T-Rex's auction is a nice hypothetical for game theory. And that is what it is, a game. Most reasonable people are going to stop bidding eventually, when the amount they stand to lose is far more than they can afford.
One way to play the game is to play a completely different game that has nothing to do with "winning." That game often goes by the name "griefing" when your intent is to ruin the experience for the other players. The best griefing method in this auction is to get into a bidding war where with the intent of making the other person pay a lot of money for nothing.
So, let's say that once you get to the $1 mark, you bid in $0.01 increments. If you get all the way to $1.50... jump to $2. The only person who's going to keep bidding in this auction is someone who is also griefing. At that point, the game becomes about who is willing to spend more money being an asshole.
I have the day off work today, so maybe later on I'll write some kind of primer in game theory. Right now, I have another comic to write about...