By rules of dominance:
- Column II dominates column III. The matrix reduces to:
|
I |
II |
IV |
I |
6 |
2 |
8 |
II |
2 |
-1 |
12 |
III |
2 |
3 |
9 |
IV |
5 |
2 |
10 |
- Column II dominates column IV. The matrix reduces to:
|
I |
II |
I |
6 |
2 |
II |
2 |
-1 |
III |
2 |
3 |
IV |
5 |
2 |
- Row III dominates row II. Matrix reduces to:
|
I |
II |
I |
6 |
2 |
III |
2 |
3 |
IV |
5 |
2 |
- Row I dominates row IV. Matrix reduces to:
By method of oddments:
$ \text{Player 1’s strategy} = [\dfrac15 , 0, \dfrac45 , 0] \\
\text{Player 2’s strategy} = [\dfrac15 , \dfrac45 , 0, 0] \\
\text{Value of the game} = 6× \dfrac15 + 2× \dfrac45 = \dfrac{14}{5}$