# game theory – Showing an inequality involiving min,max

Question: Given the two-person zero sum game represented by the matrix,
$$A = begin{bmatrix} x & y \ z & g end{bmatrix}$$.

Show that $$min(x,y,z) leq value of A leq max(x,y,z)$$(*).

I know that if there is no saddle point, then either $$x > y, y < z, z > g$$ and $$d < x$$, or $$x < y, y > z, z and $$g>x$$. And the value for 2×2 games is given by
$$v = cfrac{xg-yz}{x-y+g-z}$$

I thought of examining 9 cases (for each min. and max) and showing that (*) holds. Is there any simpler way? Thanks in advance.