Game Development Reference
In-Depth Information
Game Theory
GAME THEORY IS A
field of mathematics that analyzes the interaction be-
tween moves and countermoves in multiplayer games. Despite the name,
game designers often ignore game theory because it seems too abstract to
apply to the real world. But while we don't need to calculate exact numbers
like mathematical game theorists, the fundamentals of game theory do
illuminate key concepts in multiplayer game design.
Game theory helps analyze situations where players must anticipate and
respond to one another's decisions.
Think of the difference between knocking down an abandoned castle
and attacking an occupied one.
Knocking down an empty castle is a physics puzzle. You might have to
work out the best place to put a crane, or the best way to clear away rubble.
But while these tasks may be complex, an empty castle doesn't think back
at you—it just follows the laws of physics. This is like a single-player game,
since it's a single player's mind facing a mechanical system.
Knocking down a castle full of defenders is very different. Now there
are two intelligent minds, each trying to outthink the other. The defend-
ing general will anticipate your moves and respond. He will toss back your
ladders, drop fire on your battering ram, and send assassins to kill your
general. And he will anticipate your responses to his responses. He'll send
false signals to lure you into a trap, or try to hide a weakness in the wall.
Game theory describes the interactions between your mind and his.
Imagine that one night during the siege, you're choosing your strategy
for the next day. Your choice is between attacking the gate with the bat-
tering ram and sending sappers to blow up the wall, while the defender
chooses between readying a pot of flammable tar at the gate and preparing
archers to shoot your sappers. You've each only got enough men to do one
thing, and since you must prepare during the night, you won't know what
the other general decided until the battle is joined. Game theorists would
graph out this situation in a
payoff matrix
like this:
