Q: In a Commander game, one of my opponents controls Platinum Angel. I cast Illicit Auction targeting it. What happens?

A: Well, Illicit Auction lets you bid more life than you have (since it's not a life payment) and winning means you get a Platinum Angel that will save you from dying even if you're at negative eleven billion life, meaning people will just keep bidding higher and higher. So we go around the table taking bids, and if nobody's won the auction then we go around the table taking bids, and if nobody's won the auction then we go around the table taking bids, and if nobody's won the auction then we go around the table taking bids, and...

Hey! It's a loop! Don't be fooled by the changing values of the bids — we end up in the same state ("nobody's won the auction, go around the table taking bids") over and over and over again. So we get into the rules for breaking a loop of optional actions: first the active player has to make a different choice to try to break the loop, then each other player in turn order.

The practical result of this is that the player who's furthest away from the active player, in turn order, can always "win" the auction since all other players will get forced out by the loop-breaking mechanism.