Game Development Reference
In-Depth Information
In the end, while normative decision theory and the utility-maximizing algo-
rithms that fall out of it provide us with the sterile “should do� answers, we need to
look a little further into the basis of reason and rationality to begin to replicate it.
Because irrationality is so difficult to define, it is actually easier to start this foray by
starting from the summit of the mountain of rationality and working down. Agents
are said to have
perfect rationality
if they
always
act in the best possible manner,
even if they have to perform extensive and difficult calculations to do so.
If, for the sake of example, we were to reduce this to a simpler game space, we
could use the game of Tic-Tac-Toe. As we noted in Chapter 1, the choices available
at any point in the game can be narrowed down to a decision between whether or
not we want to win. If we do want to win, there is an obvious selection. If we do not
want to win, there is an equally obvious selection. Therefore, our success at Tic-
Tac-Toe is based entirely on whether or not we want to win. A perfectly rational
player will
always
play those correct moves. If we were to elect to play incorrectly on
even one of those moves, we would no longer be considered perfectly rational.
Other examples of perfect rationality can be applied to the games from Chapter
5. The prisoner who, without any other information to go on, elects to betray his
partner in the Prisoner's Dilemma is exhibiting perfect rationality. The person who
gives the minimum in the Ultimatum and Dictator games is acting in a perfectly
rational fashion. Cutting the cake exactly in half so as to minimize exposure to the
expected (and perfectly rational) greed of another player is perfectly rational. Even
the person who plays a mixed strategy in Matching Pennies to keep from tipping off
his opponent to patterns is being perfectly rational.
If an optimal solution exists, the perfectly rational agent will take it every time.
What could be so wrong about that? It turns out that perfect rationality has serious
weaknesses that can only be exposed by running it through a test drive. For that, we
need a test track so we can see perfect rationality in action.
T
HE
P
IRATE
G
AME
The Ultimatum Game is an interesting conflict between two people with its “take
it or leave it� game of chicken. As we noted above, it is also an excellent example of
how perfect rationality can lead to an extreme solution—in this case offering the
bare minimum payout to the other person. The possibilities get even more intrigu-
ing when it is extended to multiple people. The Pirate Game does just this.
