Nash Equilibrium

A strategy profile $(s_1^*, \ldots, s_n^*)$ is a Nash Equilibrium if no player can improve their payoff by unilaterally deviating, given the strategies of all others:

Equivalently, every player is playing a Best Response to what the others are doing — no one regrets their choice once everyone else's choice is known.

When to use

Use Nash Equilibrium whenever you want a stable prediction of behaviour in a strategic interaction. It is the workhorse equilibrium concept for normal-form games, oligopoly models (Cournot Competition, Bertrand Competition), and complementary-pricing games. Find pure-strategy NE by the best-response underlining method; if none exists, look for a Mixed Strategy equilibrium.