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Question: Given that p = (52/143; 50/143; 41/143) is optimal for Player 1 in the game with the following ma...

Given that p = (52/143; 50/143; 41/143) is optimal for Player 1 in the game

with the following matrix, what is the value?

0 5 -2

-3 0 4

6 -4 0

Explanation / Answer

If (52/143, 50/143,41/143) is optimal, then the value is the minimum of the inner product of this vector with the three columns of the matrix. This inner product with each of the three columns gives the same number, namely 96/143, which is then the value.

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