Game Theory - Behavioral Mathematics for Game AI - page 68

earnest, with us having only sustained minor damage. However, it is pretty much
an all or nothing prospect to remain where we are. We live or we die. And it's that
last part that is a little disturbing. Aren't we trying to avoid death?
The Strictly Dominant versus Optimal Strategies
So, just like in the original Prisoner's Dilemma, we have found a strictly dominant
strategy. Before, it was to betray our partner. By doing so, we were guaranteed no
worse than five years of prison, no matter what our partner did. In this case, by run-
ning out to get the rocket launcher, we are guaranteeing that we are not going to die in
the near term. If he comes out as well, we are going to take some damage, but at least
we are not dead… no matter what our enemy does. That all sounds well and good.
However, just like in the Prisoner's Dilemma, the strictly dominating strategy
isn't the optimal strategy. The optimal strategy, in a joint sense, would be for both
parties to stay put and wait for the reinforcements to arrive. This is similar to not
betraying our partner in the Prisoner's Dilemma—and hoping that he does the
same. But, as I mentioned, this is a joint strategy. In the original scenario, we could
believe that our partner was looking out for us as well as himself. If we are support-
ing ourselves on this premise, we find that it falls apart in the rocket launcher
example. Why would our enemy be looking out for our best interests as well as his
own? That line of thinking is based on the fallacy of our premise.
In both the Prisoner's Dilemma and rocket launcher problems, the other per-
son isn't looking out for our interests at all. He is looking out for his own interests
and, in looking at what we might do, believes (rightly) that we are looking out for
our own interests. Confused yet? It is the classic “I believe that he believes that I
believe…� cliché. Put another way, if I believe that my enemy is interested in “living
to fight another day� and that he realizes that I might also subscribe to that notion,
we are both going to wait it out and only fight when the reinforcements arrive.
What's to prevent him from charging out of cover, grabbing a rocket launcher,
and blowing my hidey-hole sky high? Probably the fear that I might charge out and
start blasting as well.
But can I make my decision based on that? What is preventing me from charg-
ing out and blasting him into proverbial smithereens? Only my own distaste at
limping back with half health when the troops from both armies arrive—a situation
that I may not survive. I would much rather play it safe for now, and I assume that
he is thinking the same thing. That is the optimal solution: both of us playing it safe
until the rest of the group shows up.
Certainly, there could be plenty of other issues that we would need to consider
if this were a true game environment. What does death mean, for example? In an
online game, is there a respawn rate? In a real-time strategy (RTS) game, how many