Zombies (Mmmm Brains....)

Actually, Why dont Zombies eat their own brains?  I mean really.  They need their brains to stay alive?  OK, I guess not alive but animated.  It would be like carrying your lunch around with you and needing your lunch to stay whole to function.  I guess that is why they eat other peoples lunches er uh brains.  But that still leaves the question, why not eat other zombies brains?  Oh well, we'll see in the coming apocalypse.