Minmax payoff (source code)

= Minmax payoff
{title2=$\underline v_i=\min_{\sigma_{-i}}\max_{\sigma_i}U_i(\sigma_i,\sigma_{-i})$}

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>.