Nash Equilibrium

Nash Equilibrium is a concept in Game Theory where no player can improve their payoff by unilaterally changing their strategy, assuming others’ strategies remain unchanged.

Definition

For a game with \(n\) players, a strategy profile \((s_1^*, s_2^*, ..., s_n^*)\) is a Nash Equilibrium if:

Where \(u_i\) is the payoff for player \(i\), and \(s_{-i}^*\) represents others’ strategies.

Examples

In the Prisoner’s Dilemma, both confessing is a Nash Equilibrium because neither can improve by switching alone.

Importance

It’s used in economics to predict market behavior, in negotiations, and in evolutionary biology.