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

1.7kviews

written 8.4 years ago by

teamques10 ★ 68k

• modified 4.0 years ago

enter image description here

operation research

ADD COMMENT EDIT

1 Answer

4views

written 8.4 years ago by

teamques10 ★ 68k

enter image description here

Minimax point lies on strategies a1 & a3.

So the game reduces to:

enter image description here

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

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

Optimum strategies:

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

ADD COMMENT EDIT

Please log in to add an answer.