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

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written 9.6 years ago by

teamques10 ★ 70k

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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