Struggling with networking design

hi! I'm working on a game and I'm struggling with designing for lag compensation. I can get players moving around smoothly (my current implementation for this isn't perfect, but I know what theory to use to improve it), but I'm having issues on processing collisions well.

In particular, processing collisions with the game ball. Naturally there should only ever be 1 game ball, so I'm not sure how to deal with 2 players think they've picked up the ball e.t.c.

Any hint, articles, ideas on how to do this with PUN (although from what reading I've done, it looks like I really do need an authoratiative server (sadface))