The problem surfaces when the bidders get up close to a dollar. After 99 cents the last vestige of profitability disappears, but the bidding continues between the two highest players. They now realize that they stand to lose no matter what, but that they can still buffer their losses by winning the dollar. They just have to outlast the other player. Following this strategy, the two hapless students usually run the bid up several dollars, turning the apparent shot at easy money into a ghastly battle of spiraling disaster.This is why war supporters always complain about their critics "looking backwards". It doesn't matter that the Iraq war has become more expensive than it was ever worth. All that matters is that we might end up in a situation that's slightly better than the one we are in today.
Theoretically, there is no stable outcome once the dynamic gets going. The only clear limit is the exhaustion of one of the player's total funds. In the classroom, the auction generally ends with the grudging decision of one player to "irrationally" accept the larger loss and get out of the terrible spiral. Economists call the dollar auction pattern an irrational escalation of commitment. We might also call it the war in Iraq.
h/t Andrew Sullivan