It's a second price auction. Who cares what their limit is. If it's more than the value of the item to you then they will win. Otherwise you will win.
A bidding war can make the perceived value of an item increase.
People's competitive behavior, or "you're not taking this from me," or "I've definitely got this item and have made plans" or any number of other emotional behaviors take over.
People's railing against sniping also demonstrates this.