On the Metric Approach in the Theory of Matrix Games

It is considered the problem connected with the combinatorial metric approach to the notion of solution of matrix games. According to this approach it is searched a matrix $B$ that possesses equilibrium and is the closest to the given matrix $A$ in the sense of some metric $d(A, B).$ In the case when $d(A,B)$ is the number of pairs $(i,j)$ such that $a_{ij} \neq b_{ij}$ it is established some properties of the quantity $\max_A\min_B d(A,B)$.