Let Mn,m be the space of matrices of order n × m representing two-player zero-sum games in which Player I has n pure strategies and Player II has m pure strategies.
Prove that the function that associates with every matrix A = (aij ) ∈ Mn,m the value in mixed strategies of the game that it represents is continuous in (aij ).
Remark: The sequence of matrices (Ak)k∈N in Mn,m, where to A = (aij ), if
aij = limk→∞ akij, ∀i,j.