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Each of two players chooses a number '1' or '2' independently from the other player. P1 wins if the sum is odd. If the sum

Each of two players chooses a number '1' or '2' independently from the other player. P1 wins if the sum is odd. If the sum is even, p2 wins.

The payoff to P1 is P1's number multiplied bt P2's number.

Find the matrix of this zero-sum game, the value, and the optimal strategies of the players

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