Marginal Utility - Behavioral Mathematics for Game AI - page 177

I NCREASING M ARGINAL U TILITY

In the above case, the marginal utility decreased as a certain point was approached.
Contrary to that, sometimes marginal utility can increase . In this case, something
that may not be important originally may become more important as the situation
changes. As the other end of the scale is approached, the marginal utility increases,
making each additional unit more and more important.
Often, increasing marginal utility is tied to goals. For example, the minimum
purchase price of an object is a goal that must be attained. If we wanted to purchase
a new video game at a price of $60 (I may have just unwittingly dated this topic),
the first dollar we save is not very important. We do not have much money, and the
goal is distant. In fact, we may not be certain that we are ever going get to the goal
of $60. On the other hand, if we have $59, we know we are almost at our goal. We
find ourselves saying, “Just one more!� The marginal utility of that last dollar is far
greater to us than the early ones.
Another example of increasing marginal utility is accumulating properties in
Monopoly. In Chapter 7, I related how Marci would not accumulate properties
through trading. She did not realize the value of how each additional property she
acquired gave her more leverage than the one before.
In Monopoly, it is important to continue to acquire properties. This is evi-
denced by how one single property does not provide much income. Similarly, hav-
ing two properties—even if they are the same color—does not provide a utility that
is much greater than the stated values on the deeds. Acquiring the third property in
a group, however, greatly increases the amount of income that can be collected
from an opponent landing on any one of the three properties. The marginal utility
of acquiring the third property is greater than the utilities of purchasing either the
first for the second property. It's because of this increased marginal utility of
acquiring the third property in any given set that the other players and I were so
desperate and willing to trade so heavily to acquire those properties from Marci.
We found ourselves saying, “Just one more!�
In fact, identifying scenarios that involve increasing marginal utility is often as
simple as finding situations in which the phrases “just one more� and “almost
there� are appropriate. Those phrases highlight the relative importance of the steps
that are necessary to finish a task or achieve a goal.

IN THE G AME Declining Health

In our Health Kit and Armor example in the previous chapter, we alluded briefly to
a caveat that could possibly affect our interest in pursuing the Health Kit. Specifically,