From what I understand, when solving a payoff matrix using Linear Programming with a negative $maxmin$ (or $minmax$) you need to supply a constant to add to each element in the payoff matrix. I'm not sure how to choose the constant.
Suppose I have the following payoff matrix:
\begin{bmatrix} 4 & 1 & 0 & -3 \\ 6 & -3 & -2 & 0 \\ -3 & -2 & 5 & -3 \\ -4 & 4 & -5 & 5 \end{bmatrix}
This payoff matrix has a $maxmin = -3$ (from rows 1, 2, 3) and $minmax = 4$ (from column 2). I'm inclined to use a constant say $k = 4$ to add to each element of the payoff matrix. My thinking is using $k=4$ will result is a positive value for the resulting $maxmin$ value, which would be $maxmin = 1$.
Is this the correct approach? I believe after I get the resulting value $v$ (and probabilities) of the game I will need to subtract $k$ such that $v^* = v - k$ to obtain the value $v^*$ for the original payoff matrix.