I am proving the simplest part of theory of moves. Assume that both players are rational, and consider the following $2\times 2$ ordinal game:
$$\begin{bmatrix} (3,3) && (2,4) \\ (4,2) && (1,1) \end{bmatrix} $$
Then if I start from (1.1), and Row stays (2.4) or moves to (1.1), then does row have to move? It seems that it is better for row to move from (1.1) to (2.4) but it is also better for column.
Put simply, If Row starts from (1.1) and has two choices: moves to (2.4) or stays at (1.1). If Row is rational, then does he have to move or stay?