Getting the group together in a zombie apocalypse

Hello AGM!

My players have not encountered each other, but are engaged in their own individual plots. At some point, I'd like them to be a part of the same colony, without forcing it (IE get them to becoming a "party" and working together).

I think I've hit a point where each group needs something from the other:

• Group 1 has safety and weapons, but no food
• Group 2 has safety and food, but no weapons
• Group 3 has food and weapons, but no safety

This setup was entirely on accident, but I think it will lead to them all running into each other for different reasons.

At this point, should I just airdrop hints that the other group(s) have what they need? Or how can I get to the end goal of unification?

The Zombie TTRPG is a homebrew that I made, rules are here:

https://docs.google.com/document/d/1RA-EjXm6qTo3BljSlnrYvqKnGVrDAJuI6epC7aassP4/edit?usp=sharing

If you need any additional info, ask away.