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Player A writes one of the numbers 1, 2 and 3 on a piece of paper and keeps the figures hidden in his paper. And without knowing which number he has written, player B writes one of the numbers 2 and 5 on the same paper. Then if the two numbers written by the two players are added. If this sum is odd, A pays Rs. 5 to for B otherwise B pays Rs. 10 to A. Write down the pay off matrix of A. Does the game have a saddle point.

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The payoffs matrix of player A is:

By maximin-minimax principle. The minimum payoff in each row is Circled. The maximum payoff in each column is boxed. Here columns maximums are repeated. Here none of the payoff is circled as well as boxed. 

∴ The game has no saddle point. The suggested strategies is mixed strategy.

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