Relative Utility - Behavioral Mathematics for Game AI - page 212

If I were to ask, though, what you would do (or what the rats would do if you want
to stay out of it) if the researchers were to cause the price of the quinine to go up—
that is, decrease the amount of quinine per lever press—what would your answer be?

Too Much of a Good Thing
Analyzing it at a purely surface level, our initial instinct may be that we would have
to drink less quinine per session… perhaps even increasing our intake of root beer.
(And what a tragedy that would be!) However, this is not what the rats did. When
the price of the quinine was increased (less per press), the rats actually increased
their intake of the bitter liquid by selecting the quinine lever more often. Of course,
that also meant that they drank less root beer as a result. But why would the rats use
more of something after the price went up?
The answer to that question is what lies at the heart of a concept called “ Giffen
goods .� In his 1890 book, Principles of Economics , Alfred Marshall named the
concept after the 19th century British statistician and economist Robert Giffen, to
whom he attributed the original idea . A Giffen good is an inferior product or com-
modity whose usage defies the principles of demand in that its usage increases as
the price goes up and goes down as the price lowers. There are only a few examples
of Giffen goods, yet studies of microeconomic mathematics show how this phe-
nomenon certainly can exist. In fact, the example used by Marshall of staple food-
stuffs is remarkably similar to that exhibited by our thirsty rodents.
To find where the core principle kicks in, let's break down the issue mathemat-
ically. With all the talk of the prices of the various drinks and the amounts that are
dispensed for each press, it is easy to get caught up in just those two issues. After all,
it was the “price� of the quinine that changed, so the answer must lie close to that
particular facet. There are two other important factors to remember, however.
More importantly, they seem to be the factors that get forgotten first:

1. The rats have a fixed level of need (i.e., the amount of thirst per session).
2. The rats are on a fixed income (i.e., the number of lever presses per session).

When the price of the quinine was raised, neither of these two factors changed.
Our parched pests still needed to drink something to satisfy that need. Also, they
knew that they only had a limited number of presses available to them regardless of
what they chose to drink or how much of each drink they were granted. It is these
fixed values that sets the boundaries for the possible decisions made when the vari-
able values change. What the rats realized was that to slake their thirst for the dura-
tion of the session, they were going to have to spend more of their (hard-earned?)
lever presses on the quinine than they used to get the same amount of liquid.
Therefore, if they were using more lever presses to get the quinine, they had fewer
lever presses left to “splurge� on the luxury of root beer.