  In this paper, we defined two new games - the mildly Menger game and the
compact-clopen game. In a zero-dimensional space, the Menger game is equivalent
to the mildly Menger game and the compact-open game is equivalent to the
compact-clopen game. An example is given for a space on which the mildly Menger
game is undetermined. Also we introduced a new game namely
K-quasi-component-clopen game and proved that this game is equivalent to the
compact-clopen game. Then we proved that if a topological space is a union of
countably many quasi-components of compact sets, then TWO has a winning
strategy in the mildly Menger game.
