Past exam of the Probability, statistics and options II course of the University of Oxford / 2008 / T / 2 / a / iii / Solution

The dual isFor positive payoffs and an optimal solution $y_{\ast }$, strong duality gives $1^{\mathsf{T}}{y}_{\ast }=1/v$. Normalizing gives Player I's optimal row strategy $p_{\ast }=y_{\ast }/(1^{\mathsf{T}}{y}_{\ast })$. Its expected payoff against every column is at least $v$. Thus the primal represents Player II's minimization of worst loss and the dual represents Player I's maximization of guaranteed gain.