How do I handle initiative when a new force joins a combat that’s already in progress?

I am DMing a small hunger-games-like adventure where there are multiple parties of NPC who also are participating. It is pretty likely that the PCs will happen upon some of the NPCs fighting some monsters.

How do I handle the PCs joining the fight, do I roll initiative all over again? Do I just roll for the new combatants and add them to the round?

Also see this similar question for Pathfinder:
How to handle some new NPCs who enter a fight in progress?