Rational vs. Irrational Behavior - Behavioral Mathematics for Game AI - page 84

Questioning Iterative Rationality
The solution we arrive at using iterated rationality differs from the first-glance ap-
proach. When we looked at the game initially, we figured that pirate A needed to
propose at least a marginally fair settlement. In fact, if we were to run a live Pirate
Game with real people, it is very likely that, like the Ultimatum, Dictator, and Trust
games in the previous chapter, pirate A would propose something significantly dif-
ferent from the proven optimal solution. Modeling behaviors based on this is the
descriptive behavior theory approach, that is, what people tend to do in that situa-
tion. In this case the people tend to do things they should not do.
What mechanism would cause him to do this? Certainly not the naked altruism
as is seemingly the only explanation in the Dictator Game. Pirates aren't known for
their philanthropic leanings. This would suggest something else as the cause of the
illogical offers.
If it is not benevolent other-centric interest (even on a subconscious level),
perhaps it is more self -interest? Basing the decision on self-interest, it would seem,
would more likely have led us to the maximal (that is, greedy ) solution we got. So
how can self-interest lead us in the wrong direction? There is a different way that
self-interest can be represented. Remember that money was not the only consider-
ation in the game. Pirates were trying to avoid the very real threat of becoming fish
food as well. Therefore, it is a legitimate expression of self-interest to say, “If I
appear too greedy, they will kick me off.� To that end, a pirate may tend to give
more than is required mathematically to avoid a particular fate.
At this point, we have arrived at a similar mindset that plagued the Ultimatum
Game. That is, “If I give too little, I will be rejected by the other person simply out
of spite—and will receive nothing.� In the case of the Ultimatum Game, the think-
ing error was that the other person (the Receiver) would reject an offer that was too
small and instead take nothing. Of course, that is illogical for the Receiver to do. His
decision matrix shows that getting anything at all—even one dollar—is better than
nothing. Therefore, the Giver should only offer one dollar and expect it to be ac-
cepted. But that is not what real players of the Ultimatum Game do.
In the Pirate Game, the mindset is similar, but the consequences are slightly
different. Instead of getting no money, there is the possibility of getting no money
and getting death on top of it all. (And, as we all know, one of the classic blunders
is “never go in against a pirate when death is on the line!�) Any given senior pirate
may believe he has to worry about looking altruistic to his subordinates not only so
they will accept his proposal, but so he will survive the whole process. As we discov-
ered, however, this first-blush approach is not even remotely correct. Aside from
buying a vote or two at a very small price, the ranking pirate can simply keep the
rest for himself—and no one can do anything about it. At least not without sacri-
ficing themselves later on in the process.