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Solve the following game:
  I II III IV
I 6 2 4 8
II 2 -1 1 12
III 2 3 3 9
IV 5 2 6 10
1 Answer
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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:
  I II
I 6 2
III 2 3

By method of oddments:

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$ \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}$

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