Office’s done that for a few years now, and every year I’ve heard it called the white elephant gift exchange, or just the gift exchange.
We played it at a Christmas party I threw a few years ago, at a guest’s suggestion. She called it a “white elephant” exchange.
Just sat through my first one, also called a White Elephant Exchange. The important thing was that no one opened presents until the end and no one could steal the same present twice in one round.
A couple of the gifts were true white elephants. I expect we’ll be seeing them next year.
I’ll be the 3rd to say, “white elephant exchange”. I’ve only done this once and it was in Florida. We did this with family members and friends, I think the dollar limit on the gift was around 3 dollars.
Someone bought a 4 pack of toilet paper and it turned out to be one of the more desireable gifts. As you can imagine, most 3 dollar gifts were just crap.
We call it “The Game.”
Our version:
If your gift is stolen, you may choose an unopened one or steal someone else’s, but you may not at that time steal back the one that was just taken from you.
A gift can change hands only twice.
We did this at home one year, at the behest of my sister. We were all to polite to steal anyone’s gift, so we all just picked at random and opened. :smack:
No, we haven’t tried it since.
I’ve heard it called “Chinese auction” or “White Elephant” gift exchange.
My family does it every year, when we just call it the “Grab Bag”. It usually involves quite a bit of yelling, a little physical contact, and a great deal of mothers taking dives so their kids get cool presents. My mother would never do such a thing, she thinks I’m perfectly capable of getting my own damn present. We typically have between 25-30 people, and it’s been known to take at least three hours. We only allow three steals per round, and you cannot steal back something that was just stolen from you.
At the office, it was called either Yankee Swap or Pollyanna. Seeing as my grandmother’s name actually is Pollyanna, I don’t think she’d appreciate us calling it that at home. 
As I mentioned in my LiveJournal, I know it as a “white elephant gift exchange.” Online I found references to “yankee gift swap” as well.
“Chinese auction” to me means something else, not Christmas related, but rather a type of raffle:
- You put all the raffle prizes out on a table
- Next to each item is a cup
- Everyone involved in the raffle gets one raffle ticket
- Each person can put their ticket into the cup next to the prize that they want
- Winners for each prize are drawn from the corresponding cup
“Pollyanna” to me means everyone draws names randomly of someone else involved in it, and you buy a gift for that person. I’ve also heard this called a “secret Santa.”
Interesting how things vary from region to region (I was born and raised in Philadelphia, if anyone’s curious).
Esprix
I’ve never heard it given any name except for “damn annoying”.
My mum’s office played a variant on it last year. No one was allowed to open their present until the end, so everyone was fighting over the elaborately wrapped gifts, the big presents, and the one wrapped in newspaper.
At the end, everyone got the same thing: a mug.
That’s what our department calls it. We had it yesterday, and a cactus was the most stolen item.
It’s Dirty Santa here in my part of Oklahoma.
Secret Santa = everyone puts their name in a hat and then draws a name. You select a gift for the person whose name you draw, presumeably something that they would enjoy.
White Elephant = You take something of low value that you already own but don’t like or don’t need, wrap it and put it on a table. Everyone takes one gift from the pile and, if you’re lucky, you’ll get something you like in exchange for something you don’t like.
Game mentioned in the OP = I never knew there was a name for it but in the varient I have seen, once a gift has been stolen three times it is frozen. If your gift is stolen, you can get one from the pile or steal someone else’s but you can’t take the one that was stolen from you on the same turn. You can steal it later if your new gift is stolen from you.
Haj
I had never heard of this kind of gift exchange until my roommate told me about the one his workplace had two weeks ago. They called it a Chinese auction, for what it’s worth (in Orlando, Florida).
Normally called a Yankee Swap around here, but this year at work we’re doing a Sox Swap, so we don’t have to use the term “Yankee.”
Another Yankee Swapper here. We started doing it for our extended family gatherings once the younger generation started getting married and having kids, and everyone started having to buy 30 presents each. Made things a lot simpler and a lot of fun.