Game Development Reference
In-Depth Information
FIGURE 8.7
We can restate increasing marginal utility as decreasing
by changing the direction of the axis. Because both curves are descending,
they both show decreasing marginal utility. They exhibit different characteristics,
however. Care must be taken to represent the effect in the desired way.
In contrast, both the solid line and the dashed line in Figure 8.7 show decreasing
marginal utility while moving from left to right (i.e., health increasing). The effect
is very different, however. In the case of the dashed line, the utility for a Health Kit
would start high when the agent's health is zero. It would stay high until moderate
health was reached, at which point it would slowly begin to decrease. As the level of
health approaches the maximum, there is a rapid change from one point to the
next. In fact, most of the change in utility on the dashed line takes place over a span
of health where the solid line's utility is already close to zero, that is, not important.
If we were to put this into practice in an example of an agent incrementally
losing
health (i.e., moving right to left on the graph), we would notice an almost im-
mediate jump in the utility of acquiring a Health Kit. The first small wound would
assign great importance to finding a way to heal. This is not the original behavior
that we had constructed in Figure 8.6. The dotted line is incorrect. The lesson to
learn here is that when we converted an expression of increasing marginal utility
into terms of decreasing marginal utility by flipping the axis, we had to make sure
that our resultant utility curve was the same as well.
Many more subtle caveats can trip up the unwary designer when dealing with
curves in this fashion. And yes, keeping track of the difference between value and
utility makes for magnificent headaches. (Of course, this increases the
utility
of
pain killers compared to their
value.
)
