Reaction , also known as best response correspondences, are used in the proof of the existence of mixed strategy Nash equilibria (, Section 1.3.B; , Section 2.2). Reaction correspondences are not "reaction functions" since functions must only have one value per argument, and many reaction correspondences will be undefined, i.e. a vertical line, for some opponent strategy choice. One constructs a correspondence formula_1, for each player from the set of opponent strategy profiles into the set of the player's strategies. So, for any given set of opponent's strategies formula_2, formula_3 represents player "i" 's best responses to formula_2.