To a degree, this is just an unanswered trope, similar to why zombies aren't interested in eating other zombies. This is listed as the No Zombie Cannibals trope.
And yet... isn't there still human flesh all around you? After all, the zombies are "human", just a slightly hungrier type of human, and most of the capacity for reason is gone. You still have to eat. Meat is meat. So what's to stop this horde from feeding on itself?
Ultimately, there is no reason; it just plain doesn't happen, and is left at that. We can only say for sure that there are No Zombie Cannibals. When The Virus creates zombies that are still technically alive, there's no perfectly sensible explanation. Additionally, no matter how ravenous, the zombies will cooperate, instead of fighting over the scraps.
Emphasis mine. The short answer is because it wouldn't make for an interesting plot.
The linked tropes page lists some in-universe justifications for zombie cannibalism, but it's fairly quick to see that most justifications are offhand mentions and not deeply studied.
In the case of the Reavers, it's never really explained. From the encounters we've seen (the heist in the Serenity movie is the best source afaik), Reavers seem to be able to work together towards their common goal. No hierarchy is ever discussed, the Reavers are shown to be interchangeable baddies.