Player ii chooses a number j isin 1 2 3 4 and player i, Mathematics

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Player ii chooses a number j isin 1 2 3 4 and player i

Player II chooses a number j ∈ {1, 2, 3, 4}, and Player I tries to guess what number II has chosen. If he guesses correctly and the number was j, he wins 10 - j dollars from II. If he guesses incorrectly and the guess was j, he loses j dollars. Set up the matrix of this game and solve. Hint: First it is easy to find a mixed strategy for I that guarantees I an expected gain of 0. Is there a mixed strategy for II that guarantees II an expected loss of 0?

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Mathematics: Player ii chooses a number j isin 1 2 3 4 and player i

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Mathematics: Player ii chooses a number j isin 1 2 3 4 and player i

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