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Solve the game graphically whose playoff matrix for player A is given as follows:

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enter image description here

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Minimax point lies on strategies a1 & a3.

So the game reduces to:

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$x = \dfrac{2-3}{(2+2)-(3+4)} = \dfrac13 \\ y = \dfrac{2-4}{(2+2)-(3+4)} = \dfrac23$

Value of the game: $v =\dfrac{ 2×2 - 3×4}{(2+2) - (3+4)} = 83$

Optimum strategies:

$Player \ A = \bigg(\dfrac13, 0, \dfrac23 , 0\bigg) \\ Player \ B = \bigg(\dfrac23 , \dfrac13 \bigg) \\ \text{Value of the game} = \dfrac83$

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