Minmax payoff (${\underline{v}}_i={\min }_{{\sigma }_{-i}}{\max }_{{\sigma }_i}{U}_i({\sigma }_i,{\sigma }_{-i})$)

The lowest expected payoff to which a player's opponents can hold that player when the player chooses a best response. The opponents' permitted randomization and correlation conventions should be specified for games with several opponents. In a two-player finite game, this equals the player's maximum guaranteed expected payoff by the minimax theorem applied to that player's payoff matrix. This equality does not make the original two-player game a zero-sum game.