Game Theory - Behavioral Mathematics for Game AI - page 63

So, in a situation where we treat each of our partner's choices as equally possi-
ble, it would seem that it is in our best interest to betray him. The two possible
outcomes given our action are zero and five years… or an average of 2 1 � 2 years. That
is certainly better than the average of 5 1 â?„ 2 years that we face if we stay quiet.
Put logically, rather than mathematically, this seems to make sense as well. We
are putting the possibility of 10 years of incarceration out of play. Instead, we are
looking at a maximum of five years. We are also putting the six-month sentence out
of play as well, but who cares? We are keeping the possibility of doing no time what-
soever alive and well! We have the best maximum, the best minimum, and the best
average result all on our side of the ledger. There doesn't seem to be a weakness to
this approach. In fact, if we accept all our premises as valid, our solution concept
is what is referred to in game theory as a strictly dominant strategy . That is, our
strategy of ratting out our partner makes us better off no matter what he does .
From a strictly game theory standpoint, we have achieved what we set out to
find—an optimal solution given all the possibilities. We determined that cooperat-
ing is strictly dominated by defecting. That is, the “defect� strategy is inherently
weaker. (Even defective, I suppose.)
Can We Improve on “The Best� ?
A quandary arises when we analyze our premises, however. For the sake of argu-
ment, we replaced our inability to know what our partner's choice was going to be
with equally probable outcomes—50% each. That gave us a mechanism for taking
into account the unknown. Unfortunately, we also treated our partner as if he was
no more intelligent than the randomly shuffled deck of cards that the Blackjack
dealer in Chapter 1 was using. We ascribed no rationality to him whatsoever. By
reducing him, in effect, to a flip of a coin, we are not even taking into account that
he was capable of making a choice.
Again, this may not seem to matter on the surface. After all, we have already
determined the strictly dominant strategy for ourselves (to defect). That strategy is
in our best interests of self-preservation in that it guarantees us the lowest sentence
regardless of what the other person does. If it is in my best interest to utilize that
strategy, would my partner not be of the same mind and defect as well?
The answer to this may lie in personalizing things in the other direction. If our
partner chooses the strategy of defecting, he has looked at us as a 50/50 wildcard as
well. He has determined that we are not capable of rational thought and, therefore,
has taken matters entirely into his own hands… optimizing his own benefit by
choosing to betray us . Of course, if he does betray us and we betray him , it looks like
we are both going to do five years.