Nash equilibrium

Nash equilibrium is the central solution concept of game theory, named for John Nash, who proved in 1950 that every finite game with mixed strategies has at least one equilibrium. A strategy profile is a Nash equilibrium when no player can benefit by unilaterally changing their strategy, given the strategies of all other players. The equilibrium is not necessarily optimal for any player, nor is it necessarily unique. It is merely stable: no individual has incentive to deviate.

The concept has been criticized on multiple grounds. Descriptively, humans do not always play Nash equilibria; experimentally, they cooperate in prisoner's dilemmas more often than the equilibrium predicts. Normatively, the equilibrium may be Pareto-inefficient — all players could be better off if they coordinated on a different strategy, but the equilibrium prevents such coordination. Computationally, finding a Nash equilibrium is PPAD-complete, meaning that no efficient general algorithm is known and none is likely to exist.

Despite these limitations, Nash equilibrium remains the organizing concept of strategic analysis because it provides a minimal rationality requirement: if a strategy profile is not an equilibrium, at least one player is making a mistake. The question is whether this minimal rationality is sufficient to explain real behavior, or whether it is a theoretical baseline that real behavior systematically deviates from in predictable ways. Bounded rationality and evolutionary game theory each offer frameworks for understanding such deviations, but neither has displaced Nash equilibrium as the field's reference point.