Reducing a
payoff matrix
A payoff matrix can be made smaller by eliminating certain
options if a row or column is better (if it dominates).
This can only be done if the row/column is ALWAYS better than
another row/column.

B plays 1

B plays 2

A plays 1

7

1

A plays 2

3

6

A plays 3

4

0

The 3x2 matrix above can be reduced to a 2x2 matrix.
We can see from the matrix that row 1 dominates row 3; 7 is
bigger than 4 and 1 is bigger than 0. This means that for A no matter what B
does, row 1 is always a better option to play than row 3 hence row 3 can be
eliminated as A would never rationally select it.
Therefore the new deduced matrix would look like:

B plays 1

B plays 2

A plays 1

7

1

A plays 2

3

6

The same deduction can
be done to a column if another column dominates.
