Defining Decision Theory - Behavioral Mathematics for Game AI - page 46

FIGURE 4.1 Normative decision theory takes a perfectly perceived
model of the world, accurately performs all the necessary calculations, and
rationally selects the most appropriate decision.
Most other game AI agents use normative (prescriptive) decision theory. In
fact, this is the area that encompasses much of game AI today. A pathfinding algo-
rithm uses all four of the above criteria and returns the path that an agent should
take. Likewise, a planner that utilizes A* to find a way to solve a goal theoretically
returns the “best� steps to take to accomplish its intended goal. A stereotypical bot
in a first-person shooter (FPS), as an entity tied to the game world, has all the in-
formation about its environment available to it, can perceive it all—through cheats
if necessary—and is able to perform any and all necessary calculations to make a
perfect head shot on anyone it pleases, and they are rational to a fault.
It would seem that normative decision theory is perfectly suited for computers
and, by association, game AI. If, as a designer or programmer, we are specifically
concerned with looking at our game world and solving a problem to tell our agents
what they should do, normative decision theory seems to be the channel through
which we must pass. While this is the case to some extent, there are caveats.
Predictable “Shoulds�
In Chapter 1, we examined how some games have a very defined pattern of what
should be done on any given move. In Tac-Tac-Toe, given any board arrangement,
there is one play that you should do if you want to win (or not lose). Not only does
that instruct us about what to do on our turn, but we can be reasonably certain that
our opponent will respond with the corresponding move that he should make to
counter it. Accordingly, in our opponent's eyes, our move is just as predictable.
In Blackjack, the moves on any given arrangement of cards are a bit more obscure
due to the mathematical complexity involved. However, the best mathematical
solution is printed in vivid colors on the cheat cards. Those moves represent a
statistical aggregation representing what we should do. Does it always work? No…