OK the rules may seem a little ... complex but it's pretty straightforward really.
Bad Santa:
all attendees bring a WRAPPED gift, to an agreed value - perhaps £10.
everyone is given a number (randomly selected from a hat)
in number order each person may open a gift, or steal a gift already opened by a preceding player (<obviously doesn't apply to player 1).
if player has been pinched from, they may pinch another, or open a further gift. Only when everyone who has been in play has a gift can the next player start.
a gift may only be stolen 3 times. We'd use little dot stickers to keep track of that.
I'llgo through this on the night: The main thing is, everyone brings a gift - of equal value wouldbe nice.
no mention of mistletoe or singing .. sorry skully i'm out