Game Development Reference
In-Depth Information
without building the 16th soldier for a time. The first 15 could do the job almost as
well as if they had waited for that 16th one. Likewise, the value we spent on those
first 15 would not have been wasted or left sitting idle. However, by specifically
defining that we want a patrol of
six
soldiers, it does us no good to build the first
five and then quit. In that case, the marginal utility per soldier actually
increases
as
we near the goal, rather than leveling off the closer we get.
As we have seen, marginal utility can assist us in expressing some of the subtlety in
how an agent could perceive the world. Just as utility allows us to give an object or
an action a level of importance that was different than its value, marginal utility allows
us to vary that level of importance as the number of objects or actions increases or
decreases.
Also, as we saw with Bernoulli's St. Petersburg paradox, marginal utility can
assist us in analyzing the differences between two utilities such as risk and reward.
By thinking in terms of the differences in utility rather than differences in value, we
can solve problems that would otherwise yield irrational results such as betting an
infinite amount of money.
We explored the idea of thresholds as anchors for these utility judgments. By
finding places where we say, “That's enough!� we establish targets and goals for our
marginal utility to approach. However, we also saw that the thresholds themselves
may not be as much of an anchor as we thought. Sometimes, a threshold may be
“good enough for now,� only to change to a different one later on.
In the end, we have found that marginal utility can be a powerful tool in ex-
pressing shifting opinions about things. And, because most decision makers are not
purely rational, opinions are a major component of the decision process. As we
continue through this topic, we will encounter numerous places where marginal
utility plays an important role in constructing realistic and dynamic behaviors.
