Game Development Reference
Nash equilibria are important in real multiplayer games because
play tends to gravitate toward them. Nash equilibria are stable and
self-reinforcing since no player has a reason to do anything different.
Nonequilibrium configurations are unstable and self-modifying, since
someone has a reason to change his strategy alone. The game may allow
a million strategy combinations, but only the Nash equilibria will tend to
actually occur. So the play experience will consist of those situations that
are Nash equilibria—others might as well not exist.
This is why it's important to set up a game so that the strategy interac-
tions have many or no pure Nash equilibria.
A strategy interaction with one pure Nash equilibrium is a broken game
design because it will always settle into that same equilibrium. Each
player has only one viable option, so the strategic decision vanishes.
With only one equilibrium, all players know exactly what to do, and
have no reason to anticipate or even think about one another's moves. This
is the definition of monotony. The mind game where each player tries to
predict the decisions of the others disappears.
Situations with multiple equilibria, like the stag hunt, are better be-
cause now each player is thinking about what the other will do. But we can
improve even on this.
The best outcome is to eliminate Nash equilibria entirely. For example,
in the castle battle, there are no pure Nash equilibria. No matter what the
configuration of strategies, one side can do better by changing his choice.
This is good game design because there is always a premium on know-
ing what other players will do, which creates all the human fascination of
anticipating, deceiving, and manipulating other people. So, if you've got
a strategy interaction with Nash equilibria, redesign or rebalance it to get
rid of them.
RoCk-PaPeR-sCissoRs anD matCHing Pennies
Interactions without Nash equilibria are commonly called rock-paper-
scissors mechanics because rock-paper-scissors is the most commonly
known game without a Nash equilibrium. In rock-paper-scissors, no
matter what the configuration of strategies, one player wants to change
their move. In payoff matrix form, the game looks like this:
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