0.7, 0.9, 1.1, and 1.3,
the pattern was repeated. It turns out that people very rarely get to level three. In
fact, studies have shown that most people end up with a rationality index of
between 0 and 3. (One study showed that computer science folks ended up the
highest, with an average of 3.8 iterations. That isn't to say they won; they probably
didn't because they were thinking
too
far beyond the other guessers.) So, we can
determine that, for some reason, people don't bother going any further than a cou-
ple of iterations into the logic. This could be for a variety of reasons.
They don't think of it.
They can't do the calculations.
They don't believe it is relevant because
other
people can't or won't.
An interesting twist to this is that the rationality index that people get to is
based on who the other players are. For example, if you give the game twice to an
economist who knows he is playing against the general public the first time and a
bunch of other economists the second time, he will change his answer accordingly.
He will assume that the other economists will iterate further than the general pub-
lic and adjust his selection to a lower number (a higher rationality index) accord-
ingly. This leads us to the assumption that some people aren't stopping their
iterating process because they can't think that far, but rather that they are doing so
because they realize it is pointless to continue.
If we think back to the
pure strategy
of this game, we were led to the logical con-
clusion that we should guess zero. We arrived at that conclusion under the as-
sumption of the superrationality of the participants, which we know to be
unreasonable. The above observation shows that—excluding the 2% of Danes who
guessed
zero
—many people
are
aware of that unreasonable expectation of ubiqui-
tous rationality.
Logical Irrationality
What we have found is that, when faced with the very likely absence of superrational-
ity, it actually becomes less efficient to be purely rational. With our first approach to
solving the Guess Two-Thirds Game, we were being purely rational at each step.
