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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 player’s 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 ﬁnd the the row player’s optimal strategy is y T = { . 1429 , . 6190 , . 2381 } and the column player’s 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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This note was uploaded on 04/30/2008 for the course ORF 307 taught by Professor Alexandrew.d'aspremont during the Spring '08 term at Princeton.
 Spring '08
 AlexandreW.d'Aspremont

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