Game Development Reference

In-Depth Information

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.

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