Nash Equilibrium

Economics
Updated Apr 2026

A stable strategic outcome where no player can improve their result by changing strategy unilaterally.

What is Nash Equilibrium?

A Nash equilibrium, named after mathematician John Nash, is a set of strategies in a game where each player's strategy is a best response to all other players' strategies — meaning no individual player has an incentive to deviate unilaterally. In a Nash equilibrium, each participant knows what everyone else is doing and has no better option than to continue their current strategy. The prisoner's dilemma illustrates a Nash equilibrium that is collectively suboptimal: both players defect even though mutual cooperation would benefit each. Nash equilibria can be suboptimal at the group level, explaining phenomena like price wars, arms races, and the tragedy of the commons.

Example

Example

Two competing gas stations set prices independently. If both charge $3.50, each earns good profits. If one charges $3.49, it captures most customers and the other loses business. The Nash equilibrium is for both stations to keep undercutting until they reach marginal cost — perhaps $3.10. Neither can profitably raise prices unilaterally without losing customers, even though both would prefer the $3.50 outcome.

Source: Investopedia — Nash Equilibrium