For years and years, my Norwegian friends and I have exchanged holiday gifts via the pseudonym Secret Santa.
Since there are so many of us (I think there were 15 participants in this last one), we decided long ago to opt to give one larger, useful, well-thought-out gift to one person rather than 15 tiny, useless ones to all 15 people, even though everybody loves everyone else just as much.
One designated individual, the only one who knows the whole spiel, usually draws names out of a hat and links them to the receiving end sometime in early December. On December 22nd or thereabouts, the whole gang gets together. Each person puts their parcel into a huge burlap sack, making sure no-one else is watching to see what kind of wrapping paper he or she used, and then the gifts are distributed, but not opened. Everyone must wait two more days until Christmas Eve to open the gift at the proper time. Secret Santa is not a game.