Game Theory - Behavioral Mathematics for Game AI - page 75

This illustrates a divide between the types of decision theory examined in
Chapter 4. The mathematical approach of normative decision theory (the
“shoulds�) is not reflected in what people tend to do in practice (i.e., descriptive de-
cision theory). As we move on, we will find plenty of these seeming contradictions,
and they may make us begin to second guess the seemingly reliable normative
approach to attempting to replicate behaviors.
D ICTATOR G AME
A game (if it can be called that) similar to the Ultimatum Game is the Dictator Game.
The setup is the same. A pot is available to the Giver. However, the other person is
now no longer the Decider; he can't decide to do anything at all. He will accept
whatever the Giver elects to offer him. In a way, the Giver is now the Decider as
well. (We will now refer to the other person in this exchange simply as the
Receiver—since that is his only role.)
Because the Receiver now has no control whatsoever in the arrangement, we (as
the Giver) could simply elect to give him the minimum amount (e.g., $1) and be
done with it. This would maximize the amount that we keep for ourselves: $99. In
fact, if the rules allowed for it, we could elect to give the Receiver nothing at all, and
there would be nothing he could do about it. From a decision theory standpoint,
it is obvious that the most logical solution for the Giver is to minimize the gift ( x )
because it maximizes his own take (100 - x ).
However, once again, psychological testing shows to us that people don't al-
ways act rationally. In numerous trials, it has been shown that the Givers usually
give more than the minimum amount. How much they give is not important. The
point is simply that they do so when they don't have to. After all, every dollar they
give away is one they can't keep for themselves. What could cause them to do this?
One suggested solution is similar to the first one in the Ultimatum Game—the
Giver simply fails to maximize his own position. This doesn't seem quite as likely
in the Dictator Game, however. In the Ultimatum Game, the failure to understand
how to maximize his own position would have likely been born out of a failure
to put himself in the shoes of the Decider, whose predicament was simply the in-
evitable decision between something and nothing, and seeing how that affected his
own choice. In this case, the Giver doesn't have to put himself in the shoes of the
other person at all. This should make the decision simpler than the Ultimatum Game.
The other suggested solution is that there is a factor involved that is not being
tracked and measured by the rules of the game— altruism . It could be that the people
playing the role of Giver in the Dictator Game are gaining some sort of satisfaction
out of sharing with others that outweighs whatever monetary losses they are taking.