Consider the following two-person, zero-sum game. Payoffs are the winnings for Company X. Formulate the linear program that determines the optimal mixed strategy for Company X.
Max GAINA
s.t. 4PA1 + 2PA2 + 6PA3 ? GAINA ? 0 (Strategy B1)
3PA1 + 5PA2 + 1PA3 ? GAINA ? 0 (Strategy B2)
9PA1 + 1PA2 + 7PA3 ? GAINA ? 0 (Strategy B3)
PA1 + PA2 + PA3 = 1 (Probabilities must sum to 1)
PA1, PA2, PA3, GAINA ? 0 (Nonnegativity)
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