Nash equilibrium
A stable combination of strategies where no player can gain by changing course alone.
What it means
A Nash equilibrium is a set of strategies, one for each player, such that no player can improve their own payoff by unilaterally changing their strategy while the others keep theirs fixed. It is the central solution concept of non-cooperative game theory, identifying configurations that are self-enforcing: once players are at an equilibrium, each is making a best response to the others, so no one has an individual incentive to deviate. The concept is powerful and general — Nash proved that every finite game has at least one equilibrium, possibly in mixed (randomized) strategies — but it carries important caveats. An equilibrium need not be efficient or socially desirable, as the prisoner's dilemma shows when mutual defection is the equilibrium even though both players prefer mutual cooperation; games can have multiple equilibria, raising the problem of which one will be selected; and real, boundedly rational people do not always reason their way to equilibrium, especially in complex or one-shot games. Behavioral game theory studies precisely these departures. It matters because the equilibrium concept underlies modern analysis of competition, auctions, bargaining, and strategy, while its limitations explain why predicted and observed behavior often diverge.
Examples
In the prisoner's dilemma, mutual defection is the Nash equilibrium — neither prisoner can do better by switching alone — even though both would prefer mutual cooperation.
Everyone stands up at a concert to see over the row in front. Standing is each person's best response to the others standing, so nobody sits, though all would prefer a seated hall.
Two petrol stations facing each other hold the same price: whoever cuts first surrenders margin, whoever raises alone loses the forecourt, so neither moves.
First described in John Nash (1950).