Solving Zero-Sum Games
Our row mins are
and our column maxes are
So our saddle points are
which corresponds to , and the others are , , and .
Saddle points arise from optimal pure strategies, also called Pure Nash Equilibria.
Nash Equilibrium: Strategy pairs such that neither player can do better by unilaterally deviating from that strategy.
Now take the example of
Taking and our matrix, we get
Drawing our diagram, we can see that only columns 1 and 3 matter, so we set them equal to each other: . Solving, we get .