Consider the matrix game where A has no saddle point.

a. Find a formula for the optimal strategies x̂ for R and ŷ for C. What is the value of the game?

b. Let and let α and β be real numbers with α ≠ 0. Use your answer in part (a) to show that the optimal strategies for the matrix game B = αA + βJ are the same as for A. In particular, note that the optimal strategies for A and A + βJ are the same.

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