# Note 12 - Zero-Sum Games

## 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.

## Example 2

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 .

Similarly,