Backstory: White elephant at Christmas seemed to be making a surge this year, I've done three so far. Two gifts were awesome, and one was definitely a regift from a previous year.
The Idea: A platform where you can participate in an online white elephant game.
Deep Dive: Users could either upload their gift for an exchange or opt to participate in a white elephant game with random strangers. To make the white elephant game more interesting, you could have a "random" item thrown in as a bonus, you would have to work the rules so someone has two gifts or one gift is not gifted out.
To reduce the cost to ship the goods, you could limit people in the group to be within a 500mi radius.
Validation: I'll regift my re-gifted white elephant gift :)
Monetization: You could charge a small fee for every time someone joins a white elephant game.