2nd bid also pays problem

[Paul2432]

In my business school class (CU-Boulder MBA evening program) the professor made the following offer to the class: I will sell this $10 bill to the highest bidder, with the catch that the second place bidder also pays.

You can probably guess what happened, the bidding quickly rose above $10 as the second place bidder made higher and higher bids to avoid paying the 2nd bid penalty and receiving nothing in return (e.g. a $14 2nd place bid loses $14 while a $15 winning bid only loses $5). The professor cut-off the bidding because his point had been made but it left me wondering what the proper strategy for this game would be (assuming collusion is not possible).

I figure that a bid must be $10 more than the previous bid for the second place bidder to prefer not to bid again. If this is true there would be no bids. Of course, this gives incentive for someone to make an opening bid with the hope that no other bidder will make a bid. Even that exposes you to a "spite" bid from another bidder who could force you to lose money. The higher you bid, the more money you could be forced to lose.

Has anyone seen this problem before? What is the proper strategy?

Paul