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Reducing a pay-off matrix

A pay-off 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.

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