Nash equilibrium
A Nash equilibrium is a set of strategies where no player can do better by changing their own choice alone.
The single most important concept in game theory describes a kind of stalemate: a set of choices where no one, acting alone, can do any better. That is the Nash equilibrium.
A Nash equilibrium is a combination of strategies, one for each player, such that no player can improve their outcome by changing their own strategy while the others keep theirs unchanged. It is the central solution concept in game theory, identifying outcomes that are stable and self-enforcing.
No regret, given the others
The defining feature is mutual best response: in equilibrium, each player's choice is the best they can do given what everyone else is doing. No one has an incentive to deviate unilaterally, which is what makes the outcome stable, once reached, it tends to stay reached, since any single player who departs from it only makes themselves worse off. This is why Nash equilibrium predicts where strategic situations come to rest.
Stable need not mean good
Crucially, a Nash equilibrium can be collectively terrible. The prisoner's dilemma has a single Nash equilibrium in which both players betray each other, even though both would be better off cooperating, because neither can improve their own outcome by switching alone. This is the concept's most important lesson: individually rational, self-enforcing behaviour can produce outcomes that are bad for everyone, and stability is not the same as desirability.
Complications
Nash equilibrium is powerful but comes with caveats. Many games have multiple equilibria, leaving open which one will occur and raising the problem of coordination. Some require players to randomise, mixed strategies, rather than choose a single action. And the concept assumes a level of rationality and shared knowledge that real players may lack. These complications mean it is a sharp analytical tool rather than an infallible predictor.
The Nash equilibrium, which earned John Nash a Nobel prize, gave game theory its central organising idea and reshaped economics and beyond. Its enduring insight is uncomfortable: that the stable outcomes of strategic interaction, the ones no one can unilaterally escape, are frequently outcomes that everyone would have preferred to avoid.