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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 2x3 or 3x2 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 3x3 pay-off matrix, without any dominant rows or columns, which has no saddle point. Determine the optimal mixed strategy for each player.

Sample Solution

Question 1a.

Yes, I am not going to write the solution for the graphical method. You can refer to any examples in the textbook.

Question 1b.

I used 3x2 game as example. You can refer the sample solution with complete working below

Question 2.

You can refer the sample solution with complete working below

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