DaDancing Psych, I think when someone new starts, you can tell them, in early December, "Oh, you can relax at Christmas--we don't give each other gifts, not even small things." In the manner of "tipping you off about how things get done here," much like other office-culture "secrets."
I'm a boss who gives their subordinates presents, and I always stated, in early December, "In my department gifts flow down; I'm allowed to give you something if I want, but you're not supposed to. It makes things awkward."
Set them up for it early!
I have worked at places where a few overachievers would give small edibles (I used to drop 5 Brach's Christmas Nougats and a business-card-size note on everybody's desk that I actually interacted with), but most people wouldn't do anything, and I don't think people felt bad, because the edibles were so small in value, and the givers were so clearly overachievers.