# Answer to Question #37193 in Other Math for nate ruiz

Question #37193

Matrix Games:

If we are given an arbitrary I by J matrix A, there exists a greater than 0 so that the matrix B with entries Bij = Aij + a has only positive entries. Show that any optimal randomized probability vectors for the game with pay-off matrix B are also optimal for the game with pay-off matrix A.

If we are given an arbitrary I by J matrix A, there exists a greater than 0 so that the matrix B with entries Bij = Aij + a has only positive entries. Show that any optimal randomized probability vectors for the game with pay-off matrix B are also optimal for the game with pay-off matrix A.

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