Tunneler is the better known game by Geoffrey Silverton (the other one is Popgames). Two players using the same keyboard and the same screen each control an underground tank. Goal is to find and destroy the opponent's tank. Since only small part of the map is displayed on the split screen, you might actually have some searching to do.
Tunneler runs at an undocumented low-resolution (160x100) 16-color video mode which, since it is actually some sort of mangled text mode, can be accessed with any graphics adapter. Thus you'd have 16 colors even with a CGA card. With VGA/MCGA, you get prettier colors. The screenshot was taken in DOSBox, where it runs well too.