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Unformatted text preview: minimize u s.t. u 1A T y 1 T y = 1 y 1 Equivalently, minimize u s.t. u + y 1 + y 25 y 3 u2 y 2y 2 + 2 y 3 u + 3 y 1y 2y 3 y 1 + y 2 + y 3 = 1 y 1 , y 2 , y 3 The column players strategy y could be solved by the following LP: maximize v s.t. Axv 1 1 T x = 1 x which is equivalent to maximize v s.t. v 1Ax 1 T x = 1 x or explicitly, maximize v s.t. v + x 12 x 2 + 3 x 3 v + x 2x 2x 3 v5 x 1 + 2 x 2x 3 x 1 + x 2 + x 3 = 1 x 1 , x 2 , x 3 If use MATLAB to solve either of the programs we nd the the row players optimal strategy is y T = { . 1429 , . 6190 , . 2381 } and the column players optimal strategy is x T = { . 2857 , . 5714 , . 1429 } The return value is. 4286. This implies that the row player has an advantage: he is expected to win . 4286 dollars. 2...
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 Spring '08
 AlexandreW.d'Aspremont

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