In game theory, a situation where no player can improve their outcome by changing strategy alone is a Nash equilibrium.
Named after mathematician John Nash, the concept describes a strategy profile in which each player’s choice is a best response to the choices of everyone else. If one player changes strategy while the others hold theirs fixed, that player does not receive a higher payoff.
Nash equilibrium does not mean the outcome is fair, socially best, or jointly optimal. The classic Prisoner’s Dilemma has a Nash equilibrium in which both players confess, even though both could be better off if they cooperated. A game can also have multiple equilibria, or none in pure strategies but one in mixed strategies.
The idea differs from a dominant strategy. A dominant strategy is best regardless of what opponents do; a Nash equilibrium only requires that the chosen strategies be mutual best responses. Subgame-perfect equilibrium is a refinement used especially for dynamic games.