Game Development Reference
In-Depth Information
instead of guessing 33, elect to guess 30 instead? That drags down the average even
more, and likewise our two-thirds target.
Certainly you can see where this is headed. The more people who are acting
rationally in the group, the more the average (and associated two-thirds target) is
affected. What's more, some people may be acting rationally at the shallower level
(for example, guessing 33), and some may be acting slightly
more
rationally by tak-
ing into account the first level of rational players. Even others may be assuming that
everyone
is acting rationally at a shallow level and that the average guess is going to
be 33 instead of 50. That would make their two-thirds guess 22! Kinda makes your
head spin, doesn't it?
In 2005, the Department of Economics at the University of Copenhagen in
Denmark ran a well-publicized trial of the game in the Danish newspaper
Politiken.
They offered a cash prize of 5,000 Danish kroner (about $1,000) to whoever had the
closest guess. They attracted over 19,000 submissions via an Internet site. Needless
to say, that wasn't a bad sample size. (In fact, about 1 in 300 Danes participated!) The
average of the guesses in their trial was 32.407, which led to a winning target of 21.605.
Upon examination of the histogram of the submissions (Figure 6.2), a couple of
things stand out. First, there was a wide distribution of guesses—including some
people who actually
did
guess 100. In fact, while it is definitely the sparsest area of the
chart, a surprising number of people guessed above the “impossible point� of 66.7.
FIGURE 6.2
The results of the Danish experiment show that the two
most popular guesses were 33 and 22. Indeed, the average guess was 32.4, making
the winning target 21.6. Graphic from “Making an Educated Guess� Working Paper,
Department of Economics, University of Copenhagen by Jean-Robert Tyran
and Frederik Roose Øvlisen (2009) used with permission.
