A ship with missile dodge assistance has a top and bottom radar to detect missiles.  If an enemy missile is detected by the top radar the ship automatically moves down.  If a missile is detected by the bottom radar the ship will automatically move up.

Here you can see a missile dodge sequence.  Top radar detects a missile.  Ships avoids by dodging downwards.

With harder computer players their radars increase in size making them able to respond to missiles sooner.  The hard computer opponent also has a smaller gap between radars making it a more "slippery" opponent.

Humans with assistance and computer players in exhibition mode always have the same standard mid level radars.  Easy computer opponents have useless radars so its basically a shooting gallery.