I recently saw a poster for the upcoming movie The Predator, showing a predator's hand holding a predator's skull as a trophy. At first I thought it didn't make sense and should be a human skull, but now I'm wondering if there has ever been any case of a predator taking another predator's head as a trophy?
In Predators (2010) we see two different tribes of predators, the Jungle Hunter Clan and the Super Predator Clan. In the film we see the Crucified Predator of the Jungle Hunter Clan is tied up in the camp area.
From this we can infer that the species does hunt its own in some circumstances. Since it has been shown that they take trophies from worthy prey we can assume that at least some predators have trophy skulls of other predators in their trophy room.
The Berserker in the same film decapitates the Crucified Predator and if it had survived the film we can assume it would have used it as a trophy.