The reason most carnivore predators do not pursue, kill and eat other carnivore predators is that it's just to costly as relates to energy. Other such predators can fight back while the normal, usually herbivore prey are able to only flee. In fact the running away excites most carnivores and entices them, as much as any other behavior, into killing and eating them (watch your pet cat or dog's behavior around a mouse or a sheep, for example). Additionally, most carnivore predators only come into contact with each other in the vicinity of prey that one or the other has already killed. It's at these times they can fight and possibly kill the other, but they have little interest in eating them, since they already have partially eaten the aforementioned prey. By the way, hyenas, wild dogs and other such predators regularly kill and eat young lions if left unguarded...