Game Development Reference
In-Depth Information
didn't
perceive it all. We simply left out the fact that Monty's decision on which door
to open for us was a relevant fact. Somehow, we failed to take into consideration
that
his
choice was not random—he knew where the car was and was intentionally
avoiding showing it to us. More importantly, even if we knew that he was hiding it
from us, we failed to take into account that this significantly skewed the odds in one
direction. It was available and perceivable. We just didn't think it mattered.
The lesson here is that just because all the information is available to as and we
know what to do with it, we won't necessarily think to use it. In short, humans
fail… even with the simplest of decisions. Therefore, their quest for perfect ratio-
nality is bounded.
While Monty Hall taught us that we often fail to take all the relevant factors into
account when making a decision, there is a different reason we may not reach the
pinnacle of rational decision making. Sometimes we may
elect
to not perform in a
completely rational manner. This is different from what we explored above with the
Guess Two-Thirds Game where we
decided
to not pursue a purely rational line of
thought. In this case, by conceding to
rational ignorance
, we are making a rational
decision to remain ignorant of all the relevant information. By doing so, we will be
violating the rules of normative decision theory in that we will not have all the rel-
evant information, may not perceive it accurately, or may not calculate it properly.
There are certainly reasons for each of these.
T
HE
C
OST OF
I
NFORMATION
Thinking back to Cutting the Cake in Chapter 5, as the Cutter, we knew that our
opponent (the Decider) was going to select the biggest piece of the two. Therefore,
it was in our best interests to cut as close to the middle of the cake as possible.
However, short of laboratory conditions and a handy electron microscope, there is
no way we could accurately ascertain the exact middle of the cake. Even as the
Decider, after a less-than-perfect cut, we would have very little way of knowing
which of the two pieces was bigger. In fact, the closer the cut is to being perfectly
equitable, the harder it would become to make the correct decision. Given enough
time and through painfully protracted measurements, we could eventually identify
the biggest piece, but what would we have gained? And what condition would our
confection be in after such a lengthy investigative process? That is, what is the cost
of gathering all that information?
