Weakly dominated Nash equilibrium in a zero-sum game

Question

There is a zero sum game G where player one plays T and Player two plays y and z. However y dominates z and Nash Equilibrium in this game would be (Ty). How can I prove this? Is it possible with minimax theorem or brower fixed point theorem

Answer 1

It suffices to exhibit an example, such as $$\begin{array}{|c|c|} \hline 1 & 1 \\ \hline 1 & 0 \\ \hline \end{array}$$ Here, 1 plays the top row and 2 plays (indifferently) the left or the right column, but the left column is weakly dominated by the right column.