Past exam of the probability, statistics and options I course of the University of Oxford / 2010 / T / 1 / c

Player I can choose each row with probability $1/m$. Against column $j$ the expected payoff is $m^{-1}{\sum }_i{a}_{ij}$. Nonnegativity and a strictly positive entry in each column make every one of these finitely many numbers strictly positive. Their minimumis therefore a guaranteed payoff against every mixture of columns. By the minimax theorem, $v\ge \delta >0$.