nash equilibrium
A stable state where no player benefits from unilaterally changing strategy. Everyone is doing the best they can, given what everyone else is doing. Stability, not optimality.
key principles
- 01
Stability through mutual best response
In equilibrium, each player's strategy is optimal given others' strategies. No one has incentive to deviate alone.
- 02
Equilibrium isn't optimal
Stable doesn't mean best. Prisoner's dilemma equilibrium is mutual defection—stable but suboptimal for both.
- 03
Multiple equilibria possible
Some games have many equilibria. Which one emerges depends on coordination, history, and expectations.
- 04
Expectations matter
Equilibrium depends on beliefs about others' behavior. Change expectations, change the equilibrium.
applications
The Logic of Strategic Stability
Nash equilibrium revolutionized game theory by providing a general solution concept. Instead of asking what the “right” answer is, ask what behavior is self-sustaining given everyone’s rationality.
Many social situations are Nash equilibria—stable not because they’re optimal, but because no one can improve their position by changing strategy alone.
Key Quote
“An equilibrium point is an n-tuple such that each player’s strategy maximizes his payoff given the strategies of the others.” — John Nash (paraphrased)