Game Theory - Behavioral Mathematics for Game AI - page 64

Even if we were to adjust our payoff formulas to account for an imaginary
“likelihood� that he will choose to defect, say making it 80% instead of 50%, we
would get the following:
Never mind the 2 1 â?„ 2 year average potential sentence that we were looking at. The
premise on which it was based (a 50% probability for each of our partner's choices)
was flawed the whole time. He wasn't a coin flip. He was a rational human (in dark
glasses and a stupid hat) who was fully capable of making (interesting) choices that
served his own best interest.
Pareto Optimality
Of course, if we now accept the notion that our partner is a rational human, out for
his own benefit, we may have to include the idea that he would view us the same
way. Perhaps all is not lost. If we both view each other as completely reasonable and
wise, and, in doing so, assume the other would view us as just as enlightened, we
may have to reanalyze our payoff matrix.
We have recently come to the conclusion that, despite our happy thoughts of a
2 1 â?„ 2 -year average sentence, we are looking at five years if we both choose to defect.
That 2 1 â?„ 2 -year sentence doesn't really exist. It was a mathematical fiction based on
our application of probability. Now that we are working under the assumption
that it is no longer likely that we will get off entirely with no time at all, the six-
month option that we allowed to be taken off the table looks a lot more attractive.
What if he is thinking the same way?
To simulate what would happen if we could read each other's minds, we may
as well pretend that we can speak with our partner in crime. To be honest, if we
were to do so, this entire exercise would no longer be a dilemma. We could simply
agree to keep our mouths shut, serve our six months, and go home. That would
achieve what is called a Pareto improvement . A Pareto improvement occurs when
the solution shifts so that at least one of the players has a better situation at no detri-
ment to the other. In this case, the shift actually benefits both players. In fact, a
quick glance at the Prisoner's Dilemma matrix shows that the scenario of both
prisoners keeping quiet is actually the Pareto optimum because no further im-
provements can be made.
The irony of the situation is that, in acting in what is ostensibly our own best
interests (betraying our partner), we actually avoid the optimal solution for both of
us. It seems to be a contradiction that acting in our own self-interest does not in-
clude the actual best option for ourselves. The mistake that was made, however, was