Lowest Unique-Bid Auctions

I normally won't put technical stuff on here, but this is a problem I've been thinking about that might be interesting to even the non-technical readers.

In a lowest unique bid (LUB) auction a bunch of bidders bid on some prize, say an iPod, a Mini Cooper, or even a house. All the bidders submit their bids anonymously and without knowing what anyone else has bid. The value of a bid can be any number of dollars and cents. Here's the weird part: The winner of the prize is the player that has the lowest unique bid. The winner then pays the value of their bid and gets the prize.

A lot of these have been run (usually on the Internet) and the winners of these auctions usually get the prize for a tiny fraction of it's actual value; a Mini Cooper recently went for $243.42.

There is an important legal question surrounding LUB auctions, namely whether they're really auctions or are they lotteries. Legally-speaking, the difference between a lottery and an auction is that the value paid for the prize should be related to the value of the prize. I've been working on modelling this as an n player competitive game (the bidders) and trying find the symmetric Nash equilibria to determine if the value of the winning bid is indeed an increasing function of the prize value. So far I've only been able to solve a few special cases.