In game theory, a mixed strategy best response is a strategy that mixes multiple pure strategies in such a way that it is the best response to the opponent’s strategy. A pure strategy is a strategy where the player always chooses the same action, while a mixed strategy is a strategy where the player randomizes over a set of actions. Mixed strategy best responses are often used in games where there is no pure strategy Nash equilibrium.
Mixed strategy best responses can be found by solving for the Nash equilibrium of the game. The Nash equilibrium is a set of strategies, one for each player, such that no player can improve their payoff by unilaterally changing their strategy. In other words, the Nash equilibrium is a set of strategies where each player is doing the best they can, given the strategies of the other players.