STPM 2016 Term 3 Mathematics (M) Assignment

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In a two-person zero-sum game, the gain of one player is the loss of the other. Play-safe strategies are adopted in a game having a stable solution. Mixed strategies are adopted in a game having no stable solution, where a graphical method or simplex algorithm may be used depending on the order of the pay-off matrix. 1 Find 2×3 or 3×2 pay-off matrix, without any dominant rows or columns, which has no saddle point. (a) Use a graphical method to determine the optimal mixed strategy for each player. (b) Use the simplex algorithm given below to determine the optimal mixed strategy for each player. (c) Comment on the graphical method and simplex algorithm in solving two-person zero-sum games. 2 Find a 3×3 pay-off matrix, without any dominant rows or columns, which has no saddle point. Determine the optimal mixed strategy for each player.