Given a zero sum game like this one :
\begin{array}{c|rrrr} & A & B \\\hline X & 4 & 3 \\ Y & 2 & 5 \\ \end{array} and the given LP :
minimize $ x+y $ s.t. :
$x \geq 0, y \geq 0$,
$ 4x + 2y \geq 1 $,
$ 3x + 5y \geq 1 $
If I know the solution of the LP is given by x = 3/14, y = 1/14, how can I find the optimal strategy for rows and the expected payoff?
It is a sequel of LP for zero-sum Game.
Here $x$ is $\frac{P_X}{G}$, $y$ is $\frac{P_Y}{G}$ and $G$ is the Maxmin payoff.
Therefore, $P_X:P_Y = 3:1$, $P_X+P_Y = 1$.
We can easily solve
$P_X$ = 3/4 , $P_Y$ = 1/4
Now, since $P_X = 3/4$ and $\frac{P_X}{G}$ = 3/14 then
$\frac{3}{4} = \frac{3}{14} G$
$G = \frac{3}{4} \frac{14}{3} = \frac{7}{2}$
$G$ is $\nu$ in the problem.
If you don't understand why, please read the previous one.