Territorial struggles between animals of the same species rarely lead to fights to the death. Finally one animal gets tired and leaves, conceding defeat. The animal willing to hold its ground the longest wins. The dollar auction bears some resemblance to an iterated prisoner's dilemma. Topping a bid is defecting, since it betters the bidder's short-term individual position while hurting the common good.
Every new bid chips away at the potential profit.
The usual debacle is the result of repeated defection on both sides. Sometimes the dollar auction is a better model than the iterated prisoner's dilemma for some of the conflicts conventionally treated as such. Escalation, and the possibility of ruin for both sides, is characteristic of arms races. To stop bidding is to allow oneself to be exploited. Lay the blame at the door of the first person to defect - that is, the first bidder.