What does "their" refer to?

Social connections are so essential for our survival and well-being that we not only cooperate with others to build relationships, we also compete with others for friends. And often we do both at the same time. Take gossip. Through gossip, we bond with our friends, sharing interesting details. But at the same time, we are creating potential enemies in the targets of our gossip. Or consider rival holiday parties where people compete to see who will attend (A) their party. We can even see this tension in social media as people compete for the most friends and followers. At the same time, competitive exclusion can also generate cooperation. High school social clubs and country clubs use this formula to great effect: It is through selective inclusion and exclusion that they produce loyalty and lasting social bonds.

What does the underlined (A) refer to?

Is it "rivals'" or preceding "people's"?

Thank you so much.