Multiplayer - Designing Games - page 179

This simple issue of definition may be why game theory is so often
ignored in game design. Game theory can't solve an entire round of Mortal
Kombat , so many people immediately assume it's useless in analyzing
the game. But it is the best way to analyze a specific, fraction-of-a-second
interaction between punches, blocks, or throws. It can't cover an entire
match of soccer, but it can predict where a player will aim a certain shot
and where the goalie will dive. It only works when applied at the level of
interactions between strategies, not entire designs.
nasH equiliBRia
The core concept of game theory is the Nash equilibrium .
A NASH EQUILIBRIUM is a configuration of strategies where no player
can improve his own result by changing his strategy alone.
Let's break this down.
The first part of the Nash equilibrium is the fact that it's a configu-
ration of strategies. A configuration of strategies is just a set of possible
choices that all players could make. Each box in a payoff matrix is a con-
figuration of strategies. In the stag hunt example, Blarg hunts stag/Thag
hunts hare is a configuration of strategies. So is both hunt hare , Blarg hunts
hare/Thag hunts stag , and both hunt stag .
A Nash equilibrium is just a specific kind of strategy combination.
Specifically, it's one where none of the players has any reason to change
strategy if they assume that nobody else will change theirs. This sounds like
an arbitrary distinction, but it turns out to be an extremely powerful idea.
For example, in the stag hunt, there are two Nash equilibria. The first
is when both hunters choose stag. In this case, both are getting the best
possible result; if either changed his strategy to hunting hare, he would
reduce the amount of food he got. The second is when both hunters choose
hare. This one is more interesting, because it highlights the subtle aspect
of Nash equilibria, which is that it's not necessarily optimal for anyone. If
both hunters are chasing hare, they could theoretically both change to stag
together, thus both getting much more food. But if either one switches to
stag alone, he ends up starving while the other munches on hare. So even
though it's not the best possible result for either hunter, both hunt hare is
a Nash equilibrium.