Game Development Reference
In-Depth Information
for deciding that we need six soldiers before we send out our patrol. Those thresh-
olds were entirely up to us to set. We needed to consider what would look and feel
realistic.
Generally, thresholds are set at a fixed number. How we arrive at that fixed
number, however, could be determined in many different ways. In fact, the thresh-
old target could continually be changing. From the standpoint of calculating utility
and
marginal
utility, however, we need to know what the threshold is
at that moment
.
Once we have that fixed number, we can begin to include it in our calculations.
Also, as we mentioned earlier, thresholds could represent different approaches
in the way our marginal utility behaves. Marginal utility could change as we move
toward a threshold or it could change as we move away from a threshold. Marginal
utility could either decrease or increase as a threshold is neared. There are no magic
solutions for how thresholds are either defined or constructed. What is important
is that we recognize that they exist so that we can start thinking in terms of them.
We will explore methods of calculating utility, marginal utility, and thresholds later
in the topic.
Up until this point, we have been envisioning utility curves as being somewhat
asymptotic. That is, they curve in a single direction, approaching either a specific
value or a particular slope. There are times when utility curves—both for risk and
reward—may reverse themselves. This has the effect of making the extra value
risked “worth it� again.
The quandary posed by the St. Petersburg paradox is a staple of many of the
game shows that we see on TV these days. Games like
Who Wants to Be a Millionaire
and
Deal or No Deal
have a component to them that encourages the players to
weigh the marginal utility of the money they could win by continuing. There is an
assumption that, as we saw in Figure 8.9, a person will reach a point where it is “no
longer worth it� and will quit (if he hasn't failed already). There is a subtle flaw in
this premise.
Interestingly, examples of this behavior are evident in those shows if you know
where to look for them. Often, players in those games and others like them change
their minds about whether to risk more money for achieving a greater reward. We
will use
Who Wants to Be a Millionaire
as an example.
