 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2010/t/1/c/solution

Player I can choose each row with probability

1/ m

. Against column

j

m^{- 1} \sum_{i} a_{ij}

. Nonnegativity and a strictly positive entry in each column make every one of these finitely many numbers strictly positive. Their minimum

δ = min_{j} \frac{1}{m} \sum_{i} a_{ij} > 0

is therefore a guaranteed payoff against every mixture of columns. By the minimax theorem, $v \geq δ > 0$ .

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