Best Response

A best response is the optimal strategy for a player given a specific strategy chosen by the opponent. At a Nash Equilibrium, every player is simultaneously playing a best response to everyone else's strategy.

When to use

Underlining best responses is the practical method for finding pure-strategy Nash Equilibria in a matrix: for each opponent column, mark Player 1's payoff-maximising row; for each row, mark Player 2's payoff-maximising column; any doubly underlined cell is a NE (see the How to Find Nash Equilibria — Best Response Method recipe). Best responses generalise to continuous strategies as a Best Response Function — the curve whose intersection with the opponent's gives the equilibrium in Cournot, Bertrand, and complementary-pricing games.