Game Theory - Behavioral Mathematics for Game AI - page 74

FIGURE 5.7 The decision matrix for the Ultimatum Game shows that the only possibility
for either participant to get anything is for the Decider to accept the Giver's offer.
The Failure to Act Rationally
Yet, when this test is given by psychologists, that is not what happens. They have
discovered that there is a threshold below which the Decider will not accept the gift.
For whatever reason—likely the feeling of being “stiffed�—the Decider elects to
take nothing and suffer as long as the Giver is suffering along with him. In nonclin-
ical terms, it is the equivalent of “Oh yeah? Fine! Be that way! I'll show you!�
What we have seen is that the Decider is not acting in his best interests mathe-
matically and logically. Theoretically, he is not acting “rationally.� It would be ra-
tional to choose to receive something of value over receiving nothing at all.
However, although it might be irrational, apparently it is also not unexpected.
It turns out that plenty of people playing the Giver side of the game actually do
offer more than the bare minimum to the Decider. Just as it is irrational for the
Decider to turn down a certain thing (via accepting whatever is offered), by the
same rules, it would be irrational for the Giver to offer anything more than the min-
imum. And yet, more often than not, they do so.
There could be two reasons for this. First, it could be that the Giver doesn't
have a good grasp on the theory that goes into making the decision from the point
of the Decider (i.e., something is better than nothing). Second, it could be that the
Giver is well aware that there could be something insulting about being completely
rational. That is, despite realizing the complete rationality of trying to maximize his
own position, he may realize that the Decider might not elect to do the completely
rational thing by accepting.
Put more succinctly, the Giver may find it rational to assume that the Decider
will not do the rational thing—and, therefore, the Giver should bypass what would
normally be rational for him to do. Any clearer yet?