Game Development Reference
In-Depth Information
The slope of the graph is particularly important. At any given point along the
graph, it is that slope that represents the marginal utility. As the marginal utility
between any two points changes, the slope of the line between those two points changes
as well. If the slope is changing as we progress along the line, we can identify the very
important features
decreasing marginal utility
and
increasing marginal utility
.
Figure 8.3 shows a small segment of a utility curve. As the value changes from
x
to
y
on the graph, the utility changes by
a
. Therefore
a
is the marginal utility of the
change in value from
x
to
y.
Likewise, as we change from value
y
to
z
, the utility
changes by
b.
The marginal utility of
y
to
z
is
b.
When we compare the marginal
utilities
a
and
b
, we find that
b
<
a
. Therefore, as our value moves from 0 to
n
, we
see
decreasing
marginal utility.
FIGURE 8.3
A segment of a utility curve. Despite the fact that the total utility
is increasing, the
marginal utility
of each additional unit is
decreasing
.
I
NTHE
G
AME
Building Soldiers
Marginal utility has a very important part in game mathematics. Remember that
utility represents the “importance� of something. Naturally, decision making in-
volves deciding what things are important, which things are more important than
others, and even
how much more
important things are. However, the importance of
something is not static—just as the importance of the $20 bill is not static and the
importance of any given milligram of caffeine is not static. Things change.
