I'm designing a game of some sort of battle arena, which in every session there are 4 PCs fighting each other. The whole campaign will revolve on the arena fight and amassing XP to stand at the top.
I'm not sure how the XP should be distributed when there exists different hostile (to the killed PC) parties.
For the XP being distributed, I'm using this answer.
For example:
Anne, Belle, Charlie, Dean are all fighters of same "CR", worth 400 XP when killed each. Anne lands the killing blow and kills Dean.
How much XP should Anne receive?
In one question, an answer argue that a PC being around will receive XP, because they indirectly make the victim being wary, thus deserve the XP. However, that question ask about when the PCs in one party, but this one has 4 opposing groups.
Is there a rule can be used to address this? Or rule as intended, or anything else that can be used as guide to make a DM ruling?
Best Answer
What you're doing is not supported by the 5e design philosophy.
The game that you're designing is fundamentally a different game than D&D 5e. The core assumptions that the entire system is built around is that the players are a (more or less) cohesive party, banding together against external threats. The XP system is built entirely on this assumption: The party gets XP when the party solves an encounter, and the XP gained is based on how hard that encounter was to solve. XP is a reward that the group gains for playing well.
What you're doing here is something very different. Like you say, you have what is effectively four different groups all fighting each other, and all are player characters. This is so alien to the assumptions that the 5e XP system is based on that nothing in the book is going to give you a useful answer.
What I'd suggest is that you go much further with your game modifications than what you currently describe. If you're going to be building a new game using the 5e combat engine, then using any part of the 5e progression engine is going to give you a lackluster experience. So, rather than trying to shoehorn in the same progression system, make your own. Totally throw out the existing progression and XP system and make your own that encourages the kind of fun you want your players to have.
Actually designing a progression system is beyond the scope of this question, but the most important thing to keep in mind is to make sure that your system encourages the kind of play that you want. If everyone gets some XP, and the person who died last gets bonus XP, then that encourages one kind of play. If you only get XP from getting the last hit on an enemy, then that encourages another kind of play.
Addressing the specific needs of your new game and designing a progression system that fits those needs will give you much better results than trying to follow the exact rules of what is effectively a different game.